Add css and js. Add lots of org mode files.
This commit is contained in:
parent
ca64e189b8
commit
2914d01e8f
145
css/htmlize.css
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145
css/htmlize.css
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.org-bold { /* bold */ font-weight: bold; }
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.org-bold-italic { /* bold-italic */ font-weight: bold; font-style: italic; }
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.org-buffer-menu-buffer { /* buffer-menu-buffer */ font-weight: bold; }
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.org-builtin { /* font-lock-builtin-face */ color: #7a378b; }
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.org-button { /* button */ text-decoration: underline; }
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.org-calendar-today { /* calendar-today */ text-decoration: underline; }
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.org-change-log-acknowledgement { /* change-log-acknowledgement */ color: #b22222; }
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.org-change-log-conditionals { /* change-log-conditionals */ color: #a0522d; }
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.org-change-log-date { /* change-log-date */ color: #8b2252; }
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.org-change-log-email { /* change-log-email */ color: #a0522d; }
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.org-change-log-file { /* change-log-file */ color: #0000ff; }
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.org-change-log-function { /* change-log-function */ color: #a0522d; }
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.org-change-log-list { /* change-log-list */ color: #a020f0; }
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.org-change-log-name { /* change-log-name */ color: #008b8b; }
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.org-comint-highlight-input { /* comint-highlight-input */ font-weight: bold; }
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.org-comint-highlight-prompt { /* comint-highlight-prompt */ color: #00008b; }
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.org-comment { /* font-lock-comment-face */ color: #999988; font-style: italic; }
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.org-comment-delimiter { /* font-lock-comment-delimiter-face */ color: #999988; font-style: italic; }
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.org-completions-annotations { /* completions-annotations */ font-style: italic; }
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.org-completions-common-part { /* completions-common-part */ color: #000000; background-color: #ffffff; }
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.org-completions-first-difference { /* completions-first-difference */ font-weight: bold; }
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.org-constant { /* font-lock-constant-face */ color: #008b8b; }
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.org-diary { /* diary */ color: #ff0000; }
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.org-diff-context { /* diff-context */ color: #7f7f7f; }
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.org-diff-file-header { /* diff-file-header */ background-color: #b3b3b3; font-weight: bold; }
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.org-diff-function { /* diff-function */ background-color: #cccccc; }
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.org-diff-header { /* diff-header */ background-color: #cccccc; }
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.org-diff-hunk-header { /* diff-hunk-header */ background-color: #cccccc; }
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.org-diff-index { /* diff-index */ background-color: #b3b3b3; font-weight: bold; }
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.org-diff-nonexistent { /* diff-nonexistent */ background-color: #b3b3b3; font-weight: bold; }
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.org-diff-refine-change { /* diff-refine-change */ background-color: #d9d9d9; }
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.org-dired-directory { /* dired-directory */ color: #0000ff; }
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.org-dired-flagged { /* dired-flagged */ color: #ff0000; font-weight: bold; }
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.org-dired-header { /* dired-header */ color: #228b22; }
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.org-dired-ignored { /* dired-ignored */ color: #7f7f7f; }
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.org-dired-mark { /* dired-mark */ color: #008b8b; }
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.org-dired-marked { /* dired-marked */ color: #ff0000; font-weight: bold; }
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.org-dired-perm-write { /* dired-perm-write */ color: #b22222; }
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.org-dired-symlink { /* dired-symlink */ color: #a020f0; }
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.org-dired-warning { /* dired-warning */ color: #ff0000; font-weight: bold; }
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.org-doc { /* font-lock-doc-face */ color: #8b2252; }
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.org-escape-glyph { /* escape-glyph */ color: #a52a2a; }
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.org-file-name-shadow { /* file-name-shadow */ color: #7f7f7f; }
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.org-flyspell-duplicate { /* flyspell-duplicate */ color: #cdad00; font-weight: bold; text-decoration: underline; }
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.org-flyspell-incorrect { /* flyspell-incorrect */ color: #ff4500; font-weight: bold; text-decoration: underline; }
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.org-fringe { /* fringe */ background-color: #f2f2f2; }
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.org-function-name { /* font-lock-function-name-face */ color: teal; }
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.org-header-line { /* header-line */ color: #333333; background-color: #e5e5e5; }
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.org-help-argument-name { /* help-argument-name */ font-style: italic; }
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.org-highlight { /* highlight */ background-color: #b4eeb4; }
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.org-holiday { /* holiday */ background-color: #ffc0cb; }
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.org-isearch { /* isearch */ color: #b0e2ff; background-color: #cd00cd; }
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.org-isearch-fail { /* isearch-fail */ background-color: #ffc1c1; }
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.org-italic { /* italic */ font-style: italic; }
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.org-keyword { /* font-lock-keyword-face */ color: #0086b3; }
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.org-lazy-highlight { /* lazy-highlight */ background-color: #afeeee; }
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.org-link { /* link */ color: #0000ff; text-decoration: underline; }
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.org-link-visited { /* link-visited */ color: #8b008b; text-decoration: underline; }
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.org-log-edit-header { /* log-edit-header */ color: #a020f0; }
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.org-log-edit-summary { /* log-edit-summary */ color: #0000ff; }
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.org-log-edit-unknown-header { /* log-edit-unknown-header */ color: #b22222; }
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.org-match { /* match */ background-color: #ffff00; }
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.org-next-error { /* next-error */ background-color: #eedc82; }
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.org-nobreak-space { /* nobreak-space */ color: #a52a2a; text-decoration: underline; }
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.org-org-archived { /* org-archived */ color: #7f7f7f; }
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.org-org-block { /* org-block */ color: #7f7f7f; }
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.org-org-block-begin-line { /* org-block-begin-line */ color: #b22222; }
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.org-org-block-end-line { /* org-block-end-line */ color: #b22222; }
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.org-org-checkbox { /* org-checkbox */ font-weight: bold; }
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.org-org-checkbox-statistics-done { /* org-checkbox-statistics-done */ color: #228b22; font-weight: bold; }
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.org-org-checkbox-statistics-todo { /* org-checkbox-statistics-todo */ color: #ff0000; font-weight: bold; }
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.org-org-clock-overlay { /* org-clock-overlay */ background-color: #ffff00; }
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.org-org-code { /* org-code */ color: #7f7f7f; }
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.org-org-column { /* org-column */ background-color: #e5e5e5; }
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.org-org-column-title { /* org-column-title */ background-color: #e5e5e5; font-weight: bold; text-decoration: underline; }
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.org-org-date { /* org-date */ color: #a020f0; text-decoration: underline; }
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.org-org-document-info { /* org-document-info */ color: #191970; }
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.org-org-document-info-keyword { /* org-document-info-keyword */ color: #7f7f7f; }
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.org-org-document-title { /* org-document-title */ color: #191970; font-size: 144%; font-weight: bold; }
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.org-org-done { /* org-done */ color: #228b22; font-weight: bold; }
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.org-org-drawer { /* org-drawer */ color: #0000ff; }
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.org-org-ellipsis { /* org-ellipsis */ color: #b8860b; text-decoration: underline; }
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.org-org-footnote { /* org-footnote */ color: #a020f0; text-decoration: underline; }
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.org-org-formula { /* org-formula */ color: #b22222; }
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.org-org-headline-done { /* org-headline-done */ color: #bc8f8f; }
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.org-org-hide { /* org-hide */ color: #ffffff; }
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.org-org-latex-and-export-specials { /* org-latex-and-export-specials */ color: #8b4513; }
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.org-org-level-1 { /* org-level-1 */ color: #0000ff; }
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.org-org-level-2 { /* org-level-2 */ color: #a0522d; }
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.org-org-level-3 { /* org-level-3 */ color: #a020f0; }
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.org-org-level-4 { /* org-level-4 */ color: #b22222; }
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.org-org-level-5 { /* org-level-5 */ color: #228b22; }
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.org-org-level-6 { /* org-level-6 */ color: #008b8b; }
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.org-org-level-7 { /* org-level-7 */ color: #7a378b; }
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.org-org-level-8 { /* org-level-8 */ color: #8b2252; }
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.org-org-link { /* org-link */ color: #0000ff; text-decoration: underline; }
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.org-org-meta-line { /* org-meta-line */ color: #b22222; }
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.org-org-mode-line-clock { /* org-mode-line-clock */ color: #000000; background-color: #bfbfbf; }
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.org-org-mode-line-clock-overrun { /* org-mode-line-clock-overrun */ color: #000000; background-color: #ff0000; }
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.org-org-quote { /* org-quote */ color: #7f7f7f; }
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.org-org-scheduled { /* org-scheduled */ color: #006400; }
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.org-org-scheduled-previously { /* org-scheduled-previously */ color: #b22222; }
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.org-org-scheduled-today { /* org-scheduled-today */ color: #006400; }
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.org-org-sexp-date { /* org-sexp-date */ color: #a020f0; }
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.org-org-special-keyword { /* org-special-keyword */ color: #a020f0; }
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.org-org-table { /* org-table */ color: #0000ff; }
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.org-org-tag { /* org-tag */ font-weight: bold; }
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.org-org-target { /* org-target */ text-decoration: underline; }
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.org-org-time-grid { /* org-time-grid */ color: #b8860b; }
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.org-org-todo { /* org-todo */ color: #ff0000; font-weight: bold; }
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.org-org-upcoming-deadline { /* org-upcoming-deadline */ color: #b22222; }
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.org-org-verbatim { /* org-verbatim */ color: #7f7f7f; }
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.org-org-verse { /* org-verse */ color: #7f7f7f; }
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.org-org-warning { /* org-warning */ color: #ff0000; font-weight: bold; }
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.org-outline-1 { /* outline-1 */ color: #0000ff; }
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.org-outline-2 { /* outline-2 */ color: #a0522d; }
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.org-outline-3 { /* outline-3 */ color: #a020f0; }
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.org-outline-4 { /* outline-4 */ color: #b22222; }
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.org-outline-5 { /* outline-5 */ color: #228b22; }
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.org-outline-6 { /* outline-6 */ color: #008b8b; }
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.org-outline-7 { /* outline-7 */ color: #7a378b; }
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.org-outline-8 { /* outline-8 */ color: #8b2252; }
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.org-preprocessor { /* font-lock-preprocessor-face */ color: #7a378b; }
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.org-query-replace { /* query-replace */ color: #b0e2ff; background-color: #cd00cd; }
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.org-regexp-grouping-backslash { /* font-lock-regexp-grouping-backslash */ font-weight: bold; }
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.org-regexp-grouping-construct { /* font-lock-regexp-grouping-construct */ font-weight: bold; }
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.org-region { /* region */ background-color: #eedc82; }
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.org-secondary-selection { /* secondary-selection */ background-color: #ffff00; }
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.org-shadow { /* shadow */ color: #7f7f7f; }
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.org-show-paren-match { /* show-paren-match */ background-color: #40e0d0; }
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.org-show-paren-mismatch { /* show-paren-mismatch */ color: #ffffff; background-color: #a020f0; }
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.org-string { /* font-lock-string-face */ color: #dd1144; }
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.org-tool-bar { /* tool-bar */ color: #000000; background-color: #bfbfbf; }
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.org-tooltip { /* tooltip */ color: #000000; background-color: #ffffe0; }
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.org-trailing-whitespace { /* trailing-whitespace */ background-color: #ff0000; }
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.org-type { /* font-lock-type-face */ color: #228b22; }
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.org-underline { /* underline */ text-decoration: underline; }
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.org-variable-name { /* font-lock-variable-name-face */ color: teal; }
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.org-warning { /* font-lock-warning-face */ color: #ff0000; font-weight: bold; }
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.org-widget-button { /* widget-button */ font-weight: bold; }
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.org-widget-button-pressed { /* widget-button-pressed */ color: #ff0000; }
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.org-widget-documentation { /* widget-documentation */ color: #006400; }
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.org-widget-field { /* widget-field */ background-color: #d9d9d9; }
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.org-widget-inactive { /* widget-inactive */ color: #7f7f7f; }
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.org-widget-single-line-field { /* widget-single-line-field */ background-color: #d9d9d9; }
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1095
css/readtheorg.css
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1095
css/readtheorg.css
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File diff suppressed because it is too large
Load Diff
BIN
figs/stewart_ball_joints.png
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figs/stewart_ball_joints.png
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After Width: | Height: | Size: 4.9 KiB |
BIN
figs/stewart_bottom_plate.png
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BIN
figs/stewart_bottom_plate.png
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After Width: | Height: | Size: 39 KiB |
BIN
figs/stewart_legs.png
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figs/stewart_legs.png
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After Width: | Height: | Size: 21 KiB |
571
identification.html
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571
identification.html
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2019-03-22 ven. 12:03 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Identification of the Stewart Platform using Simscape</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Thomas Dehaeze" />
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<style type="text/css">
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<!--/*--><![CDATA[/*><!--*/
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.title { text-align: center;
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margin-bottom: .2em; }
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.subtitle { text-align: center;
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font-size: medium;
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font-weight: bold;
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margin-top:0; }
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.todo { font-family: monospace; color: red; }
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.done { font-family: monospace; color: green; }
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.priority { font-family: monospace; color: orange; }
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.tag { background-color: #eee; font-family: monospace;
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padding: 2px; font-size: 80%; font-weight: normal; }
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.timestamp { color: #bebebe; }
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.timestamp-kwd { color: #5f9ea0; }
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.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
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.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
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.org-center { margin-left: auto; margin-right: auto; text-align: center; }
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.underline { text-decoration: underline; }
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#postamble p, #preamble p { font-size: 90%; margin: .2em; }
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p.verse { margin-left: 3%; }
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pre {
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border: 1px solid #ccc;
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box-shadow: 3px 3px 3px #eee;
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padding: 8pt;
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font-family: monospace;
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overflow: auto;
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margin: 1.2em;
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}
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pre.src {
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position: relative;
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overflow: visible;
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padding-top: 1.2em;
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}
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pre.src:before {
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display: none;
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position: absolute;
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background-color: white;
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top: -10px;
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right: 10px;
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padding: 3px;
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border: 1px solid black;
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}
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pre.src:hover:before { display: inline;}
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/* Languages per Org manual */
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pre.src-asymptote:before { content: 'Asymptote'; }
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pre.src-awk:before { content: 'Awk'; }
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pre.src-C:before { content: 'C'; }
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/* pre.src-C++ doesn't work in CSS */
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pre.src-clojure:before { content: 'Clojure'; }
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pre.src-css:before { content: 'CSS'; }
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pre.src-D:before { content: 'D'; }
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pre.src-ditaa:before { content: 'ditaa'; }
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pre.src-dot:before { content: 'Graphviz'; }
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pre.src-calc:before { content: 'Emacs Calc'; }
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pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
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pre.src-fortran:before { content: 'Fortran'; }
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pre.src-gnuplot:before { content: 'gnuplot'; }
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pre.src-haskell:before { content: 'Haskell'; }
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pre.src-hledger:before { content: 'hledger'; }
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pre.src-java:before { content: 'Java'; }
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pre.src-js:before { content: 'Javascript'; }
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pre.src-latex:before { content: 'LaTeX'; }
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pre.src-ledger:before { content: 'Ledger'; }
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pre.src-lisp:before { content: 'Lisp'; }
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pre.src-lilypond:before { content: 'Lilypond'; }
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pre.src-lua:before { content: 'Lua'; }
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pre.src-matlab:before { content: 'MATLAB'; }
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pre.src-mscgen:before { content: 'Mscgen'; }
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pre.src-ocaml:before { content: 'Objective Caml'; }
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pre.src-octave:before { content: 'Octave'; }
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pre.src-org:before { content: 'Org mode'; }
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pre.src-oz:before { content: 'OZ'; }
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pre.src-plantuml:before { content: 'Plantuml'; }
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pre.src-processing:before { content: 'Processing.js'; }
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|
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|
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|
||||||
|
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|
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|
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|
in ob-*.el */
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
/* add a generic configuration mode; LaTeX export needs an additional
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|
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|
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table { border-collapse:collapse; }
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|
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|
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|
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|
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|
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.equation {
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|
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|
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|
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|
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|
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|
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|
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|
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|
}
|
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|
.inlinetask {
|
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|
padding: 10px;
|
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|
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|
||||||
|
margin: 10px;
|
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|
background: #ffffcc;
|
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|
}
|
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|
#org-div-home-and-up
|
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|
{ text-align: right; font-size: 70%; white-space: nowrap; }
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|
textarea { overflow-x: auto; }
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|
.org-info-js_info-navigation { border-style: none; }
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|
#org-info-js_console-label
|
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|
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
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|
.org-info-js_search-highlight
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|
{ background-color: #ffff00; color: #000000; font-weight: bold; }
|
||||||
|
.org-svg { width: 90%; }
|
||||||
|
/*]]>*/-->
|
||||||
|
</style>
|
||||||
|
<link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
|
||||||
|
<link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
|
||||||
|
<script src="js/jquery.min.js"></script>
|
||||||
|
<script src="js/bootstrap.min.js"></script>
|
||||||
|
<script type="text/javascript" src="js/jquery.stickytableheaders.min.js"></script>
|
||||||
|
<script type="text/javascript" src="js/readtheorg.js"></script>
|
||||||
|
<script type="text/javascript">
|
||||||
|
/*
|
||||||
|
@licstart The following is the entire license notice for the
|
||||||
|
JavaScript code in this tag.
|
||||||
|
|
||||||
|
Copyright (C) 2012-2019 Free Software Foundation, Inc.
|
||||||
|
|
||||||
|
The JavaScript code in this tag is free software: you can
|
||||||
|
redistribute it and/or modify it under the terms of the GNU
|
||||||
|
General Public License (GNU GPL) as published by the Free Software
|
||||||
|
Foundation, either version 3 of the License, or (at your option)
|
||||||
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
||||||
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||||
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
||||||
|
|
||||||
|
As additional permission under GNU GPL version 3 section 7, you
|
||||||
|
may distribute non-source (e.g., minimized or compacted) forms of
|
||||||
|
that code without the copy of the GNU GPL normally required by
|
||||||
|
section 4, provided you include this license notice and a URL
|
||||||
|
through which recipients can access the Corresponding Source.
|
||||||
|
|
||||||
|
|
||||||
|
@licend The above is the entire license notice
|
||||||
|
for the JavaScript code in this tag.
|
||||||
|
*/
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
function CodeHighlightOn(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
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|
if(null != target) {
|
||||||
|
elem.cacheClassElem = elem.className;
|
||||||
|
elem.cacheClassTarget = target.className;
|
||||||
|
target.className = "code-highlighted";
|
||||||
|
elem.className = "code-highlighted";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
function CodeHighlightOff(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(elem.cacheClassElem)
|
||||||
|
elem.className = elem.cacheClassElem;
|
||||||
|
if(elem.cacheClassTarget)
|
||||||
|
target.className = elem.cacheClassTarget;
|
||||||
|
}
|
||||||
|
/*]]>*///-->
|
||||||
|
</script>
|
||||||
|
<script type="text/x-mathjax-config">
|
||||||
|
MathJax.Hub.Config({
|
||||||
|
displayAlign: "center",
|
||||||
|
displayIndent: "0em",
|
||||||
|
|
||||||
|
"HTML-CSS": { scale: 100,
|
||||||
|
linebreaks: { automatic: "false" },
|
||||||
|
webFont: "TeX"
|
||||||
|
},
|
||||||
|
SVG: {scale: 100,
|
||||||
|
linebreaks: { automatic: "false" },
|
||||||
|
font: "TeX"},
|
||||||
|
NativeMML: {scale: 100},
|
||||||
|
TeX: { equationNumbers: {autoNumber: "AMS"},
|
||||||
|
MultLineWidth: "85%",
|
||||||
|
TagSide: "right",
|
||||||
|
TagIndent: ".8em"
|
||||||
|
}
|
||||||
|
});
|
||||||
|
</script>
|
||||||
|
<script type="text/javascript"
|
||||||
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="content">
|
||||||
|
<h1 class="title">Identification of the Stewart Platform using Simscape</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org0c15748">1. Identification</a></li>
|
||||||
|
<li><a href="#orgb51bebd">2. Cartesian Plot</a></li>
|
||||||
|
<li><a href="#org8822347">3. From a force to force sensor</a></li>
|
||||||
|
<li><a href="#orgb3f97c3">4. From a force applied in the leg to the displacement of the leg</a></li>
|
||||||
|
<li><a href="#org4f7f749">5. Transmissibility</a></li>
|
||||||
|
<li><a href="#orgc027ff6">6. Compliance</a></li>
|
||||||
|
<li><a href="#orgeb43267">7. Inertial</a></li>
|
||||||
|
<li><a href="#org702dc6c">8. identifyPlant</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org0c15748" class="outline-2">
|
||||||
|
<h2 id="org0c15748"><span class="section-number-2">1</span> Identification</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<p>
|
||||||
|
The hexapod structure and Sample structure are initialized.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">initializeHexapod<span style="color: #DCDCCC;">()</span>;
|
||||||
|
initializeSample<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">G = identifyPlant<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb51bebd" class="outline-2">
|
||||||
|
<h2 id="orgb51bebd"><span class="section-number-2">2</span> Cartesian Plot</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<p>
|
||||||
|
From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_cart<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_cart<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org8822347" class="outline-2">
|
||||||
|
<h2 id="org8822347"><span class="section-number-2">3</span> From a force to force sensor</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">4</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">5</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb3f97c3" class="outline-2">
|
||||||
|
<h2 id="orgb3f97c3"><span class="section-number-2">4</span> From a force applied in the leg to the displacement of the leg</h2>
|
||||||
|
<div class="outline-text-2" id="text-4">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">4</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">5</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4f7f749" class="outline-2">
|
||||||
|
<h2 id="org4f7f749"><span class="section-number-2">5</span> Transmissibility</h2>
|
||||||
|
<div class="outline-text-2" id="text-5">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">4</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">5</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgc027ff6" class="outline-2">
|
||||||
|
<h2 id="orgc027ff6"><span class="section-number-2">6</span> Compliance</h2>
|
||||||
|
<div class="outline-text-2" id="text-6">
|
||||||
|
<p>
|
||||||
|
From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_comp<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_comp<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_comp<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgeb43267" class="outline-2">
|
||||||
|
<h2 id="orgeb43267"><span class="section-number-2">7</span> Inertial</h2>
|
||||||
|
<div class="outline-text-2" id="text-7">
|
||||||
|
<p>
|
||||||
|
From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
|
||||||
|
hold on;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_iner<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_iner<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
bode<span style="color: #DCDCCC;">(</span>G.G_iner<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
hold off;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org702dc6c" class="outline-2">
|
||||||
|
<h2 id="org702dc6c"><span class="section-number-2">8</span> identifyPlant</h2>
|
||||||
|
<div class="outline-text-2" id="text-8">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">sys</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">identifyPlant</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We use this code block to pass optional parameters.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Default values for opts</span>
|
||||||
|
opts = struct<span style="color: #DCDCCC;">()</span>;
|
||||||
|
|
||||||
|
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Populate opts with input parameters</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
||||||
|
opts.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We defined the options for the <code>linearize</code> command.
|
||||||
|
Here, we just identify the system at time \(t = 0\).
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">options = linearizeOptions;
|
||||||
|
options.SampleTime = <span style="color: #BFEBBF;">0</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We define the name of the Simulink File used to identification.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">mdl = <span style="color: #CC9393;">'stewart'</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Then we defined the input/output of the transfer function we want to identify.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Inputs</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>F'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Cartesian forces</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Fl'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Leg forces</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Fd'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Direct forces</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Dw'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Base motion</span>
|
||||||
|
|
||||||
|
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Outputs</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Dm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Relative Motion</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Dlm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Displacement of each leg</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Flm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Force sensor in each leg</span>
|
||||||
|
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">8</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Xm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Absolute motion of platform</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The linearization is run.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">G = linearize<span style="color: #DCDCCC;">(</span>mdl, io, <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We defined all the Input/Output names of the identified transfer function.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">G.InputName = <span style="color: #DCDCCC;">{</span><span style="color: #CC9393;">'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'</span><span style="color: #DCDCCC;">}</span>;
|
||||||
|
G.OutputName = <span style="color: #DCDCCC;">{</span><span style="color: #CC9393;">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span style="color: #DCDCCC;">}</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We split the transfer function into sub transfer functions and we compute their minimum realization.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">sys.G_cart = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sys.G_forc = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sys.G_legs = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sys.G_tran = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sys.G_comp = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sys.G_iner = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #7F9F7F;">% sys.G_all = minreal(G);</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Thomas Dehaeze</p>
|
||||||
|
<p class="date">Created: 2019-03-22 ven. 12:03</p>
|
||||||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
242
identification.org
Normal file
242
identification.org
Normal file
@ -0,0 +1,242 @@
|
|||||||
|
#+TITLE: Identification of the Stewart Platform using Simscape
|
||||||
|
:DRAWER:
|
||||||
|
#+STARTUP: overview
|
||||||
|
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
|
||||||
|
#+HTML_HEAD: <script src="js/jquery.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script src="js/bootstrap.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="js/jquery.stickytableheaders.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="js/readtheorg.js"></script>
|
||||||
|
|
||||||
|
#+LATEX_CLASS: cleanreport
|
||||||
|
#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
|
||||||
|
#+LaTeX_HEADER: \usepackage{svg}
|
||||||
|
#+LaTeX_HEADER: \newcommand{\authorFirstName}{Thomas}
|
||||||
|
#+LaTeX_HEADER: \newcommand{\authorLastName}{Dehaeze}
|
||||||
|
#+LaTeX_HEADER: \newcommand{\authorEmail}{dehaeze.thomas@gmail.com}
|
||||||
|
|
||||||
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||||
|
#+PROPERTY: header-args:matlab+ :comments org
|
||||||
|
#+PROPERTY: header-args:matlab+ :exports both
|
||||||
|
#+PROPERTY: header-args:matlab+ :eval no-export
|
||||||
|
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||||
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||||||
|
:END:
|
||||||
|
|
||||||
|
* Identification
|
||||||
|
#+begin_src matlab :results none :exports none
|
||||||
|
<<matlab-init>>
|
||||||
|
addpath('src');
|
||||||
|
addpath('library');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :results none :exports none
|
||||||
|
open stewart
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The hexapod structure and Sample structure are initialized.
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
initializeHexapod();
|
||||||
|
initializeSample();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
G = identifyPlant();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Cartesian Plot
|
||||||
|
From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_cart(1, 1));
|
||||||
|
bode(G.G_cart(3, 3));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* From a force to force sensor
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_forc(1, 1));
|
||||||
|
bode(G.G_forc(2, 2));
|
||||||
|
bode(G.G_forc(3, 3));
|
||||||
|
bode(G.G_forc(4, 4));
|
||||||
|
bode(G.G_forc(5, 5));
|
||||||
|
bode(G.G_forc(6, 6));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_forc(1, 1));
|
||||||
|
bode(G.G_forc(1, 2));
|
||||||
|
bode(G.G_forc(1, 3));
|
||||||
|
bode(G.G_forc(1, 4));
|
||||||
|
bode(G.G_forc(1, 5));
|
||||||
|
bode(G.G_forc(1, 6));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* From a force applied in the leg to the displacement of the leg
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_legs(1, 1));
|
||||||
|
bode(G.G_legs(2, 2));
|
||||||
|
bode(G.G_legs(3, 3));
|
||||||
|
bode(G.G_legs(4, 4));
|
||||||
|
bode(G.G_legs(5, 5));
|
||||||
|
bode(G.G_legs(6, 6));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_legs(1, 1));
|
||||||
|
bode(G.G_legs(1, 2));
|
||||||
|
bode(G.G_legs(1, 3));
|
||||||
|
bode(G.G_legs(1, 4));
|
||||||
|
bode(G.G_legs(1, 5));
|
||||||
|
bode(G.G_legs(1, 6));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Transmissibility
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_tran(1, 1));
|
||||||
|
bode(G.G_tran(2, 2));
|
||||||
|
bode(G.G_tran(3, 3));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_tran(4, 4));
|
||||||
|
bode(G.G_tran(5, 5));
|
||||||
|
bode(G.G_tran(6, 6));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_tran(1, 1));
|
||||||
|
bode(G.G_tran(2, 1));
|
||||||
|
bode(G.G_tran(3, 1));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Compliance
|
||||||
|
From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_comp(1, 1));
|
||||||
|
bode(G.G_comp(2, 2));
|
||||||
|
bode(G.G_comp(3, 3));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Inertial
|
||||||
|
From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
|
||||||
|
|
||||||
|
#+begin_src matlab :results none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
bode(G.G_iner(1, 1));
|
||||||
|
bode(G.G_iner(2, 2));
|
||||||
|
bode(G.G_iner(3, 3));
|
||||||
|
hold off;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* identifyPlant
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :exports code
|
||||||
|
:HEADER-ARGS:matlab+: :comments yes
|
||||||
|
:HEADER-ARGS:matlab+: :eval no
|
||||||
|
:HEADER-ARGS:matlab+: :tangle src/identifyPlant.m
|
||||||
|
:END:
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
function [sys] = identifyPlant(opts_param)
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We use this code block to pass optional parameters.
|
||||||
|
#+begin_src matlab
|
||||||
|
%% Default values for opts
|
||||||
|
opts = struct();
|
||||||
|
|
||||||
|
%% Populate opts with input parameters
|
||||||
|
if exist('opts_param','var')
|
||||||
|
for opt = fieldnames(opts_param)'
|
||||||
|
opts.(opt{1}) = opts_param.(opt{1});
|
||||||
|
end
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We defined the options for the =linearize= command.
|
||||||
|
Here, we just identify the system at time $t = 0$.
|
||||||
|
#+begin_src matlab
|
||||||
|
options = linearizeOptions;
|
||||||
|
options.SampleTime = 0;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We define the name of the Simulink File used to identification.
|
||||||
|
#+begin_src matlab
|
||||||
|
mdl = 'stewart';
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Then we defined the input/output of the transfer function we want to identify.
|
||||||
|
#+begin_src matlab
|
||||||
|
%% Inputs
|
||||||
|
io(1) = linio([mdl, '/F'], 1, 'input'); % Cartesian forces
|
||||||
|
io(2) = linio([mdl, '/Fl'], 1, 'input'); % Leg forces
|
||||||
|
io(3) = linio([mdl, '/Fd'], 1, 'input'); % Direct forces
|
||||||
|
io(4) = linio([mdl, '/Dw'], 1, 'input'); % Base motion
|
||||||
|
|
||||||
|
%% Outputs
|
||||||
|
io(5) = linio([mdl, '/Dm'], 1, 'output'); % Relative Motion
|
||||||
|
io(6) = linio([mdl, '/Dlm'], 1, 'output'); % Displacement of each leg
|
||||||
|
io(7) = linio([mdl, '/Flm'], 1, 'output'); % Force sensor in each leg
|
||||||
|
io(8) = linio([mdl, '/Xm'], 1, 'output'); % Absolute motion of platform
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The linearization is run.
|
||||||
|
#+begin_src matlab
|
||||||
|
G = linearize(mdl, io, 0);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We defined all the Input/Output names of the identified transfer function.
|
||||||
|
#+begin_src matlab
|
||||||
|
G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz', ...
|
||||||
|
'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ...
|
||||||
|
'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz', ...
|
||||||
|
'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'};
|
||||||
|
G.OutputName = {'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm', ...
|
||||||
|
'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m', ...
|
||||||
|
'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m', ...
|
||||||
|
'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'};
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We split the transfer function into sub transfer functions and we compute their minimum realization.
|
||||||
|
#+begin_src matlab
|
||||||
|
sys.G_cart = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}));
|
||||||
|
sys.G_forc = minreal(G({'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
|
||||||
|
sys.G_legs = minreal(G({'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
|
||||||
|
sys.G_tran = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'}));
|
||||||
|
sys.G_comp = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
||||||
|
sys.G_iner = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
||||||
|
% sys.G_all = minreal(G);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
301
index.html
Normal file
301
index.html
Normal file
@ -0,0 +1,301 @@
|
|||||||
|
<?xml version="1.0" encoding="utf-8"?>
|
||||||
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||||
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
|
<head>
|
||||||
|
<!-- 2019-03-22 ven. 12:03 -->
|
||||||
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||||
|
<title>Stewart Platform Studies</title>
|
||||||
|
<meta name="generator" content="Org mode" />
|
||||||
|
<meta name="author" content="Thomas Dehaeze" />
|
||||||
|
<style type="text/css">
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
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|
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||||||
|
#org-div-home-and-up
|
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|
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|
||||||
|
/*]]>*/-->
|
||||||
|
</style>
|
||||||
|
<link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
|
||||||
|
<link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
|
||||||
|
<script src="js/jquery.min.js"></script>
|
||||||
|
<script src="js/bootstrap.min.js"></script>
|
||||||
|
<script type="text/javascript" src="js/jquery.stickytableheaders.min.js"></script>
|
||||||
|
<script type="text/javascript" src="js/readtheorg.js"></script>
|
||||||
|
<script type="text/javascript">
|
||||||
|
/*
|
||||||
|
@licstart The following is the entire license notice for the
|
||||||
|
JavaScript code in this tag.
|
||||||
|
|
||||||
|
Copyright (C) 2012-2019 Free Software Foundation, Inc.
|
||||||
|
|
||||||
|
The JavaScript code in this tag is free software: you can
|
||||||
|
redistribute it and/or modify it under the terms of the GNU
|
||||||
|
General Public License (GNU GPL) as published by the Free Software
|
||||||
|
Foundation, either version 3 of the License, or (at your option)
|
||||||
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
||||||
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||||
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
||||||
|
|
||||||
|
As additional permission under GNU GPL version 3 section 7, you
|
||||||
|
may distribute non-source (e.g., minimized or compacted) forms of
|
||||||
|
that code without the copy of the GNU GPL normally required by
|
||||||
|
section 4, provided you include this license notice and a URL
|
||||||
|
through which recipients can access the Corresponding Source.
|
||||||
|
|
||||||
|
|
||||||
|
@licend The above is the entire license notice
|
||||||
|
for the JavaScript code in this tag.
|
||||||
|
*/
|
||||||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
function CodeHighlightOff(elem, id)
|
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|
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|
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|
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|
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|
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|
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|
/*]]>*///-->
|
||||||
|
</script>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="content">
|
||||||
|
<h1 class="title">Stewart Platform Studies</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org2b3b6a5">1. Simscape Model</a></li>
|
||||||
|
<li><a href="#org5dc817d">2. Architecture Study</a></li>
|
||||||
|
<li><a href="#orgccde31a">3. Motion Control</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org2b3b6a5" class="outline-2">
|
||||||
|
<h2 id="org2b3b6a5"><span class="section-number-2">1</span> Simscape Model</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li><a href="simscape-model.html">Model of the Stewart Platform</a></li>
|
||||||
|
<li><a href="identification.html">Identification</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org5dc817d" class="outline-2">
|
||||||
|
<h2 id="org5dc817d"><span class="section-number-2">2</span> Architecture Study</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li><a href="kinematic-study.html">Kinematic Study</a></li>
|
||||||
|
<li><a href="stiffness-study.html">Stiffness Matrix Study</a></li>
|
||||||
|
<li>Jacobian Study</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgccde31a" class="outline-2">
|
||||||
|
<h2 id="orgccde31a"><span class="section-number-2">3</span> Motion Control</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>Active Damping</li>
|
||||||
|
<li>Inertial Control</li>
|
||||||
|
<li>Decentralized Control</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Thomas Dehaeze</p>
|
||||||
|
<p class="date">Created: 2019-03-22 ven. 12:03</p>
|
||||||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
639
index.org
639
index.org
@ -1,4 +1,4 @@
|
|||||||
#+TITLE: Stewart Platform with Simscape
|
#+TITLE: Stewart Platform Studies
|
||||||
:DRAWER:
|
:DRAWER:
|
||||||
#+STARTUP: overview
|
#+STARTUP: overview
|
||||||
|
|
||||||
@ -11,6 +11,7 @@
|
|||||||
|
|
||||||
#+LATEX_CLASS: cleanreport
|
#+LATEX_CLASS: cleanreport
|
||||||
#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
|
#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
|
||||||
|
#+LaTeX_HEADER: \usepackage{svg}
|
||||||
#+LaTeX_HEADER: \newcommand{\authorFirstName}{Thomas}
|
#+LaTeX_HEADER: \newcommand{\authorFirstName}{Thomas}
|
||||||
#+LaTeX_HEADER: \newcommand{\authorLastName}{Dehaeze}
|
#+LaTeX_HEADER: \newcommand{\authorLastName}{Dehaeze}
|
||||||
#+LaTeX_HEADER: \newcommand{\authorEmail}{dehaeze.thomas@gmail.com}
|
#+LaTeX_HEADER: \newcommand{\authorEmail}{dehaeze.thomas@gmail.com}
|
||||||
@ -23,626 +24,16 @@
|
|||||||
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||||||
:END:
|
:END:
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
* Simscape Model
|
||||||
<<matlab-init>>
|
- [[file:simscape-model.org][Model of the Stewart Platform]]
|
||||||
addpath('src');
|
- [[file:identification.org][Identification]]
|
||||||
addpath('library');
|
|
||||||
#+end_src
|
* Architecture Study
|
||||||
|
- [[file:kinematic-study.org][Kinematic Study]]
|
||||||
#+begin_src matlab :results none
|
- [[file:stiffness-study.org][Stiffness Matrix Study]]
|
||||||
open stewart
|
- Jacobian Study
|
||||||
#+end_src
|
|
||||||
|
* Motion Control
|
||||||
#+begin_src matlab
|
- Active Damping
|
||||||
hexapod = initializeHexapod();
|
- Inertial Control
|
||||||
#+end_src
|
- Decentralized Control
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
: org_babel_eoe
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
initializeSample();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
G = identifyPlant();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+RESULTS:
|
|
||||||
|
|
||||||
* Functions
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :exports code
|
|
||||||
:HEADER-ARGS:matlab+: :comments no
|
|
||||||
:HEADER-ARGS:matlab+: :mkdir yes
|
|
||||||
:HEADER-ARGS:matlab+: :eval no
|
|
||||||
:END:
|
|
||||||
** getMaxPositions
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle src/getMaxPositions.m
|
|
||||||
:END:
|
|
||||||
#+begin_src matlab
|
|
||||||
function [X, Y, Z] = getMaxPositions(stewart)
|
|
||||||
Leg = stewart.Leg;
|
|
||||||
J = stewart.J;
|
|
||||||
theta = linspace(0, 2*pi, 100);
|
|
||||||
phi = linspace(-pi/2 , pi/2, 100);
|
|
||||||
dmax = zeros(length(theta), length(phi));
|
|
||||||
|
|
||||||
for i = 1:length(theta)
|
|
||||||
for j = 1:length(phi)
|
|
||||||
L = J*[cos(phi(j))*cos(theta(i)) cos(phi(j))*sin(theta(i)) sin(phi(j)) 0 0 0]';
|
|
||||||
dmax(i, j) = Leg.stroke/max(abs(L));
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
X = dmax.*cos(repmat(phi,length(theta),1)).*cos(repmat(theta,length(phi),1))';
|
|
||||||
Y = dmax.*cos(repmat(phi,length(theta),1)).*sin(repmat(theta,length(phi),1))';
|
|
||||||
Z = dmax.*sin(repmat(phi,length(theta),1));
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** getMaxPureDisplacement
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle src/getMaxPureDisplacement.m
|
|
||||||
:END:
|
|
||||||
#+begin_src matlab
|
|
||||||
function [max_disp] = getMaxPureDisplacement(Leg, J)
|
|
||||||
max_disp = zeros(6, 1);
|
|
||||||
max_disp(1) = Leg.stroke/max(abs(J*[1 0 0 0 0 0]'));
|
|
||||||
max_disp(2) = Leg.stroke/max(abs(J*[0 1 0 0 0 0]'));
|
|
||||||
max_disp(3) = Leg.stroke/max(abs(J*[0 0 1 0 0 0]'));
|
|
||||||
max_disp(4) = Leg.stroke/max(abs(J*[0 0 0 1 0 0]'));
|
|
||||||
max_disp(5) = Leg.stroke/max(abs(J*[0 0 0 0 1 0]'));
|
|
||||||
max_disp(6) = Leg.stroke/max(abs(J*[0 0 0 0 0 1]'));
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** getStiffnessMatrix
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle src/getStiffnessMatrix.m
|
|
||||||
:END:
|
|
||||||
#+begin_src matlab
|
|
||||||
function [K] = getStiffnessMatrix(k, J)
|
|
||||||
% k - leg stiffness
|
|
||||||
% J - Jacobian matrix
|
|
||||||
K = k*(J'*J);
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** identifyPlant
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle src/identifyPlant.m
|
|
||||||
:END:
|
|
||||||
#+begin_src matlab
|
|
||||||
function [sys] = identifyPlant(opts_param)
|
|
||||||
%% Default values for opts
|
|
||||||
opts = struct();
|
|
||||||
|
|
||||||
%% Populate opts with input parameters
|
|
||||||
if exist('opts_param','var')
|
|
||||||
for opt = fieldnames(opts_param)'
|
|
||||||
opts.(opt{1}) = opts_param.(opt{1});
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
%% Options for Linearized
|
|
||||||
options = linearizeOptions;
|
|
||||||
options.SampleTime = 0;
|
|
||||||
|
|
||||||
%% Name of the Simulink File
|
|
||||||
mdl = 'stewart_identification';
|
|
||||||
|
|
||||||
%% Input/Output definition
|
|
||||||
io(1) = linio([mdl, '/F'], 1, 'input'); % Cartesian forces
|
|
||||||
io(2) = linio([mdl, '/Fl'], 1, 'input'); % Leg forces
|
|
||||||
io(3) = linio([mdl, '/Fd'], 1, 'input'); % Direct forces
|
|
||||||
io(4) = linio([mdl, '/Dw'], 1, 'input'); % Base motion
|
|
||||||
|
|
||||||
io(5) = linio([mdl, '/Dm'], 1, 'output'); % Relative Motion
|
|
||||||
io(6) = linio([mdl, '/Dlm'], 1, 'output'); % Displacement of each leg
|
|
||||||
io(7) = linio([mdl, '/Flm'], 1, 'output'); % Force sensor in each leg
|
|
||||||
io(8) = linio([mdl, '/Xm'], 1, 'output'); % Absolute motion of platform
|
|
||||||
|
|
||||||
%% Run the linearization
|
|
||||||
G = linearize(mdl, io, 0);
|
|
||||||
|
|
||||||
%% Input/Output names
|
|
||||||
G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz', ...
|
|
||||||
'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ...
|
|
||||||
'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz', ...
|
|
||||||
'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'};
|
|
||||||
G.OutputName = {'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm', ...
|
|
||||||
'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m', ...
|
|
||||||
'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m', ...
|
|
||||||
'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'};
|
|
||||||
|
|
||||||
%% Cut into sub transfer functions
|
|
||||||
sys.G_cart = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}));
|
|
||||||
sys.G_forc = minreal(G({'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
|
|
||||||
sys.G_legs = G({'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'});
|
|
||||||
sys.G_tran = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'}));
|
|
||||||
sys.G_comp = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
|
||||||
sys.G_iner = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
|
||||||
sys.G_all = minreal(G);
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** initializeHexapod
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle src/initializeHexapod.m
|
|
||||||
:END:
|
|
||||||
*** Function description and arguments
|
|
||||||
The =initializeHexapod= function takes one structure that contains configurations for the hexapod and returns one structure representing the hexapod.
|
|
||||||
#+begin_src matlab
|
|
||||||
function [stewart] = initializeHexapod(opts_param)
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Default values for opts.
|
|
||||||
#+begin_src matlab
|
|
||||||
opts = struct(...
|
|
||||||
'height', 90, ... % Height of the platform [mm]
|
|
||||||
'density', 8000, ... % Density of the material used for the hexapod [kg/m3]
|
|
||||||
'k_ax', 1e8, ... % Stiffness of each actuator [N/m]
|
|
||||||
'c_ax', 100, ... % Damping of each actuator [N/(m/s)]
|
|
||||||
'stroke', 50e-6, ... % Maximum stroke of each actuator [m]
|
|
||||||
'name', 'stewart' ... % Name of the file
|
|
||||||
);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Populate opts with input parameters
|
|
||||||
#+begin_src matlab
|
|
||||||
if exist('opts_param','var')
|
|
||||||
for opt = fieldnames(opts_param)'
|
|
||||||
opts.(opt{1}) = opts_param.(opt{1});
|
|
||||||
end
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** Initialization of the stewart structure
|
|
||||||
We initialize the Stewart structure
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart = struct();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
And we defined its total height.
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.H = opts.height; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** Bottom Plate
|
|
||||||
#+name: fig:stewart_bottom_plate
|
|
||||||
#+caption: Schematic of the bottom plates with all the parameters
|
|
||||||
[[file:./figs/stewart_bottom_plate.png]]
|
|
||||||
|
|
||||||
|
|
||||||
The bottom plate structure is initialized.
|
|
||||||
#+begin_src matlab
|
|
||||||
BP = struct();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We defined its internal radius (if there is a hole in the bottom plate) and its outer radius.
|
|
||||||
#+begin_src matlab
|
|
||||||
BP.Rint = 0; % Internal Radius [mm]
|
|
||||||
BP.Rext = 150; % External Radius [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We define its thickness.
|
|
||||||
#+begin_src matlab
|
|
||||||
BP.H = 10; % Thickness of the Bottom Plate [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
At which radius legs will be fixed and with that angle offset.
|
|
||||||
#+begin_src matlab
|
|
||||||
BP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
|
||||||
BP.alpha = 10; % Angle Offset [deg]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We defined the density of the material of the bottom plate.
|
|
||||||
#+begin_src matlab
|
|
||||||
BP.density = opts.density; % Density of the material [kg/m3]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
And its color.
|
|
||||||
#+begin_src matlab
|
|
||||||
BP.color = [0.7 0.7 0.7]; % Color [RGB]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Then the profile of the bottom plate is computed and will be used by Simscape
|
|
||||||
#+begin_src matlab
|
|
||||||
BP.shape = [BP.Rint BP.H; BP.Rint 0; BP.Rext 0; BP.Rext BP.H]; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The structure is added to the stewart structure
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.BP = BP;
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** Top Plate
|
|
||||||
The top plate structure is initialized.
|
|
||||||
#+begin_src matlab
|
|
||||||
TP = struct();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We defined the internal and external radius of the top plate.
|
|
||||||
#+begin_src matlab
|
|
||||||
TP.Rint = 0; % [mm]
|
|
||||||
TP.Rext = 100; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The thickness of the top plate.
|
|
||||||
#+begin_src matlab
|
|
||||||
TP.H = 10; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
At which radius and angle are fixed the legs.
|
|
||||||
#+begin_src matlab
|
|
||||||
TP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
|
||||||
TP.alpha = 20; % Angle [deg]
|
|
||||||
TP.dalpha = 0; % Angle Offset from 0 position [deg]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The density of its material.
|
|
||||||
#+begin_src matlab
|
|
||||||
TP.density = opts.density; % Density of the material [kg/m3]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Its color.
|
|
||||||
#+begin_src matlab
|
|
||||||
TP.color = [0.7 0.7 0.7]; % Color [RGB]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Then the shape of the top plate is computed
|
|
||||||
#+begin_src matlab
|
|
||||||
TP.shape = [TP.Rint TP.H; TP.Rint 0; TP.Rext 0; TP.Rext TP.H];
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The structure is added to the stewart structure
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.TP = TP;
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** Legs
|
|
||||||
#+name: fig:stewart_legs
|
|
||||||
#+caption: Schematic for the legs of the Stewart platform
|
|
||||||
[[file:./figs/stewart_legs.png]]
|
|
||||||
|
|
||||||
|
|
||||||
The leg structure is initialized.
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg = struct();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The maximum Stroke of each leg is defined.
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg.stroke = opts.stroke; % [m]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The stiffness and damping of each leg are defined
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg.k_ax = opts.k_ax; % Stiffness of each leg [N/m]
|
|
||||||
Leg.c_ax = opts.c_ax; % Damping of each leg [N/(m/s)]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The radius of the legs are defined
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg.Rtop = 10; % Radius of the cylinder of the top part of the leg[mm]
|
|
||||||
Leg.Rbot = 12; % Radius of the cylinder of the bottom part of the leg [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The density of its material.
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg.density = opts.density; % Density of the material used for the legs [kg/m3]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Its color.
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg.color = [0.5 0.5 0.5]; % Color of the top part of the leg [RGB]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The radius of spheres representing the ball joints are defined.
|
|
||||||
#+begin_src matlab
|
|
||||||
Leg.R = 1.3*Leg.Rbot; % Size of the sphere at the extremity of the leg [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The structure is added to the stewart structure
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.Leg = Leg;
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** Ball Joints
|
|
||||||
#+name: fig:stewart_ball_joints
|
|
||||||
#+caption: Schematic of the support for the ball joints
|
|
||||||
[[file:./figs/stewart_ball_joints.png]]
|
|
||||||
|
|
||||||
=SP= is the structure representing the support for the ball joints at the extremity of each leg.
|
|
||||||
|
|
||||||
The =SP= structure is initialized.
|
|
||||||
#+begin_src matlab
|
|
||||||
SP = struct();
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We can define its rotational stiffness and damping. For now, we use perfect joints.
|
|
||||||
#+begin_src matlab
|
|
||||||
SP.k = 0; % [N*m/deg]
|
|
||||||
SP.c = 0; % [N*m/deg]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Its height is defined
|
|
||||||
#+begin_src matlab
|
|
||||||
SP.H = 15; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Its radius is based on the radius on the sphere at the end of the legs.
|
|
||||||
#+begin_src matlab
|
|
||||||
SP.R = Leg.R; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
SP.section = [0 SP.H-SP.R;
|
|
||||||
0 0;
|
|
||||||
SP.R 0;
|
|
||||||
SP.R SP.H];
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The density of its material is defined.
|
|
||||||
#+begin_src matlab
|
|
||||||
SP.density = opts.density; % [kg/m^3]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Its color is defined.
|
|
||||||
#+begin_src matlab
|
|
||||||
SP.color = [0.7 0.7 0.7]; % [RGB]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
The structure is added to the Hexapod structure
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.SP = SP;
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** More parameters are initialized
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart = initializeParameters(stewart);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** Save the Stewart Structure
|
|
||||||
#+begin_src matlab
|
|
||||||
save('./mat/stewart.mat', 'stewart')
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** initializeParameters Function
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle no
|
|
||||||
:END:
|
|
||||||
#+begin_src matlab
|
|
||||||
function [stewart] = initializeParameters(stewart)
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Computation of the position of the connection points on the base and moving platform
|
|
||||||
We first initialize =pos_base= corresponding to $[a_1, a_2, a_3, a_4, a_5, a_6]^T$ and =pos_top= corresponding to $[b_1, b_2, b_3, b_4, b_5, b_6]^T$.
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.pos_base = zeros(6, 3);
|
|
||||||
stewart.pos_top = zeros(6, 3);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We estimate the height between the ball joints of the bottom platform and of the top platform.
|
|
||||||
#+begin_src matlab
|
|
||||||
height = stewart.H - stewart.BP.H - stewart.TP.H - 2*stewart.SP.H; % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
for i = 1:3
|
|
||||||
% base points
|
|
||||||
angle_m_b = 120*(i-1) - stewart.BP.alpha;
|
|
||||||
angle_p_b = 120*(i-1) + stewart.BP.alpha;
|
|
||||||
|
|
||||||
stewart.pos_base(2*i-1,:) = [stewart.BP.Rleg*cos(angle_m_b), stewart.BP.Rleg*sin(angle_m_b), 0.0];
|
|
||||||
stewart.pos_base(2*i,:) = [stewart.BP.Rleg*cos(angle_p_b), stewart.BP.Rleg*sin(angle_p_b), 0.0];
|
|
||||||
|
|
||||||
% top points
|
|
||||||
angle_m_t = 120*(i-1) - stewart.TP.alpha + stewart.TP.dalpha;
|
|
||||||
angle_p_t = 120*(i-1) + stewart.TP.alpha + stewart.TP.dalpha;
|
|
||||||
|
|
||||||
stewart.pos_top(2*i-1,:) = [stewart.TP.Rleg*cos(angle_m_t), stewart.TP.Rleg*sin(angle_m_t), height];
|
|
||||||
stewart.pos_top(2*i,:) = [stewart.TP.Rleg*cos(angle_p_t), stewart.TP.Rleg*sin(angle_p_t), height];
|
|
||||||
end
|
|
||||||
|
|
||||||
% permute pos_top points so that legs are end points of base and top points
|
|
||||||
stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
|
|
||||||
stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
leg vectors
|
|
||||||
#+begin_src matlab
|
|
||||||
legs = stewart.pos_top - stewart.pos_base;
|
|
||||||
leg_length = zeros(6, 1);
|
|
||||||
leg_vectors = zeros(6, 3);
|
|
||||||
for i = 1:6
|
|
||||||
leg_length(i) = norm(legs(i,:));
|
|
||||||
leg_vectors(i,:) = legs(i,:) / leg_length(i);
|
|
||||||
end
|
|
||||||
|
|
||||||
stewart.Leg.lenght = 1000*leg_length(1)/1.5;
|
|
||||||
stewart.Leg.shape.bot = [0 0; ...
|
|
||||||
stewart.Leg.rad.bottom 0; ...
|
|
||||||
stewart.Leg.rad.bottom stewart.Leg.lenght; ...
|
|
||||||
stewart.Leg.rad.top stewart.Leg.lenght; ...
|
|
||||||
stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
|
|
||||||
0 0.2*stewart.Leg.lenght];
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Calculate revolute and cylindrical axes
|
|
||||||
#+begin_src matlab
|
|
||||||
rev1 = zeros(6, 3);
|
|
||||||
rev2 = zeros(6, 3);
|
|
||||||
cyl1 = zeros(6, 3);
|
|
||||||
for i = 1:6
|
|
||||||
rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
|
|
||||||
rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
|
|
||||||
|
|
||||||
rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
|
|
||||||
rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
|
|
||||||
|
|
||||||
cyl1(i,:) = leg_vectors(i,:);
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Coordinate systems
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.lower_leg = struct('rotation', eye(3));
|
|
||||||
stewart.upper_leg = struct('rotation', eye(3));
|
|
||||||
|
|
||||||
for i = 1:6
|
|
||||||
stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
|
|
||||||
stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Position Matrix
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.h+stewart.Leg.sphere.top+stewart.SP.h.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)];
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Compute Jacobian Matrix
|
|
||||||
#+begin_src matlab
|
|
||||||
% aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.h - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
|
|
||||||
bb = stewart.pos_top_tranform - (stewart.TP.h + stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
|
|
||||||
bb = bb - stewart.jacobian*1e-3*[zeros(6, 2),ones(6, 1)];
|
|
||||||
stewart.J = getJacobianMatrix(leg_vectors', bb');
|
|
||||||
|
|
||||||
stewart.K = stewart.Leg.k.ax*stewart.J'*stewart.J;
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
*** initializeParameters Function - BIS
|
|
||||||
#+begin_src matlab
|
|
||||||
function [stewart] = initializeParameters(stewart)
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We first compute $[a_1, a_2, a_3, a_4, a_5, a_6]^T$ and $[b_1, b_2, b_3, b_4, b_5, b_6]^T$.
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.Aa = zeros(6, 3); % [mm]
|
|
||||||
stewart.Ab = zeros(6, 3); % [mm]
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
for i = 1:3
|
|
||||||
stewart.Aa(2*i-1,:) = [stewart.BP.Rleg*cos( pi/180*(120*(i-1) - stewart.BP.alpha) ), ...
|
|
||||||
stewart.BP.Rleg*sin( pi/180*(120*(i-1) - stewart.BP.alpha) ), ...
|
|
||||||
stewart.BP.H+stewart.SP.H];
|
|
||||||
stewart.Aa(2*i,:) = [stewart.BP.Rleg*cos( pi/180*(120*(i-1) + stewart.BP.alpha) ), ...
|
|
||||||
stewart.BP.Rleg*sin( pi/180*(120*(i-1) + stewart.BP.alpha) ), ...
|
|
||||||
stewart.BP.H+stewart.SP.H];
|
|
||||||
|
|
||||||
stewart.Ab(2*i-1,:) = [stewart.TP.Rleg*cos( pi/180*(120*(i-1) + stewart.TP.dalpha - stewart.TP.alpha) ), ...
|
|
||||||
stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha - stewart.TP.alpha) ), ...
|
|
||||||
stewart.H - stewart.TP.H - stewart.SP.H];
|
|
||||||
stewart.Ab(2*i,:) = [stewart.TP.Rleg*cos( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
|
|
||||||
stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
|
|
||||||
stewart.H - stewart.TP.H - stewart.SP.H];
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Now, we compute the leg vectors $\hat{s}_i$ and leg position $l_i$:
|
|
||||||
\[ b_i - a_i = l_i \hat{s}_i \]
|
|
||||||
|
|
||||||
We initialize $l_i$ and $\hat{s}_i$
|
|
||||||
#+begin_src matlab
|
|
||||||
leg_length = zeros(6, 1); % [mm]
|
|
||||||
leg_vectors = zeros(6, 3);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We compute $b_i - a_i$, and then:
|
|
||||||
\begin{align*}
|
|
||||||
l_i &= \left|b_i - a_i\right| \\
|
|
||||||
\hat{s}_i &= \frac{b_i - a_i}{l_i}
|
|
||||||
\end{align*}
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
legs = stewart.Ab - stewart.Aa;
|
|
||||||
|
|
||||||
for i = 1:6
|
|
||||||
leg_length(i) = norm(legs(i,:));
|
|
||||||
leg_vectors(i,:) = legs(i,:) / leg_length(i);
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Then the shape of the bottom leg is estimated
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.Leg.lenght = leg_length(1)/1.5;
|
|
||||||
stewart.Leg.shape.bot = ...
|
|
||||||
[0 0; ...
|
|
||||||
stewart.Leg.Rbot 0; ...
|
|
||||||
stewart.Leg.Rbot stewart.Leg.lenght; ...
|
|
||||||
stewart.Leg.Rtop stewart.Leg.lenght; ...
|
|
||||||
stewart.Leg.Rtop 0.2*stewart.Leg.lenght; ...
|
|
||||||
0 0.2*stewart.Leg.lenght];
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
We compute rotation matrices to have the orientation of the legs.
|
|
||||||
The rotation matrix transforms the $z$ axis to the axis of the leg. The other axis are not important here.
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.Rm = struct('R', eye(3));
|
|
||||||
|
|
||||||
for i = 1:6
|
|
||||||
sx = cross(leg_vectors(i,:), [1 0 0]);
|
|
||||||
sx = sx/norm(sx);
|
|
||||||
|
|
||||||
sy = -cross(sx, leg_vectors(i,:));
|
|
||||||
sy = sy/norm(sy);
|
|
||||||
|
|
||||||
sz = leg_vectors(i,:);
|
|
||||||
sz = sz/norm(sz);
|
|
||||||
|
|
||||||
stewart.Rm(i).R = [sx', sy', sz'];
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
Compute Jacobian Matrix
|
|
||||||
#+begin_src matlab
|
|
||||||
J = zeros(6);
|
|
||||||
|
|
||||||
for i = 1:6
|
|
||||||
J(i, 1:3) = leg_vectors(i, :);
|
|
||||||
J(i, 4:6) = cross(0.001*(stewart.Ab - stewart.H*[0,0,1]), leg_vectors(i, :));
|
|
||||||
end
|
|
||||||
|
|
||||||
stewart.J = J;
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart.K = stewart.Leg.k_ax*stewart.J'*stewart.J;
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
end
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** initializeSample
|
|
||||||
:PROPERTIES:
|
|
||||||
:HEADER-ARGS:matlab+: :tangle src/initializeSample.m
|
|
||||||
:END:
|
|
||||||
#+begin_src matlab
|
|
||||||
function [] = initializeSample(opts_param)
|
|
||||||
%% Default values for opts
|
|
||||||
sample = struct( ...
|
|
||||||
'radius', 100, ... % radius of the cylinder [mm]
|
|
||||||
'height', 300, ... % height of the cylinder [mm]
|
|
||||||
'mass', 50, ... % mass of the cylinder [kg]
|
|
||||||
'measheight', 150, ... % measurement point z-offset [mm]
|
|
||||||
'offset', [0, 0, 0], ... % offset position of the sample [mm]
|
|
||||||
'color', [0.9 0.1 0.1] ...
|
|
||||||
);
|
|
||||||
|
|
||||||
%% Populate opts with input parameters
|
|
||||||
if exist('opts_param','var')
|
|
||||||
for opt = fieldnames(opts_param)'
|
|
||||||
sample.(opt{1}) = opts_param.(opt{1});
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
%% Save
|
|
||||||
save('./mat/sample.mat', 'sample');
|
|
||||||
end
|
|
||||||
#+end_src
|
|
||||||
|
|||||||
7
js/bootstrap.min.js
vendored
Normal file
7
js/bootstrap.min.js
vendored
Normal file
File diff suppressed because one or more lines are too long
4
js/jquery.min.js
vendored
Normal file
4
js/jquery.min.js
vendored
Normal file
File diff suppressed because one or more lines are too long
1
js/jquery.stickytableheaders.min.js
vendored
Normal file
1
js/jquery.stickytableheaders.min.js
vendored
Normal file
@ -0,0 +1 @@
|
|||||||
|
!function(a,b){"use strict";function c(c,g){var h=this;h.$el=a(c),h.el=c,h.id=e++,h.$window=a(b),h.$document=a(document),h.$el.bind("destroyed",a.proxy(h.teardown,h)),h.$clonedHeader=null,h.$originalHeader=null,h.isSticky=!1,h.hasBeenSticky=!1,h.leftOffset=null,h.topOffset=null,h.init=function(){h.$el.each(function(){var b=a(this);b.css("padding",0),h.$originalHeader=a("thead:first",this),h.$clonedHeader=h.$originalHeader.clone(),b.trigger("clonedHeader."+d,[h.$clonedHeader]),h.$clonedHeader.addClass("tableFloatingHeader"),h.$clonedHeader.css("display","none"),h.$originalHeader.addClass("tableFloatingHeaderOriginal"),h.$originalHeader.after(h.$clonedHeader),h.$printStyle=a('<style type="text/css" media="print">.tableFloatingHeader{display:none !important;}.tableFloatingHeaderOriginal{position:static !important;}</style>'),a("head").append(h.$printStyle)}),h.setOptions(g),h.updateWidth(),h.toggleHeaders(),h.bind()},h.destroy=function(){h.$el.unbind("destroyed",h.teardown),h.teardown()},h.teardown=function(){h.isSticky&&h.$originalHeader.css("position","static"),a.removeData(h.el,"plugin_"+d),h.unbind(),h.$clonedHeader.remove(),h.$originalHeader.removeClass("tableFloatingHeaderOriginal"),h.$originalHeader.css("visibility","visible"),h.$printStyle.remove(),h.el=null,h.$el=null},h.bind=function(){h.$scrollableArea.on("scroll."+d,h.toggleHeaders),h.isWindowScrolling||(h.$window.on("scroll."+d+h.id,h.setPositionValues),h.$window.on("resize."+d+h.id,h.toggleHeaders)),h.$scrollableArea.on("resize."+d,h.toggleHeaders),h.$scrollableArea.on("resize."+d,h.updateWidth)},h.unbind=function(){h.$scrollableArea.off("."+d,h.toggleHeaders),h.isWindowScrolling||(h.$window.off("."+d+h.id,h.setPositionValues),h.$window.off("."+d+h.id,h.toggleHeaders)),h.$scrollableArea.off("."+d,h.updateWidth)},h.toggleHeaders=function(){h.$el&&h.$el.each(function(){var b,c=a(this),d=h.isWindowScrolling?isNaN(h.options.fixedOffset)?h.options.fixedOffset.outerHeight():h.options.fixedOffset:h.$scrollableArea.offset().top+(isNaN(h.options.fixedOffset)?0:h.options.fixedOffset),e=c.offset(),f=h.$scrollableArea.scrollTop()+d,g=h.$scrollableArea.scrollLeft(),i=h.isWindowScrolling?f>e.top:d>e.top,j=(h.isWindowScrolling?f:0)<e.top+c.height()-h.$clonedHeader.height()-(h.isWindowScrolling?0:d);i&&j?(b=e.left-g+h.options.leftOffset,h.$originalHeader.css({position:"fixed","margin-top":h.options.marginTop,left:b,"z-index":3}),h.leftOffset=b,h.topOffset=d,h.$clonedHeader.css("display",""),h.isSticky||(h.isSticky=!0,h.updateWidth()),h.setPositionValues()):h.isSticky&&(h.$originalHeader.css("position","static"),h.$clonedHeader.css("display","none"),h.isSticky=!1,h.resetWidth(a("td,th",h.$clonedHeader),a("td,th",h.$originalHeader)))})},h.setPositionValues=function(){var a=h.$window.scrollTop(),b=h.$window.scrollLeft();!h.isSticky||0>a||a+h.$window.height()>h.$document.height()||0>b||b+h.$window.width()>h.$document.width()||h.$originalHeader.css({top:h.topOffset-(h.isWindowScrolling?0:a),left:h.leftOffset-(h.isWindowScrolling?0:b)})},h.updateWidth=function(){if(h.isSticky){h.$originalHeaderCells||(h.$originalHeaderCells=a("th,td",h.$originalHeader)),h.$clonedHeaderCells||(h.$clonedHeaderCells=a("th,td",h.$clonedHeader));var b=h.getWidth(h.$clonedHeaderCells);h.setWidth(b,h.$clonedHeaderCells,h.$originalHeaderCells),h.$originalHeader.css("width",h.$clonedHeader.width())}},h.getWidth=function(c){var d=[];return c.each(function(c){var e,f=a(this);if("border-box"===f.css("box-sizing"))e=f[0].getBoundingClientRect().width;else{var g=a("th",h.$originalHeader);if("collapse"===g.css("border-collapse"))if(b.getComputedStyle)e=parseFloat(b.getComputedStyle(this,null).width);else{var i=parseFloat(f.css("padding-left")),j=parseFloat(f.css("padding-right")),k=parseFloat(f.css("border-width"));e=f.outerWidth()-i-j-k}else e=f.width()}d[c]=e}),d},h.setWidth=function(a,b,c){b.each(function(b){var d=a[b];c.eq(b).css({"min-width":d,"max-width":d})})},h.resetWidth=function(b,c){b.each(function(b){var d=a(this);c.eq(b).css({"min-width":d.css("min-width"),"max-width":d.css("max-width")})})},h.setOptions=function(c){h.options=a.extend({},f,c),h.$scrollableArea=a(h.options.scrollableArea),h.isWindowScrolling=h.$scrollableArea[0]===b},h.updateOptions=function(a){h.setOptions(a),h.unbind(),h.bind(),h.updateWidth(),h.toggleHeaders()},h.init()}var d="stickyTableHeaders",e=0,f={fixedOffset:0,leftOffset:0,marginTop:0,scrollableArea:b};a.fn[d]=function(b){return this.each(function(){var e=a.data(this,"plugin_"+d);e?"string"==typeof b?e[b].apply(e):e.updateOptions(b):"destroy"!==b&&a.data(this,"plugin_"+d,new c(this,b))})}}(jQuery,window);
|
||||||
85
js/readtheorg.js
Normal file
85
js/readtheorg.js
Normal file
@ -0,0 +1,85 @@
|
|||||||
|
$(function() {
|
||||||
|
$('.note').before("<p class='admonition-title note'>Note</p>");
|
||||||
|
$('.seealso').before("<p class='admonition-title seealso'>See also</p>");
|
||||||
|
$('.warning').before("<p class='admonition-title warning'>Warning</p>");
|
||||||
|
$('.caution').before("<p class='admonition-title caution'>Caution</p>");
|
||||||
|
$('.attention').before("<p class='admonition-title attention'>Attention</p>");
|
||||||
|
$('.tip').before("<p class='admonition-title tip'>Tip</p>");
|
||||||
|
$('.important').before("<p class='admonition-title important'>Important</p>");
|
||||||
|
$('.hint').before("<p class='admonition-title hint'>Hint</p>");
|
||||||
|
$('.error').before("<p class='admonition-title error'>Error</p>");
|
||||||
|
$('.danger').before("<p class='admonition-title danger'>Danger</p>");
|
||||||
|
});
|
||||||
|
|
||||||
|
$( document ).ready(function() {
|
||||||
|
|
||||||
|
// Shift nav in mobile when clicking the menu.
|
||||||
|
$(document).on('click', "[data-toggle='wy-nav-top']", function() {
|
||||||
|
$("[data-toggle='wy-nav-shift']").toggleClass("shift");
|
||||||
|
$("[data-toggle='rst-versions']").toggleClass("shift");
|
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|
});
|
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|
// Close menu when you click a link.
|
||||||
|
$(document).on('click', ".wy-menu-vertical .current ul li a", function() {
|
||||||
|
$("[data-toggle='wy-nav-shift']").removeClass("shift");
|
||||||
|
$("[data-toggle='rst-versions']").toggleClass("shift");
|
||||||
|
});
|
||||||
|
$(document).on('click', "[data-toggle='rst-current-version']", function() {
|
||||||
|
$("[data-toggle='rst-versions']").toggleClass("shift-up");
|
||||||
|
});
|
||||||
|
// Make tables responsive
|
||||||
|
$("table.docutils:not(.field-list)").wrap("<div class='wy-table-responsive'></div>");
|
||||||
|
});
|
||||||
|
|
||||||
|
$( document ).ready(function() {
|
||||||
|
$('#text-table-of-contents ul').first().addClass('nav');
|
||||||
|
// ScrollSpy also requires that we use
|
||||||
|
// a Bootstrap nav component.
|
||||||
|
$('body').scrollspy({target: '#text-table-of-contents'});
|
||||||
|
|
||||||
|
// add sticky table headers
|
||||||
|
$('table').stickyTableHeaders();
|
||||||
|
|
||||||
|
// set the height of tableOfContents
|
||||||
|
var $postamble = $('#postamble');
|
||||||
|
var $tableOfContents = $('#table-of-contents');
|
||||||
|
$tableOfContents.css({paddingBottom: $postamble.outerHeight()});
|
||||||
|
|
||||||
|
// add TOC button
|
||||||
|
var toggleSidebar = $('<div id="toggle-sidebar"><a href="#table-of-contents"><h2>Table of Contents</h2></a></div>');
|
||||||
|
$('#content').prepend(toggleSidebar);
|
||||||
|
|
||||||
|
// add close button when sidebar showed in mobile screen
|
||||||
|
var closeBtn = $('<a class="close-sidebar" href="#">Close</a>');
|
||||||
|
var tocTitle = $('#table-of-contents').find('h2');
|
||||||
|
tocTitle.append(closeBtn);
|
||||||
|
});
|
||||||
|
|
||||||
|
window.SphinxRtdTheme = (function (jquery) {
|
||||||
|
var stickyNav = (function () {
|
||||||
|
var navBar,
|
||||||
|
win,
|
||||||
|
stickyNavCssClass = 'stickynav',
|
||||||
|
applyStickNav = function () {
|
||||||
|
if (navBar.height() <= win.height()) {
|
||||||
|
navBar.addClass(stickyNavCssClass);
|
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|
} else {
|
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|
navBar.removeClass(stickyNavCssClass);
|
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|
}
|
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|
},
|
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|
enable = function () {
|
||||||
|
applyStickNav();
|
||||||
|
win.on('resize', applyStickNav);
|
||||||
|
},
|
||||||
|
init = function () {
|
||||||
|
navBar = jquery('nav.wy-nav-side:first');
|
||||||
|
win = jquery(window);
|
||||||
|
};
|
||||||
|
jquery(init);
|
||||||
|
return {
|
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|
enable : enable
|
||||||
|
};
|
||||||
|
}());
|
||||||
|
return {
|
||||||
|
StickyNav : stickyNav
|
||||||
|
};
|
||||||
|
}($));
|
||||||
2
js/siunitx.js
Normal file
2
js/siunitx.js
Normal file
File diff suppressed because one or more lines are too long
316
kinematic-study.html
Normal file
316
kinematic-study.html
Normal file
@ -0,0 +1,316 @@
|
|||||||
|
<?xml version="1.0" encoding="utf-8"?>
|
||||||
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||||
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
|
<head>
|
||||||
|
<!-- 2019-03-22 ven. 12:03 -->
|
||||||
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||||
|
<title>Kinematic Study of the Stewart Platform</title>
|
||||||
|
<meta name="generator" content="Org mode" />
|
||||||
|
<meta name="author" content="Thomas Dehaeze" />
|
||||||
|
<style type="text/css">
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
.title { text-align: center;
|
||||||
|
margin-bottom: .2em; }
|
||||||
|
.subtitle { text-align: center;
|
||||||
|
font-size: medium;
|
||||||
|
font-weight: bold;
|
||||||
|
margin-top:0; }
|
||||||
|
.todo { font-family: monospace; color: red; }
|
||||||
|
.done { font-family: monospace; color: green; }
|
||||||
|
.priority { font-family: monospace; color: orange; }
|
||||||
|
.tag { background-color: #eee; font-family: monospace;
|
||||||
|
padding: 2px; font-size: 80%; font-weight: normal; }
|
||||||
|
.timestamp { color: #bebebe; }
|
||||||
|
.timestamp-kwd { color: #5f9ea0; }
|
||||||
|
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
||||||
|
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
|
||||||
|
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
|
||||||
|
.underline { text-decoration: underline; }
|
||||||
|
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
|
||||||
|
p.verse { margin-left: 3%; }
|
||||||
|
pre {
|
||||||
|
border: 1px solid #ccc;
|
||||||
|
box-shadow: 3px 3px 3px #eee;
|
||||||
|
padding: 8pt;
|
||||||
|
font-family: monospace;
|
||||||
|
overflow: auto;
|
||||||
|
margin: 1.2em;
|
||||||
|
}
|
||||||
|
pre.src {
|
||||||
|
position: relative;
|
||||||
|
overflow: visible;
|
||||||
|
padding-top: 1.2em;
|
||||||
|
}
|
||||||
|
pre.src:before {
|
||||||
|
display: none;
|
||||||
|
position: absolute;
|
||||||
|
background-color: white;
|
||||||
|
top: -10px;
|
||||||
|
right: 10px;
|
||||||
|
padding: 3px;
|
||||||
|
border: 1px solid black;
|
||||||
|
}
|
||||||
|
pre.src:hover:before { display: inline;}
|
||||||
|
/* Languages per Org manual */
|
||||||
|
pre.src-asymptote:before { content: 'Asymptote'; }
|
||||||
|
pre.src-awk:before { content: 'Awk'; }
|
||||||
|
pre.src-C:before { content: 'C'; }
|
||||||
|
/* pre.src-C++ doesn't work in CSS */
|
||||||
|
pre.src-clojure:before { content: 'Clojure'; }
|
||||||
|
pre.src-css:before { content: 'CSS'; }
|
||||||
|
pre.src-D:before { content: 'D'; }
|
||||||
|
pre.src-ditaa:before { content: 'ditaa'; }
|
||||||
|
pre.src-dot:before { content: 'Graphviz'; }
|
||||||
|
pre.src-calc:before { content: 'Emacs Calc'; }
|
||||||
|
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
|
||||||
|
pre.src-fortran:before { content: 'Fortran'; }
|
||||||
|
pre.src-gnuplot:before { content: 'gnuplot'; }
|
||||||
|
pre.src-haskell:before { content: 'Haskell'; }
|
||||||
|
pre.src-hledger:before { content: 'hledger'; }
|
||||||
|
pre.src-java:before { content: 'Java'; }
|
||||||
|
pre.src-js:before { content: 'Javascript'; }
|
||||||
|
pre.src-latex:before { content: 'LaTeX'; }
|
||||||
|
pre.src-ledger:before { content: 'Ledger'; }
|
||||||
|
pre.src-lisp:before { content: 'Lisp'; }
|
||||||
|
pre.src-lilypond:before { content: 'Lilypond'; }
|
||||||
|
pre.src-lua:before { content: 'Lua'; }
|
||||||
|
pre.src-matlab:before { content: 'MATLAB'; }
|
||||||
|
pre.src-mscgen:before { content: 'Mscgen'; }
|
||||||
|
pre.src-ocaml:before { content: 'Objective Caml'; }
|
||||||
|
pre.src-octave:before { content: 'Octave'; }
|
||||||
|
pre.src-org:before { content: 'Org mode'; }
|
||||||
|
pre.src-oz:before { content: 'OZ'; }
|
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|
pre.src-plantuml:before { content: 'Plantuml'; }
|
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|
pre.src-processing:before { content: 'Processing.js'; }
|
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|
pre.src-python:before { content: 'Python'; }
|
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|
pre.src-R:before { content: 'R'; }
|
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|
pre.src-ruby:before { content: 'Ruby'; }
|
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|
pre.src-sass:before { content: 'Sass'; }
|
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|
pre.src-scheme:before { content: 'Scheme'; }
|
||||||
|
pre.src-screen:before { content: 'Gnu Screen'; }
|
||||||
|
pre.src-sed:before { content: 'Sed'; }
|
||||||
|
pre.src-sh:before { content: 'shell'; }
|
||||||
|
pre.src-sql:before { content: 'SQL'; }
|
||||||
|
pre.src-sqlite:before { content: 'SQLite'; }
|
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|
/* additional languages in org.el's org-babel-load-languages alist */
|
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|
pre.src-forth:before { content: 'Forth'; }
|
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|
pre.src-io:before { content: 'IO'; }
|
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|
pre.src-J:before { content: 'J'; }
|
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|
pre.src-makefile:before { content: 'Makefile'; }
|
||||||
|
pre.src-maxima:before { content: 'Maxima'; }
|
||||||
|
pre.src-perl:before { content: 'Perl'; }
|
||||||
|
pre.src-picolisp:before { content: 'Pico Lisp'; }
|
||||||
|
pre.src-scala:before { content: 'Scala'; }
|
||||||
|
pre.src-shell:before { content: 'Shell Script'; }
|
||||||
|
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
|
||||||
|
/* additional language identifiers per "defun org-babel-execute"
|
||||||
|
in ob-*.el */
|
||||||
|
pre.src-cpp:before { content: 'C++'; }
|
||||||
|
pre.src-abc:before { content: 'ABC'; }
|
||||||
|
pre.src-coq:before { content: 'Coq'; }
|
||||||
|
pre.src-groovy:before { content: 'Groovy'; }
|
||||||
|
/* additional language identifiers from org-babel-shell-names in
|
||||||
|
ob-shell.el: ob-shell is the only babel language using a lambda to put
|
||||||
|
the execution function name together. */
|
||||||
|
pre.src-bash:before { content: 'bash'; }
|
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|
pre.src-csh:before { content: 'csh'; }
|
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|
pre.src-ash:before { content: 'ash'; }
|
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|
pre.src-dash:before { content: 'dash'; }
|
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|
pre.src-ksh:before { content: 'ksh'; }
|
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|
pre.src-mksh:before { content: 'mksh'; }
|
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|
pre.src-posh:before { content: 'posh'; }
|
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|
/* Additional Emacs modes also supported by the LaTeX listings package */
|
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|
pre.src-ada:before { content: 'Ada'; }
|
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|
pre.src-asm:before { content: 'Assembler'; }
|
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|
pre.src-caml:before { content: 'Caml'; }
|
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|
pre.src-delphi:before { content: 'Delphi'; }
|
||||||
|
pre.src-html:before { content: 'HTML'; }
|
||||||
|
pre.src-idl:before { content: 'IDL'; }
|
||||||
|
pre.src-mercury:before { content: 'Mercury'; }
|
||||||
|
pre.src-metapost:before { content: 'MetaPost'; }
|
||||||
|
pre.src-modula-2:before { content: 'Modula-2'; }
|
||||||
|
pre.src-pascal:before { content: 'Pascal'; }
|
||||||
|
pre.src-ps:before { content: 'PostScript'; }
|
||||||
|
pre.src-prolog:before { content: 'Prolog'; }
|
||||||
|
pre.src-simula:before { content: 'Simula'; }
|
||||||
|
pre.src-tcl:before { content: 'tcl'; }
|
||||||
|
pre.src-tex:before { content: 'TeX'; }
|
||||||
|
pre.src-plain-tex:before { content: 'Plain TeX'; }
|
||||||
|
pre.src-verilog:before { content: 'Verilog'; }
|
||||||
|
pre.src-vhdl:before { content: 'VHDL'; }
|
||||||
|
pre.src-xml:before { content: 'XML'; }
|
||||||
|
pre.src-nxml:before { content: 'XML'; }
|
||||||
|
/* add a generic configuration mode; LaTeX export needs an additional
|
||||||
|
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
|
||||||
|
pre.src-conf:before { content: 'Configuration File'; }
|
||||||
|
|
||||||
|
table { border-collapse:collapse; }
|
||||||
|
caption.t-above { caption-side: top; }
|
||||||
|
caption.t-bottom { caption-side: bottom; }
|
||||||
|
td, th { vertical-align:top; }
|
||||||
|
th.org-right { text-align: center; }
|
||||||
|
th.org-left { text-align: center; }
|
||||||
|
th.org-center { text-align: center; }
|
||||||
|
td.org-right { text-align: right; }
|
||||||
|
td.org-left { text-align: left; }
|
||||||
|
td.org-center { text-align: center; }
|
||||||
|
dt { font-weight: bold; }
|
||||||
|
.footpara { display: inline; }
|
||||||
|
.footdef { margin-bottom: 1em; }
|
||||||
|
.figure { padding: 1em; }
|
||||||
|
.figure p { text-align: center; }
|
||||||
|
.equation-container {
|
||||||
|
display: table;
|
||||||
|
text-align: center;
|
||||||
|
width: 100%;
|
||||||
|
}
|
||||||
|
.equation {
|
||||||
|
vertical-align: middle;
|
||||||
|
}
|
||||||
|
.equation-label {
|
||||||
|
display: table-cell;
|
||||||
|
text-align: right;
|
||||||
|
vertical-align: middle;
|
||||||
|
}
|
||||||
|
.inlinetask {
|
||||||
|
padding: 10px;
|
||||||
|
border: 2px solid gray;
|
||||||
|
margin: 10px;
|
||||||
|
background: #ffffcc;
|
||||||
|
}
|
||||||
|
#org-div-home-and-up
|
||||||
|
{ text-align: right; font-size: 70%; white-space: nowrap; }
|
||||||
|
textarea { overflow-x: auto; }
|
||||||
|
.linenr { font-size: smaller }
|
||||||
|
.code-highlighted { background-color: #ffff00; }
|
||||||
|
.org-info-js_info-navigation { border-style: none; }
|
||||||
|
#org-info-js_console-label
|
||||||
|
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
|
||||||
|
.org-info-js_search-highlight
|
||||||
|
{ background-color: #ffff00; color: #000000; font-weight: bold; }
|
||||||
|
.org-svg { width: 90%; }
|
||||||
|
/*]]>*/-->
|
||||||
|
</style>
|
||||||
|
<script type="text/javascript">
|
||||||
|
/*
|
||||||
|
@licstart The following is the entire license notice for the
|
||||||
|
JavaScript code in this tag.
|
||||||
|
|
||||||
|
Copyright (C) 2012-2019 Free Software Foundation, Inc.
|
||||||
|
|
||||||
|
The JavaScript code in this tag is free software: you can
|
||||||
|
redistribute it and/or modify it under the terms of the GNU
|
||||||
|
General Public License (GNU GPL) as published by the Free Software
|
||||||
|
Foundation, either version 3 of the License, or (at your option)
|
||||||
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
||||||
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||||
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
||||||
|
|
||||||
|
As additional permission under GNU GPL version 3 section 7, you
|
||||||
|
may distribute non-source (e.g., minimized or compacted) forms of
|
||||||
|
that code without the copy of the GNU GPL normally required by
|
||||||
|
section 4, provided you include this license notice and a URL
|
||||||
|
through which recipients can access the Corresponding Source.
|
||||||
|
|
||||||
|
|
||||||
|
@licend The above is the entire license notice
|
||||||
|
for the JavaScript code in this tag.
|
||||||
|
*/
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
function CodeHighlightOn(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(null != target) {
|
||||||
|
elem.cacheClassElem = elem.className;
|
||||||
|
elem.cacheClassTarget = target.className;
|
||||||
|
target.className = "code-highlighted";
|
||||||
|
elem.className = "code-highlighted";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
function CodeHighlightOff(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(elem.cacheClassElem)
|
||||||
|
elem.className = elem.cacheClassElem;
|
||||||
|
if(elem.cacheClassTarget)
|
||||||
|
target.className = elem.cacheClassTarget;
|
||||||
|
}
|
||||||
|
/*]]>*///-->
|
||||||
|
</script>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="content">
|
||||||
|
<h1 class="title">Kinematic Study of the Stewart Platform</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orgc1c40d5">1. Functions</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org3d6cf9e">1.1. getMaxPositions</a></li>
|
||||||
|
<li><a href="#orge3ee3ac">1.2. getMaxPureDisplacement</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgc1c40d5" class="outline-2">
|
||||||
|
<h2 id="orgc1c40d5"><span class="section-number-2">1</span> Functions</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org3d6cf9e" class="outline-3">
|
||||||
|
<h3 id="org3d6cf9e"><span class="section-number-3">1.1</span> getMaxPositions</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">X, Y, Z</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">getMaxPositions</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
Leg = stewart.Leg;
|
||||||
|
J = stewart.J;
|
||||||
|
theta = linspace<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span>, <span style="color: #BFEBBF;">100</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
phi = linspace<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span> , <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">100</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
dmax = zeros<span style="color: #DCDCCC;">(</span>length<span style="color: #BFEBBF;">(</span>theta<span style="color: #BFEBBF;">)</span>, length<span style="color: #BFEBBF;">(</span>phi<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:length</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">theta</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">j</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:length</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">phi</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
L = J<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span>cos<span style="color: #BFEBBF;">(</span>phi<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">j</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span>theta<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span> cos<span style="color: #BFEBBF;">(</span>phi<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">j</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span>theta<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span> sin<span style="color: #BFEBBF;">(</span>phi<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">j</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">]</span>';
|
||||||
|
dmax<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">j</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>L<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
|
||||||
|
X = dmax<span style="color: #7CB8BB;">.*</span>cos<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>phi,length<span style="color: #D0BF8F;">(</span>theta<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">.*</span>cos<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>theta,length<span style="color: #D0BF8F;">(</span>phi<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>';
|
||||||
|
Y = dmax<span style="color: #7CB8BB;">.*</span>cos<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>phi,length<span style="color: #D0BF8F;">(</span>theta<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">.*</span>sin<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>theta,length<span style="color: #D0BF8F;">(</span>phi<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>';
|
||||||
|
Z = dmax<span style="color: #7CB8BB;">.*</span>sin<span style="color: #DCDCCC;">(</span>repmat<span style="color: #BFEBBF;">(</span>phi,length<span style="color: #D0BF8F;">(</span>theta<span style="color: #D0BF8F;">)</span>,<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orge3ee3ac" class="outline-3">
|
||||||
|
<h3 id="orge3ee3ac"><span class="section-number-3">1.2</span> getMaxPureDisplacement</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">max_disp</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">getMaxPureDisplacement</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">Leg</span>, <span style="color: #DFAF8F;">J</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
max_disp = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
max_disp<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = Leg.stroke<span style="color: #7CB8BB;">/</span>max<span style="color: #DCDCCC;">(</span>abs<span style="color: #BFEBBF;">(</span>J<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">]</span>'<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Thomas Dehaeze</p>
|
||||||
|
<p class="date">Created: 2019-03-22 ven. 12:03</p>
|
||||||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
49
kinematic-study.org
Normal file
49
kinematic-study.org
Normal file
@ -0,0 +1,49 @@
|
|||||||
|
#+TITLE: Kinematic Study of the Stewart Platform
|
||||||
|
|
||||||
|
* Functions
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :exports code
|
||||||
|
:HEADER-ARGS:matlab+: :comments no
|
||||||
|
:HEADER-ARGS:matlab+: :mkdir yes
|
||||||
|
:HEADER-ARGS:matlab+: :eval no
|
||||||
|
:END:
|
||||||
|
** getMaxPositions
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :tangle src/getMaxPositions.m
|
||||||
|
:END:
|
||||||
|
#+begin_src matlab
|
||||||
|
function [X, Y, Z] = getMaxPositions(stewart)
|
||||||
|
Leg = stewart.Leg;
|
||||||
|
J = stewart.J;
|
||||||
|
theta = linspace(0, 2*pi, 100);
|
||||||
|
phi = linspace(-pi/2 , pi/2, 100);
|
||||||
|
dmax = zeros(length(theta), length(phi));
|
||||||
|
|
||||||
|
for i = 1:length(theta)
|
||||||
|
for j = 1:length(phi)
|
||||||
|
L = J*[cos(phi(j))*cos(theta(i)) cos(phi(j))*sin(theta(i)) sin(phi(j)) 0 0 0]';
|
||||||
|
dmax(i, j) = Leg.stroke/max(abs(L));
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
X = dmax.*cos(repmat(phi,length(theta),1)).*cos(repmat(theta,length(phi),1))';
|
||||||
|
Y = dmax.*cos(repmat(phi,length(theta),1)).*sin(repmat(theta,length(phi),1))';
|
||||||
|
Z = dmax.*sin(repmat(phi,length(theta),1));
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** getMaxPureDisplacement
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :tangle src/getMaxPureDisplacement.m
|
||||||
|
:END:
|
||||||
|
#+begin_src matlab
|
||||||
|
function [max_disp] = getMaxPureDisplacement(Leg, J)
|
||||||
|
max_disp = zeros(6, 1);
|
||||||
|
max_disp(1) = Leg.stroke/max(abs(J*[1 0 0 0 0 0]'));
|
||||||
|
max_disp(2) = Leg.stroke/max(abs(J*[0 1 0 0 0 0]'));
|
||||||
|
max_disp(3) = Leg.stroke/max(abs(J*[0 0 1 0 0 0]'));
|
||||||
|
max_disp(4) = Leg.stroke/max(abs(J*[0 0 0 1 0 0]'));
|
||||||
|
max_disp(5) = Leg.stroke/max(abs(J*[0 0 0 0 1 0]'));
|
||||||
|
max_disp(6) = Leg.stroke/max(abs(J*[0 0 0 0 0 1]'));
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
BIN
mat/G_iff.mat
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mat/K_iff.mat
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855
simscape-model.html
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855
simscape-model.html
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@ -0,0 +1,855 @@
|
|||||||
|
<?xml version="1.0" encoding="utf-8"?>
|
||||||
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||||
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
|
<head>
|
||||||
|
<!-- 2019-03-22 ven. 12:03 -->
|
||||||
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||||
|
<title>Stewart Platform - Simscape Model</title>
|
||||||
|
<meta name="generator" content="Org mode" />
|
||||||
|
<meta name="author" content="Thomas Dehaeze" />
|
||||||
|
<style type="text/css">
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
.title { text-align: center;
|
||||||
|
margin-bottom: .2em; }
|
||||||
|
.subtitle { text-align: center;
|
||||||
|
font-size: medium;
|
||||||
|
font-weight: bold;
|
||||||
|
margin-top:0; }
|
||||||
|
.todo { font-family: monospace; color: red; }
|
||||||
|
.done { font-family: monospace; color: green; }
|
||||||
|
.priority { font-family: monospace; color: orange; }
|
||||||
|
.tag { background-color: #eee; font-family: monospace;
|
||||||
|
padding: 2px; font-size: 80%; font-weight: normal; }
|
||||||
|
.timestamp { color: #bebebe; }
|
||||||
|
.timestamp-kwd { color: #5f9ea0; }
|
||||||
|
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
||||||
|
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
|
||||||
|
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
|
||||||
|
.underline { text-decoration: underline; }
|
||||||
|
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
|
||||||
|
p.verse { margin-left: 3%; }
|
||||||
|
pre {
|
||||||
|
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|
||||||
|
box-shadow: 3px 3px 3px #eee;
|
||||||
|
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|
||||||
|
font-family: monospace;
|
||||||
|
overflow: auto;
|
||||||
|
margin: 1.2em;
|
||||||
|
}
|
||||||
|
pre.src {
|
||||||
|
position: relative;
|
||||||
|
overflow: visible;
|
||||||
|
padding-top: 1.2em;
|
||||||
|
}
|
||||||
|
pre.src:before {
|
||||||
|
display: none;
|
||||||
|
position: absolute;
|
||||||
|
background-color: white;
|
||||||
|
top: -10px;
|
||||||
|
right: 10px;
|
||||||
|
padding: 3px;
|
||||||
|
border: 1px solid black;
|
||||||
|
}
|
||||||
|
pre.src:hover:before { display: inline;}
|
||||||
|
/* Languages per Org manual */
|
||||||
|
pre.src-asymptote:before { content: 'Asymptote'; }
|
||||||
|
pre.src-awk:before { content: 'Awk'; }
|
||||||
|
pre.src-C:before { content: 'C'; }
|
||||||
|
/* pre.src-C++ doesn't work in CSS */
|
||||||
|
pre.src-clojure:before { content: 'Clojure'; }
|
||||||
|
pre.src-css:before { content: 'CSS'; }
|
||||||
|
pre.src-D:before { content: 'D'; }
|
||||||
|
pre.src-ditaa:before { content: 'ditaa'; }
|
||||||
|
pre.src-dot:before { content: 'Graphviz'; }
|
||||||
|
pre.src-calc:before { content: 'Emacs Calc'; }
|
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</head>
|
||||||
|
<body>
|
||||||
|
<div id="content">
|
||||||
|
<h1 class="title">Stewart Platform - Simscape Model</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org9a10766">1. Function description and arguments</a></li>
|
||||||
|
<li><a href="#orgb6911a1">2. Initialization of the stewart structure</a></li>
|
||||||
|
<li><a href="#org030aed6">3. Bottom Plate</a></li>
|
||||||
|
<li><a href="#orged8012a">4. Top Plate</a></li>
|
||||||
|
<li><a href="#orgc74617a">5. Legs</a></li>
|
||||||
|
<li><a href="#org7cd2aa5">6. Ball Joints</a></li>
|
||||||
|
<li><a href="#org1d76ed9">7. More parameters are initialized</a></li>
|
||||||
|
<li><a href="#orge9faa26">8. Save the Stewart Structure</a></li>
|
||||||
|
<li><a href="#orga207d03">9. initializeParameters Function</a></li>
|
||||||
|
<li><a href="#org724c1a1">10. initializeSample</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
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|
||||||
|
|
||||||
|
<div id="outline-container-org9a10766" class="outline-2">
|
||||||
|
<h2 id="org9a10766"><span class="section-number-2">1</span> Function description and arguments</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<p>
|
||||||
|
The <code>initializeHexapod</code> function takes one structure that contains configurations for the hexapod and returns one structure representing the hexapod.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">initializeHexapod</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Default values for opts.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">opts = struct<span style="color: #DCDCCC;">(</span><span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'height'</span>, <span style="color: #BFEBBF;">90</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Height of the platform [mm]</span>
|
||||||
|
<span style="color: #CC9393;">'density'</span>, <span style="color: #BFEBBF;">8000</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Density of the material used for the hexapod [kg/m3]</span>
|
||||||
|
<span style="color: #CC9393;">'k_ax'</span>, <span style="color: #BFEBBF;">1e8</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Stiffness of each actuator [N/m]</span>
|
||||||
|
<span style="color: #CC9393;">'c_ax'</span>, <span style="color: #BFEBBF;">1000</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Damping of each actuator [N/(m/s)]</span>
|
||||||
|
<span style="color: #CC9393;">'stroke'</span>, <span style="color: #BFEBBF;">50e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Maximum stroke of each actuator [m]</span>
|
||||||
|
<span style="color: #CC9393;">'name', 'stewart'</span> <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% Name of the file</span>
|
||||||
|
<span style="color: #DCDCCC;">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Populate opts with input parameters
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
||||||
|
opts.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb6911a1" class="outline-2">
|
||||||
|
<h2 id="orgb6911a1"><span class="section-number-2">2</span> Initialization of the stewart structure</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<p>
|
||||||
|
We initialize the Stewart structure
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart = struct<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And we defined its total height.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.H = opts.height; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org030aed6" class="outline-2">
|
||||||
|
<h2 id="org030aed6"><span class="section-number-2">3</span> Bottom Plate</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
|
||||||
|
<div id="org3d7fe71" class="figure">
|
||||||
|
<p><img src="./figs/stewart_bottom_plate.png" alt="stewart_bottom_plate.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 1: </span>Schematic of the bottom plates with all the parameters</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The bottom plate structure is initialized.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP = struct<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We defined its internal radius (if there is a hole in the bottom plate) and its outer radius.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP.Rint = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% Internal Radius [mm]</span>
|
||||||
|
BP.Rext = <span style="color: #BFEBBF;">150</span>; <span style="color: #7F9F7F;">% External Radius [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We define its thickness.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP.H = <span style="color: #BFEBBF;">10</span>; <span style="color: #7F9F7F;">% Thickness of the Bottom Plate [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
At which radius legs will be fixed and with that angle offset.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP.Rleg = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">% Radius where the legs articulations are positionned [mm]</span>
|
||||||
|
BP.alpha = <span style="color: #BFEBBF;">10</span>; <span style="color: #7F9F7F;">% Angle Offset [deg]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We defined the density of the material of the bottom plate.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP.density = opts.density; <span style="color: #7F9F7F;">% Density of the material [kg/m3]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And its color.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% Color [RGB]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Then the profile of the bottom plate is computed and will be used by Simscape
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">BP.shape = <span style="color: #DCDCCC;">[</span>BP.Rint BP.H; BP.Rint <span style="color: #BFEBBF;">0</span>; BP.Rext <span style="color: #BFEBBF;">0</span>; BP.Rext BP.H<span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The structure is added to the stewart structure
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.BP = BP;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orged8012a" class="outline-2">
|
||||||
|
<h2 id="orged8012a"><span class="section-number-2">4</span> Top Plate</h2>
|
||||||
|
<div class="outline-text-2" id="text-4">
|
||||||
|
<p>
|
||||||
|
The top plate structure is initialized.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP = struct<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We defined the internal and external radius of the top plate.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP.Rint = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
TP.Rext = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The thickness of the top plate.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP.H = <span style="color: #BFEBBF;">10</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
At which radius and angle are fixed the legs.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP.Rleg = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">% Radius where the legs articulations are positionned [mm]</span>
|
||||||
|
TP.alpha = <span style="color: #BFEBBF;">20</span>; <span style="color: #7F9F7F;">% Angle [deg]</span>
|
||||||
|
TP.dalpha = <span style="color: #BFEBBF;">0</span>; % Angle Offset from <span style="color: #BFEBBF;">0</span> position [deg]
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The density of its material.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP.density = opts.density; <span style="color: #7F9F7F;">% Density of the material [kg/m3]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Its color.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% Color [RGB]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Then the shape of the top plate is computed
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">TP.shape = <span style="color: #DCDCCC;">[</span>TP.Rint TP.H; TP.Rint <span style="color: #BFEBBF;">0</span>; TP.Rext <span style="color: #BFEBBF;">0</span>; TP.Rext TP.H<span style="color: #DCDCCC;">]</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The structure is added to the stewart structure
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.TP = TP;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgc74617a" class="outline-2">
|
||||||
|
<h2 id="orgc74617a"><span class="section-number-2">5</span> Legs</h2>
|
||||||
|
<div class="outline-text-2" id="text-5">
|
||||||
|
|
||||||
|
<div id="orgc225133" class="figure">
|
||||||
|
<p><img src="./figs/stewart_legs.png" alt="stewart_legs.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 2: </span>Schematic for the legs of the Stewart platform</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The leg structure is initialized.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg = struct<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The maximum Stroke of each leg is defined.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg.stroke = opts.stroke; <span style="color: #7F9F7F;">% [m]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The stiffness and damping of each leg are defined
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg.k_ax = opts.k_ax; <span style="color: #7F9F7F;">% Stiffness of each leg [N/m]</span>
|
||||||
|
Leg.c_ax = opts.c_ax; <span style="color: #7F9F7F;">% Damping of each leg [N/(m/s)]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The radius of the legs are defined
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg.Rtop = <span style="color: #BFEBBF;">10</span>; <span style="color: #7F9F7F;">% Radius of the cylinder of the top part of the leg[mm]</span>
|
||||||
|
Leg.Rbot = <span style="color: #BFEBBF;">12</span>; <span style="color: #7F9F7F;">% Radius of the cylinder of the bottom part of the leg [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The density of its material.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg.density = opts.density; <span style="color: #7F9F7F;">% Density of the material used for the legs [kg/m3]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Its color.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">5</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">5</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% Color of the top part of the leg [RGB]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The radius of spheres representing the ball joints are defined.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Leg.R = <span style="color: #BFEBBF;">1</span>.<span style="color: #BFEBBF;">3</span><span style="color: #7CB8BB;">*</span>Leg.Rbot; <span style="color: #7F9F7F;">% Size of the sphere at the extremity of the leg [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The structure is added to the stewart structure
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.Leg = Leg;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org7cd2aa5" class="outline-2">
|
||||||
|
<h2 id="org7cd2aa5"><span class="section-number-2">6</span> Ball Joints</h2>
|
||||||
|
<div class="outline-text-2" id="text-6">
|
||||||
|
|
||||||
|
<div id="org7b92b11" class="figure">
|
||||||
|
<p><img src="./figs/stewart_ball_joints.png" alt="stewart_ball_joints.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 3: </span>Schematic of the support for the ball joints</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
<code>SP</code> is the structure representing the support for the ball joints at the extremity of each leg.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The <code>SP</code> structure is initialized.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP = struct<span style="color: #DCDCCC;">()</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We can define its rotational stiffness and damping. For now, we use perfect joints.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP.k = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% [N*m/deg]</span>
|
||||||
|
SP.c = <span style="color: #BFEBBF;">0</span>; <span style="color: #7F9F7F;">% [N*m/deg]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Its height is defined
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP.H = <span style="color: #BFEBBF;">15</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Its radius is based on the radius on the sphere at the end of the legs.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP.R = Leg.R; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP.section = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> SP.H<span style="color: #7CB8BB;">-</span>SP.R;
|
||||||
|
<span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span>;
|
||||||
|
SP.R <span style="color: #BFEBBF;">0</span>;
|
||||||
|
SP.R SP.H<span style="color: #DCDCCC;">]</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The density of its material is defined.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP.density = opts.density; % [kg<span style="color: #7CB8BB;">/</span>m<span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">3</span>]
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Its color is defined.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">SP.color = <span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">]</span>; <span style="color: #7F9F7F;">% [RGB]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The structure is added to the Hexapod structure
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.SP = SP;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org1d76ed9" class="outline-2">
|
||||||
|
<h2 id="org1d76ed9"><span class="section-number-2">7</span> More parameters are initialized</h2>
|
||||||
|
<div class="outline-text-2" id="text-7">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart = initializeParameters<span style="color: #DCDCCC;">(</span>stewart<span style="color: #DCDCCC;">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orge9faa26" class="outline-2">
|
||||||
|
<h2 id="orge9faa26"><span class="section-number-2">8</span> Save the Stewart Structure</h2>
|
||||||
|
<div class="outline-text-2" id="text-8">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">save<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/stewart.mat', 'stewart'</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orga207d03" class="outline-2">
|
||||||
|
<h2 id="orga207d03"><span class="section-number-2">9</span> initializeParameters Function</h2>
|
||||||
|
<div class="outline-text-2" id="text-9">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">initializeParameters</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">stewart</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We first compute \([a_1, a_2, a_3, a_4, a_5, a_6]^T\) and \([b_1, b_2, b_3, b_4, b_5, b_6]^T\).
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.Aa = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
stewart.Ab = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
stewart.Bb = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">3</span>
|
||||||
|
stewart.Aa<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>stewart.BP.Rleg<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">-</span> stewart.BP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.BP.Rleg<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">-</span> stewart.BP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.BP.H<span style="color: #7CB8BB;">+</span>stewart.SP.H<span style="color: #DCDCCC;">]</span>;
|
||||||
|
stewart.Aa<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>stewart.BP.Rleg<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> stewart.BP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.BP.Rleg<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> stewart.BP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.BP.H<span style="color: #7CB8BB;">+</span>stewart.SP.H<span style="color: #DCDCCC;">]</span>;
|
||||||
|
|
||||||
|
stewart.Ab<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>stewart.TP.Rleg<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> stewart.TP.dalpha <span style="color: #7CB8BB;">-</span> stewart.TP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.TP.Rleg<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> stewart.TP.dalpha <span style="color: #7CB8BB;">-</span> stewart.TP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.H <span style="color: #7CB8BB;">-</span> stewart.TP.H <span style="color: #7CB8BB;">-</span> stewart.SP.H<span style="color: #DCDCCC;">]</span>;
|
||||||
|
stewart.Ab<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = <span style="color: #DCDCCC;">[</span>stewart.TP.Rleg<span style="color: #7CB8BB;">*</span>cos<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> stewart.TP.dalpha <span style="color: #7CB8BB;">+</span> stewart.TP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.TP.Rleg<span style="color: #7CB8BB;">*</span>sin<span style="color: #BFEBBF;">(</span> <span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">180</span><span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">120</span><span style="color: #7CB8BB;">*</span><span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">+</span> stewart.TP.dalpha <span style="color: #7CB8BB;">+</span> stewart.TP.alpha<span style="color: #D0BF8F;">)</span> <span style="color: #BFEBBF;">)</span>, <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.H <span style="color: #7CB8BB;">-</span> stewart.TP.H <span style="color: #7CB8BB;">-</span> stewart.SP.H<span style="color: #DCDCCC;">]</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
stewart.Bb = stewart.Ab <span style="color: #7CB8BB;">-</span> stewart.H<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span>,<span style="color: #BFEBBF;">0</span>,<span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Now, we compute the leg vectors \(\hat{s}_i\) and leg position \(l_i\):
|
||||||
|
\[ b_i - a_i = l_i \hat{s}_i \]
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We initialize \(l_i\) and \(\hat{s}_i\)
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">leg_length = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% [mm]</span>
|
||||||
|
leg_vectors = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We compute \(b_i - a_i\), and then:
|
||||||
|
</p>
|
||||||
|
\begin{align*}
|
||||||
|
l_i &= \left|b_i - a_i\right| \\
|
||||||
|
\hat{s}_i &= \frac{b_i - a_i}{l_i}
|
||||||
|
\end{align*}
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">legs = stewart.Ab <span style="color: #7CB8BB;">-</span> stewart.Aa;
|
||||||
|
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
||||||
|
leg_length<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span> = norm<span style="color: #DCDCCC;">(</span>legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> = legs<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span> <span style="color: #7CB8BB;">/</span> leg_length<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Then the shape of the bottom leg is estimated
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.Leg.lenght = leg_length<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">1</span>.<span style="color: #BFEBBF;">5</span>;
|
||||||
|
stewart.Leg.shape.bot = <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span>; <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.Leg.Rbot <span style="color: #BFEBBF;">0</span>; <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.Leg.Rbot stewart.Leg.lenght; <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.Leg.Rtop stewart.Leg.lenght; <span style="text-decoration: underline;">...</span>
|
||||||
|
stewart.Leg.Rtop <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>stewart.Leg.lenght; <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>stewart.Leg.lenght<span style="color: #DCDCCC;">]</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We compute rotation matrices to have the orientation of the legs.
|
||||||
|
The rotation matrix transforms the \(z\) axis to the axis of the leg. The other axis are not important here.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.Rm = struct<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'R'</span>, eye<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
||||||
|
sx = cross<span style="color: #DCDCCC;">(</span>leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span> <span style="color: #BFEBBF;">0</span><span style="color: #BFEBBF;">]</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sx = sx<span style="color: #7CB8BB;">/</span>norm<span style="color: #DCDCCC;">(</span>sx<span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
sy = <span style="color: #7CB8BB;">-</span>cross<span style="color: #DCDCCC;">(</span>sx, leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sy = sy<span style="color: #7CB8BB;">/</span>norm<span style="color: #DCDCCC;">(</span>sy<span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
sz = leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>,<span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
sz = sz<span style="color: #7CB8BB;">/</span>norm<span style="color: #DCDCCC;">(</span>sz<span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
stewart.Rm<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span>.R = <span style="color: #DCDCCC;">[</span>sx', sy', sz'<span style="color: #DCDCCC;">]</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Compute Jacobian Matrix
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">J = zeros<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span> = <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:</span><span style="color: #BFEBBF;">6</span>
|
||||||
|
J<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = leg_vectors<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
J<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">4</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = cross<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">001</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">(</span>stewart.Ab<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">-</span> stewart.H<span style="color: #7CB8BB;">*</span><span style="color: #D0BF8F;">[</span><span style="color: #BFEBBF;">0</span>,<span style="color: #BFEBBF;">0</span>,<span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">]</span><span style="color: #BFEBBF;">)</span>, leg_vectors<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">i</span>, <span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
|
||||||
|
stewart.J = J;
|
||||||
|
stewart.Jinv = inv<span style="color: #DCDCCC;">(</span>J<span style="color: #DCDCCC;">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">stewart.K = stewart.Leg.k_ax<span style="color: #7CB8BB;">*</span>stewart.J'<span style="color: #7CB8BB;">*</span>stewart.J;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"> <span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org724c1a1" class="outline-2">
|
||||||
|
<h2 id="org724c1a1"><span class="section-number-2">10</span> initializeSample</h2>
|
||||||
|
<div class="outline-text-2" id="text-10">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[]</span> = <span style="color: #93E0E3;">initializeSample</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Default values for opts</span>
|
||||||
|
sample = struct<span style="color: #DCDCCC;">(</span> <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #CC9393;">'radius'</span>, <span style="color: #BFEBBF;">100</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% radius of the cylinder [mm]</span>
|
||||||
|
<span style="color: #CC9393;">'height'</span>, <span style="color: #BFEBBF;">100</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% height of the cylinder [mm]</span>
|
||||||
|
<span style="color: #CC9393;">'mass'</span>, <span style="color: #BFEBBF;">10</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% mass of the cylinder [kg]</span>
|
||||||
|
<span style="color: #CC9393;">'measheight'</span>, <span style="color: #BFEBBF;">50</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% measurement point z-offset [mm]</span>
|
||||||
|
<span style="color: #CC9393;">'offset'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">0</span><span style="color: #BFEBBF;">]</span>, <span style="text-decoration: underline;">...</span> <span style="color: #7F9F7F;">% offset position of the sample [mm]</span>
|
||||||
|
<span style="color: #CC9393;">'color'</span>, <span style="color: #BFEBBF;">[</span><span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">9</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">1</span> <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">]</span> <span style="text-decoration: underline;">...</span>
|
||||||
|
<span style="color: #DCDCCC;">)</span>;
|
||||||
|
|
||||||
|
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Populate opts with input parameters</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
|
||||||
|
sample.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
|
||||||
|
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Save</span>
|
||||||
|
save<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/sample.mat', 'sample'</span><span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Thomas Dehaeze</p>
|
||||||
|
<p class="date">Created: 2019-03-22 ven. 12:03</p>
|
||||||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
503
simscape-model.org
Normal file
503
simscape-model.org
Normal file
@ -0,0 +1,503 @@
|
|||||||
|
#+TITLE: Stewart Platform - Simscape Model
|
||||||
|
:DRAWER:
|
||||||
|
#+STARTUP: overview
|
||||||
|
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
|
||||||
|
#+HTML_HEAD: <script src="js/jquery.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script src="js/bootstrap.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="js/jquery.stickytableheaders.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="js/readtheorg.js"></script>
|
||||||
|
|
||||||
|
#+LATEX_CLASS: cleanreport
|
||||||
|
#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
|
||||||
|
#+LaTeX_HEADER: \usepackage{svg}
|
||||||
|
#+LaTeX_HEADER: \newcommand{\authorFirstName}{Thomas}
|
||||||
|
#+LaTeX_HEADER: \newcommand{\authorLastName}{Dehaeze}
|
||||||
|
#+LaTeX_HEADER: \newcommand{\authorEmail}{dehaeze.thomas@gmail.com}
|
||||||
|
|
||||||
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||||
|
#+PROPERTY: header-args:matlab+ :comments no
|
||||||
|
#+PROPERTY: header-args:matlab+ :exports bode
|
||||||
|
#+PROPERTY: header-args:matlab+ :eval no
|
||||||
|
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||||
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||||||
|
#+PROPERTY: header-args:matlab+ :tangle src/initializeHexapod.m
|
||||||
|
:END:
|
||||||
|
|
||||||
|
* Function description and arguments
|
||||||
|
The =initializeHexapod= function takes one structure that contains configurations for the hexapod and returns one structure representing the hexapod.
|
||||||
|
#+begin_src matlab
|
||||||
|
function [stewart] = initializeHexapod(opts_param)
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Default values for opts.
|
||||||
|
#+begin_src matlab
|
||||||
|
opts = struct(...
|
||||||
|
'height', 90, ... % Height of the platform [mm]
|
||||||
|
'density', 8000, ... % Density of the material used for the hexapod [kg/m3]
|
||||||
|
'k_ax', 1e8, ... % Stiffness of each actuator [N/m]
|
||||||
|
'c_ax', 1000, ... % Damping of each actuator [N/(m/s)]
|
||||||
|
'stroke', 50e-6, ... % Maximum stroke of each actuator [m]
|
||||||
|
'name', 'stewart' ... % Name of the file
|
||||||
|
);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Populate opts with input parameters
|
||||||
|
#+begin_src matlab
|
||||||
|
if exist('opts_param','var')
|
||||||
|
for opt = fieldnames(opts_param)'
|
||||||
|
opts.(opt{1}) = opts_param.(opt{1});
|
||||||
|
end
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Initialization of the stewart structure
|
||||||
|
We initialize the Stewart structure
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart = struct();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
And we defined its total height.
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.H = opts.height; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Bottom Plate
|
||||||
|
#+name: fig:stewart_bottom_plate
|
||||||
|
#+caption: Schematic of the bottom plates with all the parameters
|
||||||
|
[[file:./figs/stewart_bottom_plate.png]]
|
||||||
|
|
||||||
|
|
||||||
|
The bottom plate structure is initialized.
|
||||||
|
#+begin_src matlab
|
||||||
|
BP = struct();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We defined its internal radius (if there is a hole in the bottom plate) and its outer radius.
|
||||||
|
#+begin_src matlab
|
||||||
|
BP.Rint = 0; % Internal Radius [mm]
|
||||||
|
BP.Rext = 150; % External Radius [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We define its thickness.
|
||||||
|
#+begin_src matlab
|
||||||
|
BP.H = 10; % Thickness of the Bottom Plate [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
At which radius legs will be fixed and with that angle offset.
|
||||||
|
#+begin_src matlab
|
||||||
|
BP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
||||||
|
BP.alpha = 10; % Angle Offset [deg]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We defined the density of the material of the bottom plate.
|
||||||
|
#+begin_src matlab
|
||||||
|
BP.density = opts.density; % Density of the material [kg/m3]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
And its color.
|
||||||
|
#+begin_src matlab
|
||||||
|
BP.color = [0.7 0.7 0.7]; % Color [RGB]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Then the profile of the bottom plate is computed and will be used by Simscape
|
||||||
|
#+begin_src matlab
|
||||||
|
BP.shape = [BP.Rint BP.H; BP.Rint 0; BP.Rext 0; BP.Rext BP.H]; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The structure is added to the stewart structure
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.BP = BP;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Top Plate
|
||||||
|
The top plate structure is initialized.
|
||||||
|
#+begin_src matlab
|
||||||
|
TP = struct();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We defined the internal and external radius of the top plate.
|
||||||
|
#+begin_src matlab
|
||||||
|
TP.Rint = 0; % [mm]
|
||||||
|
TP.Rext = 100; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The thickness of the top plate.
|
||||||
|
#+begin_src matlab
|
||||||
|
TP.H = 10; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
At which radius and angle are fixed the legs.
|
||||||
|
#+begin_src matlab
|
||||||
|
TP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
||||||
|
TP.alpha = 20; % Angle [deg]
|
||||||
|
TP.dalpha = 0; % Angle Offset from 0 position [deg]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The density of its material.
|
||||||
|
#+begin_src matlab
|
||||||
|
TP.density = opts.density; % Density of the material [kg/m3]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Its color.
|
||||||
|
#+begin_src matlab
|
||||||
|
TP.color = [0.7 0.7 0.7]; % Color [RGB]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Then the shape of the top plate is computed
|
||||||
|
#+begin_src matlab
|
||||||
|
TP.shape = [TP.Rint TP.H; TP.Rint 0; TP.Rext 0; TP.Rext TP.H];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The structure is added to the stewart structure
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.TP = TP;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Legs
|
||||||
|
#+name: fig:stewart_legs
|
||||||
|
#+caption: Schematic for the legs of the Stewart platform
|
||||||
|
[[file:./figs/stewart_legs.png]]
|
||||||
|
|
||||||
|
|
||||||
|
The leg structure is initialized.
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg = struct();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The maximum Stroke of each leg is defined.
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg.stroke = opts.stroke; % [m]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The stiffness and damping of each leg are defined
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg.k_ax = opts.k_ax; % Stiffness of each leg [N/m]
|
||||||
|
Leg.c_ax = opts.c_ax; % Damping of each leg [N/(m/s)]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The radius of the legs are defined
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg.Rtop = 10; % Radius of the cylinder of the top part of the leg[mm]
|
||||||
|
Leg.Rbot = 12; % Radius of the cylinder of the bottom part of the leg [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The density of its material.
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg.density = opts.density; % Density of the material used for the legs [kg/m3]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Its color.
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg.color = [0.5 0.5 0.5]; % Color of the top part of the leg [RGB]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The radius of spheres representing the ball joints are defined.
|
||||||
|
#+begin_src matlab
|
||||||
|
Leg.R = 1.3*Leg.Rbot; % Size of the sphere at the extremity of the leg [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The structure is added to the stewart structure
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.Leg = Leg;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Ball Joints
|
||||||
|
#+name: fig:stewart_ball_joints
|
||||||
|
#+caption: Schematic of the support for the ball joints
|
||||||
|
[[file:./figs/stewart_ball_joints.png]]
|
||||||
|
|
||||||
|
=SP= is the structure representing the support for the ball joints at the extremity of each leg.
|
||||||
|
|
||||||
|
The =SP= structure is initialized.
|
||||||
|
#+begin_src matlab
|
||||||
|
SP = struct();
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We can define its rotational stiffness and damping. For now, we use perfect joints.
|
||||||
|
#+begin_src matlab
|
||||||
|
SP.k = 0; % [N*m/deg]
|
||||||
|
SP.c = 0; % [N*m/deg]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Its height is defined
|
||||||
|
#+begin_src matlab
|
||||||
|
SP.H = 15; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Its radius is based on the radius on the sphere at the end of the legs.
|
||||||
|
#+begin_src matlab
|
||||||
|
SP.R = Leg.R; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
SP.section = [0 SP.H-SP.R;
|
||||||
|
0 0;
|
||||||
|
SP.R 0;
|
||||||
|
SP.R SP.H];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The density of its material is defined.
|
||||||
|
#+begin_src matlab
|
||||||
|
SP.density = opts.density; % [kg/m^3]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Its color is defined.
|
||||||
|
#+begin_src matlab
|
||||||
|
SP.color = [0.7 0.7 0.7]; % [RGB]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
The structure is added to the Hexapod structure
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.SP = SP;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* More parameters are initialized
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart = initializeParameters(stewart);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* Save the Stewart Structure
|
||||||
|
#+begin_src matlab
|
||||||
|
save('./mat/stewart.mat', 'stewart')
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* initializeParameters Function :noexport:
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :tangle no
|
||||||
|
:END:
|
||||||
|
#+begin_src matlab
|
||||||
|
function [stewart] = initializeParameters(stewart)
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Computation of the position of the connection points on the base and moving platform
|
||||||
|
We first initialize =pos_base= corresponding to $[a_1, a_2, a_3, a_4, a_5, a_6]^T$ and =pos_top= corresponding to $[b_1, b_2, b_3, b_4, b_5, b_6]^T$.
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.pos_base = zeros(6, 3);
|
||||||
|
stewart.pos_top = zeros(6, 3);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We estimate the height between the ball joints of the bottom platform and of the top platform.
|
||||||
|
#+begin_src matlab
|
||||||
|
height = stewart.H - stewart.BP.H - stewart.TP.H - 2*stewart.SP.H; % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
for i = 1:3
|
||||||
|
% base points
|
||||||
|
angle_m_b = 120*(i-1) - stewart.BP.alpha;
|
||||||
|
angle_p_b = 120*(i-1) + stewart.BP.alpha;
|
||||||
|
|
||||||
|
stewart.pos_base(2*i-1,:) = [stewart.BP.Rleg*cos(angle_m_b), stewart.BP.Rleg*sin(angle_m_b), 0.0];
|
||||||
|
stewart.pos_base(2*i,:) = [stewart.BP.Rleg*cos(angle_p_b), stewart.BP.Rleg*sin(angle_p_b), 0.0];
|
||||||
|
|
||||||
|
% top points
|
||||||
|
angle_m_t = 120*(i-1) - stewart.TP.alpha + stewart.TP.dalpha;
|
||||||
|
angle_p_t = 120*(i-1) + stewart.TP.alpha + stewart.TP.dalpha;
|
||||||
|
|
||||||
|
stewart.pos_top(2*i-1,:) = [stewart.TP.Rleg*cos(angle_m_t), stewart.TP.Rleg*sin(angle_m_t), height];
|
||||||
|
stewart.pos_top(2*i,:) = [stewart.TP.Rleg*cos(angle_p_t), stewart.TP.Rleg*sin(angle_p_t), height];
|
||||||
|
end
|
||||||
|
|
||||||
|
% permute pos_top points so that legs are end points of base and top points
|
||||||
|
stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
|
||||||
|
stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
leg vectors
|
||||||
|
#+begin_src matlab
|
||||||
|
legs = stewart.pos_top - stewart.pos_base;
|
||||||
|
leg_length = zeros(6, 1);
|
||||||
|
leg_vectors = zeros(6, 3);
|
||||||
|
for i = 1:6
|
||||||
|
leg_length(i) = norm(legs(i,:));
|
||||||
|
leg_vectors(i,:) = legs(i,:) / leg_length(i);
|
||||||
|
end
|
||||||
|
|
||||||
|
stewart.Leg.lenght = 1000*leg_length(1)/1.5;
|
||||||
|
stewart.Leg.shape.bot = [0 0; ...
|
||||||
|
stewart.Leg.rad.bottom 0; ...
|
||||||
|
stewart.Leg.rad.bottom stewart.Leg.lenght; ...
|
||||||
|
stewart.Leg.rad.top stewart.Leg.lenght; ...
|
||||||
|
stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
|
||||||
|
0 0.2*stewart.Leg.lenght];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Calculate revolute and cylindrical axes
|
||||||
|
#+begin_src matlab
|
||||||
|
rev1 = zeros(6, 3);
|
||||||
|
rev2 = zeros(6, 3);
|
||||||
|
cyl1 = zeros(6, 3);
|
||||||
|
for i = 1:6
|
||||||
|
rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
|
||||||
|
rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
|
||||||
|
|
||||||
|
rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
|
||||||
|
rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
|
||||||
|
|
||||||
|
cyl1(i,:) = leg_vectors(i,:);
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Coordinate systems
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.lower_leg = struct('rotation', eye(3));
|
||||||
|
stewart.upper_leg = struct('rotation', eye(3));
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
|
||||||
|
stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Position Matrix
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.h+stewart.Leg.sphere.top+stewart.SP.h.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Compute Jacobian Matrix
|
||||||
|
#+begin_src matlab
|
||||||
|
% aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.h - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
|
||||||
|
bb = stewart.pos_top_tranform - (stewart.TP.h + stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
|
||||||
|
bb = bb - stewart.jacobian*1e-3*[zeros(6, 2),ones(6, 1)];
|
||||||
|
stewart.J = getJacobianMatrix(leg_vectors', bb');
|
||||||
|
|
||||||
|
stewart.K = stewart.Leg.k.ax*stewart.J'*stewart.J;
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
* initializeParameters Function
|
||||||
|
#+begin_src matlab
|
||||||
|
function [stewart] = initializeParameters(stewart)
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We first compute $[a_1, a_2, a_3, a_4, a_5, a_6]^T$ and $[b_1, b_2, b_3, b_4, b_5, b_6]^T$.
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.Aa = zeros(6, 3); % [mm]
|
||||||
|
stewart.Ab = zeros(6, 3); % [mm]
|
||||||
|
stewart.Bb = zeros(6, 3); % [mm]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
for i = 1:3
|
||||||
|
stewart.Aa(2*i-1,:) = [stewart.BP.Rleg*cos( pi/180*(120*(i-1) - stewart.BP.alpha) ), ...
|
||||||
|
stewart.BP.Rleg*sin( pi/180*(120*(i-1) - stewart.BP.alpha) ), ...
|
||||||
|
stewart.BP.H+stewart.SP.H];
|
||||||
|
stewart.Aa(2*i,:) = [stewart.BP.Rleg*cos( pi/180*(120*(i-1) + stewart.BP.alpha) ), ...
|
||||||
|
stewart.BP.Rleg*sin( pi/180*(120*(i-1) + stewart.BP.alpha) ), ...
|
||||||
|
stewart.BP.H+stewart.SP.H];
|
||||||
|
|
||||||
|
stewart.Ab(2*i-1,:) = [stewart.TP.Rleg*cos( pi/180*(120*(i-1) + stewart.TP.dalpha - stewart.TP.alpha) ), ...
|
||||||
|
stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha - stewart.TP.alpha) ), ...
|
||||||
|
stewart.H - stewart.TP.H - stewart.SP.H];
|
||||||
|
stewart.Ab(2*i,:) = [stewart.TP.Rleg*cos( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
|
||||||
|
stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
|
||||||
|
stewart.H - stewart.TP.H - stewart.SP.H];
|
||||||
|
end
|
||||||
|
stewart.Bb = stewart.Ab - stewart.H*[0,0,1];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Now, we compute the leg vectors $\hat{s}_i$ and leg position $l_i$:
|
||||||
|
\[ b_i - a_i = l_i \hat{s}_i \]
|
||||||
|
|
||||||
|
We initialize $l_i$ and $\hat{s}_i$
|
||||||
|
#+begin_src matlab
|
||||||
|
leg_length = zeros(6, 1); % [mm]
|
||||||
|
leg_vectors = zeros(6, 3);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We compute $b_i - a_i$, and then:
|
||||||
|
\begin{align*}
|
||||||
|
l_i &= \left|b_i - a_i\right| \\
|
||||||
|
\hat{s}_i &= \frac{b_i - a_i}{l_i}
|
||||||
|
\end{align*}
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
legs = stewart.Ab - stewart.Aa;
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
leg_length(i) = norm(legs(i,:));
|
||||||
|
leg_vectors(i,:) = legs(i,:) / leg_length(i);
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Then the shape of the bottom leg is estimated
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.Leg.lenght = leg_length(1)/1.5;
|
||||||
|
stewart.Leg.shape.bot = ...
|
||||||
|
[0 0; ...
|
||||||
|
stewart.Leg.Rbot 0; ...
|
||||||
|
stewart.Leg.Rbot stewart.Leg.lenght; ...
|
||||||
|
stewart.Leg.Rtop stewart.Leg.lenght; ...
|
||||||
|
stewart.Leg.Rtop 0.2*stewart.Leg.lenght; ...
|
||||||
|
0 0.2*stewart.Leg.lenght];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We compute rotation matrices to have the orientation of the legs.
|
||||||
|
The rotation matrix transforms the $z$ axis to the axis of the leg. The other axis are not important here.
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.Rm = struct('R', eye(3));
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
sx = cross(leg_vectors(i,:), [1 0 0]);
|
||||||
|
sx = sx/norm(sx);
|
||||||
|
|
||||||
|
sy = -cross(sx, leg_vectors(i,:));
|
||||||
|
sy = sy/norm(sy);
|
||||||
|
|
||||||
|
sz = leg_vectors(i,:);
|
||||||
|
sz = sz/norm(sz);
|
||||||
|
|
||||||
|
stewart.Rm(i).R = [sx', sy', sz'];
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Compute Jacobian Matrix
|
||||||
|
#+begin_src matlab
|
||||||
|
J = zeros(6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
J(i, 1:3) = leg_vectors(i, :);
|
||||||
|
J(i, 4:6) = cross(0.001*(stewart.Ab(i, :)- stewart.H*[0,0,1]), leg_vectors(i, :));
|
||||||
|
end
|
||||||
|
|
||||||
|
stewart.J = J;
|
||||||
|
stewart.Jinv = inv(J);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
stewart.K = stewart.Leg.k_ax*stewart.J'*stewart.J;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
end
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
* initializeSample
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :tangle src/initializeSample.m
|
||||||
|
:END:
|
||||||
|
#+begin_src matlab
|
||||||
|
function [] = initializeSample(opts_param)
|
||||||
|
%% Default values for opts
|
||||||
|
sample = struct( ...
|
||||||
|
'radius', 100, ... % radius of the cylinder [mm]
|
||||||
|
'height', 100, ... % height of the cylinder [mm]
|
||||||
|
'mass', 10, ... % mass of the cylinder [kg]
|
||||||
|
'measheight', 50, ... % measurement point z-offset [mm]
|
||||||
|
'offset', [0, 0, 0], ... % offset position of the sample [mm]
|
||||||
|
'color', [0.9 0.1 0.1] ...
|
||||||
|
);
|
||||||
|
|
||||||
|
%% Populate opts with input parameters
|
||||||
|
if exist('opts_param','var')
|
||||||
|
for opt = fieldnames(opts_param)'
|
||||||
|
sample.(opt{1}) = opts_param.(opt{1});
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
%% Save
|
||||||
|
save('./mat/sample.mat', 'sample');
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
@ -1,51 +1,67 @@
|
|||||||
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:1]]
|
||||||
function [sys] = identifyPlant(opts_param)
|
function [sys] = identifyPlant(opts_param)
|
||||||
%% Default values for opts
|
% identifyPlant:1 ends here
|
||||||
opts = struct();
|
|
||||||
|
|
||||||
%% Populate opts with input parameters
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:2]]
|
||||||
if exist('opts_param','var')
|
%% Default values for opts
|
||||||
|
opts = struct();
|
||||||
|
|
||||||
|
%% Populate opts with input parameters
|
||||||
|
if exist('opts_param','var')
|
||||||
for opt = fieldnames(opts_param)'
|
for opt = fieldnames(opts_param)'
|
||||||
opts.(opt{1}) = opts_param.(opt{1});
|
opts.(opt{1}) = opts_param.(opt{1});
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
|
% identifyPlant:2 ends here
|
||||||
|
|
||||||
%% Options for Linearized
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:3]]
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
% identifyPlant:3 ends here
|
||||||
|
|
||||||
%% Name of the Simulink File
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:4]]
|
||||||
mdl = 'stewart_identification';
|
mdl = 'stewart';
|
||||||
|
% identifyPlant:4 ends here
|
||||||
|
|
||||||
%% Input/Output definition
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:5]]
|
||||||
io(1) = linio([mdl, '/F'], 1, 'input'); % Cartesian forces
|
%% Inputs
|
||||||
io(2) = linio([mdl, '/Fl'], 1, 'input'); % Leg forces
|
io(1) = linio([mdl, '/F'], 1, 'input'); % Cartesian forces
|
||||||
io(3) = linio([mdl, '/Fd'], 1, 'input'); % Direct forces
|
io(2) = linio([mdl, '/Fl'], 1, 'input'); % Leg forces
|
||||||
io(4) = linio([mdl, '/Dw'], 1, 'input'); % Base motion
|
io(3) = linio([mdl, '/Fd'], 1, 'input'); % Direct forces
|
||||||
|
io(4) = linio([mdl, '/Dw'], 1, 'input'); % Base motion
|
||||||
|
|
||||||
io(5) = linio([mdl, '/Dm'], 1, 'output'); % Relative Motion
|
%% Outputs
|
||||||
io(6) = linio([mdl, '/Dlm'], 1, 'output'); % Displacement of each leg
|
io(5) = linio([mdl, '/Dm'], 1, 'output'); % Relative Motion
|
||||||
io(7) = linio([mdl, '/Flm'], 1, 'output'); % Force sensor in each leg
|
io(6) = linio([mdl, '/Dlm'], 1, 'output'); % Displacement of each leg
|
||||||
io(8) = linio([mdl, '/Xm'], 1, 'output'); % Absolute motion of platform
|
io(7) = linio([mdl, '/Flm'], 1, 'output'); % Force sensor in each leg
|
||||||
|
io(8) = linio([mdl, '/Xm'], 1, 'output'); % Absolute motion of platform
|
||||||
|
% identifyPlant:5 ends here
|
||||||
|
|
||||||
%% Run the linearization
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:6]]
|
||||||
G = linearize(mdl, io, 0);
|
G = linearize(mdl, io, 0);
|
||||||
|
% identifyPlant:6 ends here
|
||||||
|
|
||||||
%% Input/Output names
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:7]]
|
||||||
G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz', ...
|
G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz', ...
|
||||||
'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ...
|
'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ...
|
||||||
'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz', ...
|
'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz', ...
|
||||||
'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'};
|
'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'};
|
||||||
G.OutputName = {'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm', ...
|
G.OutputName = {'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm', ...
|
||||||
'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m', ...
|
'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m', ...
|
||||||
'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m', ...
|
'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m', ...
|
||||||
'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'};
|
'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'};
|
||||||
|
% identifyPlant:7 ends here
|
||||||
|
|
||||||
%% Cut into sub transfer functions
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:8]]
|
||||||
sys.G_cart = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}));
|
sys.G_cart = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}));
|
||||||
sys.G_forc = minreal(G({'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
|
sys.G_forc = minreal(G({'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
|
||||||
sys.G_legs = G({'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'});
|
sys.G_legs = minreal(G({'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}));
|
||||||
sys.G_tran = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'}));
|
sys.G_tran = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'}));
|
||||||
sys.G_comp = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
sys.G_comp = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
||||||
sys.G_iner = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
sys.G_iner = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'}));
|
||||||
sys.G_all = minreal(G);
|
% sys.G_all = minreal(G);
|
||||||
|
% identifyPlant:8 ends here
|
||||||
|
|
||||||
|
% [[file:~/MEGA/These/Matlab/Simscape/stewart-simscape/identification.org::*identifyPlant][identifyPlant:9]]
|
||||||
end
|
end
|
||||||
|
% identifyPlant:9 ends here
|
||||||
|
|||||||
@ -1,86 +1,228 @@
|
|||||||
|
% Function description and arguments
|
||||||
|
% The =initializeHexapod= function takes one structure that contains configurations for the hexapod and returns one structure representing the hexapod.
|
||||||
|
|
||||||
function [stewart] = initializeHexapod(opts_param)
|
function [stewart] = initializeHexapod(opts_param)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Default values for opts.
|
||||||
|
|
||||||
opts = struct(...
|
opts = struct(...
|
||||||
'height', 90, ... % Height of the platform [mm]
|
'height', 90, ... % Height of the platform [mm]
|
||||||
'density', 8000, ... % Density of the material used for the hexapod [kg/m3]
|
'density', 8000, ... % Density of the material used for the hexapod [kg/m3]
|
||||||
'k_ax', 1e8, ... % Stiffness of each actuator [N/m]
|
'k_ax', 1e8, ... % Stiffness of each actuator [N/m]
|
||||||
'c_ax', 100, ... % Damping of each actuator [N/(m/s)]
|
'c_ax', 1000, ... % Damping of each actuator [N/(m/s)]
|
||||||
'stroke', 50e-6, ... % Maximum stroke of each actuator [m]
|
'stroke', 50e-6, ... % Maximum stroke of each actuator [m]
|
||||||
'name', 'stewart' ... % Name of the file
|
'name', 'stewart' ... % Name of the file
|
||||||
);
|
);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Populate opts with input parameters
|
||||||
|
|
||||||
if exist('opts_param','var')
|
if exist('opts_param','var')
|
||||||
for opt = fieldnames(opts_param)'
|
for opt = fieldnames(opts_param)'
|
||||||
opts.(opt{1}) = opts_param.(opt{1});
|
opts.(opt{1}) = opts_param.(opt{1});
|
||||||
end
|
end
|
||||||
end
|
end
|
||||||
|
|
||||||
|
% Initialization of the stewart structure
|
||||||
|
% We initialize the Stewart structure
|
||||||
|
|
||||||
stewart = struct();
|
stewart = struct();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And we defined its total height.
|
||||||
|
|
||||||
stewart.H = opts.height; % [mm]
|
stewart.H = opts.height; % [mm]
|
||||||
|
|
||||||
|
% Bottom Plate
|
||||||
|
% #+name: fig:stewart_bottom_plate
|
||||||
|
% #+caption: Schematic of the bottom plates with all the parameters
|
||||||
|
% [[file:./figs/stewart_bottom_plate.png]]
|
||||||
|
|
||||||
|
|
||||||
|
% The bottom plate structure is initialized.
|
||||||
|
|
||||||
BP = struct();
|
BP = struct();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We defined its internal radius (if there is a hole in the bottom plate) and its outer radius.
|
||||||
|
|
||||||
BP.Rint = 0; % Internal Radius [mm]
|
BP.Rint = 0; % Internal Radius [mm]
|
||||||
BP.Rext = 150; % External Radius [mm]
|
BP.Rext = 150; % External Radius [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We define its thickness.
|
||||||
|
|
||||||
BP.H = 10; % Thickness of the Bottom Plate [mm]
|
BP.H = 10; % Thickness of the Bottom Plate [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% At which radius legs will be fixed and with that angle offset.
|
||||||
|
|
||||||
BP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
BP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
||||||
BP.alpha = 10; % Angle Offset [deg]
|
BP.alpha = 10; % Angle Offset [deg]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We defined the density of the material of the bottom plate.
|
||||||
|
|
||||||
BP.density = opts.density; % Density of the material [kg/m3]
|
BP.density = opts.density; % Density of the material [kg/m3]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And its color.
|
||||||
|
|
||||||
BP.color = [0.7 0.7 0.7]; % Color [RGB]
|
BP.color = [0.7 0.7 0.7]; % Color [RGB]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Then the profile of the bottom plate is computed and will be used by Simscape
|
||||||
|
|
||||||
BP.shape = [BP.Rint BP.H; BP.Rint 0; BP.Rext 0; BP.Rext BP.H]; % [mm]
|
BP.shape = [BP.Rint BP.H; BP.Rint 0; BP.Rext 0; BP.Rext BP.H]; % [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The structure is added to the stewart structure
|
||||||
|
|
||||||
stewart.BP = BP;
|
stewart.BP = BP;
|
||||||
|
|
||||||
|
% Top Plate
|
||||||
|
% The top plate structure is initialized.
|
||||||
|
|
||||||
TP = struct();
|
TP = struct();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We defined the internal and external radius of the top plate.
|
||||||
|
|
||||||
TP.Rint = 0; % [mm]
|
TP.Rint = 0; % [mm]
|
||||||
TP.Rext = 100; % [mm]
|
TP.Rext = 100; % [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The thickness of the top plate.
|
||||||
|
|
||||||
TP.H = 10; % [mm]
|
TP.H = 10; % [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% At which radius and angle are fixed the legs.
|
||||||
|
|
||||||
TP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
TP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
|
||||||
TP.alpha = 20; % Angle [deg]
|
TP.alpha = 20; % Angle [deg]
|
||||||
TP.dalpha = 0; % Angle Offset from 0 position [deg]
|
TP.dalpha = 0; % Angle Offset from 0 position [deg]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The density of its material.
|
||||||
|
|
||||||
TP.density = opts.density; % Density of the material [kg/m3]
|
TP.density = opts.density; % Density of the material [kg/m3]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Its color.
|
||||||
|
|
||||||
TP.color = [0.7 0.7 0.7]; % Color [RGB]
|
TP.color = [0.7 0.7 0.7]; % Color [RGB]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Then the shape of the top plate is computed
|
||||||
|
|
||||||
TP.shape = [TP.Rint TP.H; TP.Rint 0; TP.Rext 0; TP.Rext TP.H];
|
TP.shape = [TP.Rint TP.H; TP.Rint 0; TP.Rext 0; TP.Rext TP.H];
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The structure is added to the stewart structure
|
||||||
|
|
||||||
stewart.TP = TP;
|
stewart.TP = TP;
|
||||||
|
|
||||||
|
% Legs
|
||||||
|
% #+name: fig:stewart_legs
|
||||||
|
% #+caption: Schematic for the legs of the Stewart platform
|
||||||
|
% [[file:./figs/stewart_legs.png]]
|
||||||
|
|
||||||
|
|
||||||
|
% The leg structure is initialized.
|
||||||
|
|
||||||
Leg = struct();
|
Leg = struct();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The maximum Stroke of each leg is defined.
|
||||||
|
|
||||||
Leg.stroke = opts.stroke; % [m]
|
Leg.stroke = opts.stroke; % [m]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The stiffness and damping of each leg are defined
|
||||||
|
|
||||||
Leg.k_ax = opts.k_ax; % Stiffness of each leg [N/m]
|
Leg.k_ax = opts.k_ax; % Stiffness of each leg [N/m]
|
||||||
Leg.c_ax = opts.c_ax; % Damping of each leg [N/(m/s)]
|
Leg.c_ax = opts.c_ax; % Damping of each leg [N/(m/s)]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The radius of the legs are defined
|
||||||
|
|
||||||
Leg.Rtop = 10; % Radius of the cylinder of the top part of the leg[mm]
|
Leg.Rtop = 10; % Radius of the cylinder of the top part of the leg[mm]
|
||||||
Leg.Rbot = 12; % Radius of the cylinder of the bottom part of the leg [mm]
|
Leg.Rbot = 12; % Radius of the cylinder of the bottom part of the leg [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The density of its material.
|
||||||
|
|
||||||
Leg.density = opts.density; % Density of the material used for the legs [kg/m3]
|
Leg.density = opts.density; % Density of the material used for the legs [kg/m3]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Its color.
|
||||||
|
|
||||||
Leg.color = [0.5 0.5 0.5]; % Color of the top part of the leg [RGB]
|
Leg.color = [0.5 0.5 0.5]; % Color of the top part of the leg [RGB]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The radius of spheres representing the ball joints are defined.
|
||||||
|
|
||||||
Leg.R = 1.3*Leg.Rbot; % Size of the sphere at the extremity of the leg [mm]
|
Leg.R = 1.3*Leg.Rbot; % Size of the sphere at the extremity of the leg [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The structure is added to the stewart structure
|
||||||
|
|
||||||
stewart.Leg = Leg;
|
stewart.Leg = Leg;
|
||||||
|
|
||||||
|
% Ball Joints
|
||||||
|
% #+name: fig:stewart_ball_joints
|
||||||
|
% #+caption: Schematic of the support for the ball joints
|
||||||
|
% [[file:./figs/stewart_ball_joints.png]]
|
||||||
|
|
||||||
|
% =SP= is the structure representing the support for the ball joints at the extremity of each leg.
|
||||||
|
|
||||||
|
% The =SP= structure is initialized.
|
||||||
|
|
||||||
SP = struct();
|
SP = struct();
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We can define its rotational stiffness and damping. For now, we use perfect joints.
|
||||||
|
|
||||||
SP.k = 0; % [N*m/deg]
|
SP.k = 0; % [N*m/deg]
|
||||||
SP.c = 0; % [N*m/deg]
|
SP.c = 0; % [N*m/deg]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Its height is defined
|
||||||
|
|
||||||
SP.H = 15; % [mm]
|
SP.H = 15; % [mm]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Its radius is based on the radius on the sphere at the end of the legs.
|
||||||
|
|
||||||
SP.R = Leg.R; % [mm]
|
SP.R = Leg.R; % [mm]
|
||||||
|
|
||||||
SP.section = [0 SP.H-SP.R;
|
SP.section = [0 SP.H-SP.R;
|
||||||
@ -88,18 +230,40 @@ SP.section = [0 SP.H-SP.R;
|
|||||||
SP.R 0;
|
SP.R 0;
|
||||||
SP.R SP.H];
|
SP.R SP.H];
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The density of its material is defined.
|
||||||
|
|
||||||
SP.density = opts.density; % [kg/m^3]
|
SP.density = opts.density; % [kg/m^3]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Its color is defined.
|
||||||
|
|
||||||
SP.color = [0.7 0.7 0.7]; % [RGB]
|
SP.color = [0.7 0.7 0.7]; % [RGB]
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% The structure is added to the Hexapod structure
|
||||||
|
|
||||||
stewart.SP = SP;
|
stewart.SP = SP;
|
||||||
|
|
||||||
|
% More parameters are initialized
|
||||||
|
|
||||||
stewart = initializeParameters(stewart);
|
stewart = initializeParameters(stewart);
|
||||||
|
|
||||||
|
% Save the Stewart Structure
|
||||||
|
|
||||||
save('./mat/stewart.mat', 'stewart')
|
save('./mat/stewart.mat', 'stewart')
|
||||||
|
|
||||||
|
% initializeParameters Function
|
||||||
|
|
||||||
function [stewart] = initializeParameters(stewart)
|
function [stewart] = initializeParameters(stewart)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We first compute $[a_1, a_2, a_3, a_4, a_5, a_6]^T$ and $[b_1, b_2, b_3, b_4, b_5, b_6]^T$.
|
||||||
|
|
||||||
stewart.Aa = zeros(6, 3); % [mm]
|
stewart.Aa = zeros(6, 3); % [mm]
|
||||||
stewart.Ab = zeros(6, 3); % [mm]
|
stewart.Ab = zeros(6, 3); % [mm]
|
||||||
stewart.Bb = zeros(6, 3); % [mm]
|
stewart.Bb = zeros(6, 3); % [mm]
|
||||||
@ -119,12 +283,27 @@ for i = 1:3
|
|||||||
stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
|
stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
|
||||||
stewart.H - stewart.TP.H - stewart.SP.H];
|
stewart.H - stewart.TP.H - stewart.SP.H];
|
||||||
end
|
end
|
||||||
|
|
||||||
stewart.Bb = stewart.Ab - stewart.H*[0,0,1];
|
stewart.Bb = stewart.Ab - stewart.H*[0,0,1];
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Now, we compute the leg vectors $\hat{s}_i$ and leg position $l_i$:
|
||||||
|
% \[ b_i - a_i = l_i \hat{s}_i \]
|
||||||
|
|
||||||
|
% We initialize $l_i$ and $\hat{s}_i$
|
||||||
|
|
||||||
leg_length = zeros(6, 1); % [mm]
|
leg_length = zeros(6, 1); % [mm]
|
||||||
leg_vectors = zeros(6, 3);
|
leg_vectors = zeros(6, 3);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We compute $b_i - a_i$, and then:
|
||||||
|
% \begin{align*}
|
||||||
|
% l_i &= \left|b_i - a_i\right| \\
|
||||||
|
% \hat{s}_i &= \frac{b_i - a_i}{l_i}
|
||||||
|
% \end{align*}
|
||||||
|
|
||||||
|
|
||||||
legs = stewart.Ab - stewart.Aa;
|
legs = stewart.Ab - stewart.Aa;
|
||||||
|
|
||||||
for i = 1:6
|
for i = 1:6
|
||||||
@ -132,6 +311,10 @@ for i = 1:6
|
|||||||
leg_vectors(i,:) = legs(i,:) / leg_length(i);
|
leg_vectors(i,:) = legs(i,:) / leg_length(i);
|
||||||
end
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Then the shape of the bottom leg is estimated
|
||||||
|
|
||||||
stewart.Leg.lenght = leg_length(1)/1.5;
|
stewart.Leg.lenght = leg_length(1)/1.5;
|
||||||
stewart.Leg.shape.bot = ...
|
stewart.Leg.shape.bot = ...
|
||||||
[0 0; ...
|
[0 0; ...
|
||||||
@ -141,6 +324,11 @@ stewart.Leg.shape.bot = ...
|
|||||||
stewart.Leg.Rtop 0.2*stewart.Leg.lenght; ...
|
stewart.Leg.Rtop 0.2*stewart.Leg.lenght; ...
|
||||||
0 0.2*stewart.Leg.lenght];
|
0 0.2*stewart.Leg.lenght];
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% We compute rotation matrices to have the orientation of the legs.
|
||||||
|
% The rotation matrix transforms the $z$ axis to the axis of the leg. The other axis are not important here.
|
||||||
|
|
||||||
stewart.Rm = struct('R', eye(3));
|
stewart.Rm = struct('R', eye(3));
|
||||||
|
|
||||||
for i = 1:6
|
for i = 1:6
|
||||||
@ -156,14 +344,19 @@ for i = 1:6
|
|||||||
stewart.Rm(i).R = [sx', sy', sz'];
|
stewart.Rm(i).R = [sx', sy', sz'];
|
||||||
end
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Compute Jacobian Matrix
|
||||||
|
|
||||||
J = zeros(6);
|
J = zeros(6);
|
||||||
|
|
||||||
for i = 1:6
|
for i = 1:6
|
||||||
J(i, 1:3) = leg_vectors(i, :);
|
J(i, 1:3) = leg_vectors(i, :);
|
||||||
J(i, 4:6) = cross(0.001*stewart.Bb(i, :), leg_vectors(i, :));
|
J(i, 4:6) = cross(0.001*(stewart.Ab(i, :)- stewart.H*[0,0,1]), leg_vectors(i, :));
|
||||||
end
|
end
|
||||||
|
|
||||||
stewart.J = J;
|
stewart.J = J;
|
||||||
|
stewart.Jinv = inv(J);
|
||||||
|
|
||||||
stewart.K = stewart.Leg.k_ax*stewart.J'*stewart.J;
|
stewart.K = stewart.Leg.k_ax*stewart.J'*stewart.J;
|
||||||
|
|
||||||
|
|||||||
@ -2,9 +2,9 @@ function [] = initializeSample(opts_param)
|
|||||||
%% Default values for opts
|
%% Default values for opts
|
||||||
sample = struct( ...
|
sample = struct( ...
|
||||||
'radius', 100, ... % radius of the cylinder [mm]
|
'radius', 100, ... % radius of the cylinder [mm]
|
||||||
'height', 300, ... % height of the cylinder [mm]
|
'height', 100, ... % height of the cylinder [mm]
|
||||||
'mass', 50, ... % mass of the cylinder [kg]
|
'mass', 10, ... % mass of the cylinder [kg]
|
||||||
'measheight', 150, ... % measurement point z-offset [mm]
|
'measheight', 50, ... % measurement point z-offset [mm]
|
||||||
'offset', [0, 0, 0], ... % offset position of the sample [mm]
|
'offset', [0, 0, 0], ... % offset position of the sample [mm]
|
||||||
'color', [0.9 0.1 0.1] ...
|
'color', [0.9 0.1 0.1] ...
|
||||||
);
|
);
|
||||||
|
|||||||
BIN
stewart.slx
BIN
stewart.slx
Binary file not shown.
284
stiffness-study.html
Normal file
284
stiffness-study.html
Normal file
@ -0,0 +1,284 @@
|
|||||||
|
<?xml version="1.0" encoding="utf-8"?>
|
||||||
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||||||
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
|
<head>
|
||||||
|
<!-- 2019-03-22 ven. 12:03 -->
|
||||||
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||||
|
<title>Stiffness of the Stewart Platform</title>
|
||||||
|
<meta name="generator" content="Org mode" />
|
||||||
|
<meta name="author" content="Thomas Dehaeze" />
|
||||||
|
<style type="text/css">
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
.title { text-align: center;
|
||||||
|
margin-bottom: .2em; }
|
||||||
|
.subtitle { text-align: center;
|
||||||
|
font-size: medium;
|
||||||
|
font-weight: bold;
|
||||||
|
margin-top:0; }
|
||||||
|
.todo { font-family: monospace; color: red; }
|
||||||
|
.done { font-family: monospace; color: green; }
|
||||||
|
.priority { font-family: monospace; color: orange; }
|
||||||
|
.tag { background-color: #eee; font-family: monospace;
|
||||||
|
padding: 2px; font-size: 80%; font-weight: normal; }
|
||||||
|
.timestamp { color: #bebebe; }
|
||||||
|
.timestamp-kwd { color: #5f9ea0; }
|
||||||
|
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
||||||
|
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
|
||||||
|
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
|
||||||
|
.underline { text-decoration: underline; }
|
||||||
|
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
|
||||||
|
p.verse { margin-left: 3%; }
|
||||||
|
pre {
|
||||||
|
border: 1px solid #ccc;
|
||||||
|
box-shadow: 3px 3px 3px #eee;
|
||||||
|
padding: 8pt;
|
||||||
|
font-family: monospace;
|
||||||
|
overflow: auto;
|
||||||
|
margin: 1.2em;
|
||||||
|
}
|
||||||
|
pre.src {
|
||||||
|
position: relative;
|
||||||
|
overflow: visible;
|
||||||
|
padding-top: 1.2em;
|
||||||
|
}
|
||||||
|
pre.src:before {
|
||||||
|
display: none;
|
||||||
|
position: absolute;
|
||||||
|
background-color: white;
|
||||||
|
top: -10px;
|
||||||
|
right: 10px;
|
||||||
|
padding: 3px;
|
||||||
|
border: 1px solid black;
|
||||||
|
}
|
||||||
|
pre.src:hover:before { display: inline;}
|
||||||
|
/* Languages per Org manual */
|
||||||
|
pre.src-asymptote:before { content: 'Asymptote'; }
|
||||||
|
pre.src-awk:before { content: 'Awk'; }
|
||||||
|
pre.src-C:before { content: 'C'; }
|
||||||
|
/* pre.src-C++ doesn't work in CSS */
|
||||||
|
pre.src-clojure:before { content: 'Clojure'; }
|
||||||
|
pre.src-css:before { content: 'CSS'; }
|
||||||
|
pre.src-D:before { content: 'D'; }
|
||||||
|
pre.src-ditaa:before { content: 'ditaa'; }
|
||||||
|
pre.src-dot:before { content: 'Graphviz'; }
|
||||||
|
pre.src-calc:before { content: 'Emacs Calc'; }
|
||||||
|
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
|
||||||
|
pre.src-fortran:before { content: 'Fortran'; }
|
||||||
|
pre.src-gnuplot:before { content: 'gnuplot'; }
|
||||||
|
pre.src-haskell:before { content: 'Haskell'; }
|
||||||
|
pre.src-hledger:before { content: 'hledger'; }
|
||||||
|
pre.src-java:before { content: 'Java'; }
|
||||||
|
pre.src-js:before { content: 'Javascript'; }
|
||||||
|
pre.src-latex:before { content: 'LaTeX'; }
|
||||||
|
pre.src-ledger:before { content: 'Ledger'; }
|
||||||
|
pre.src-lisp:before { content: 'Lisp'; }
|
||||||
|
pre.src-lilypond:before { content: 'Lilypond'; }
|
||||||
|
pre.src-lua:before { content: 'Lua'; }
|
||||||
|
pre.src-matlab:before { content: 'MATLAB'; }
|
||||||
|
pre.src-mscgen:before { content: 'Mscgen'; }
|
||||||
|
pre.src-ocaml:before { content: 'Objective Caml'; }
|
||||||
|
pre.src-octave:before { content: 'Octave'; }
|
||||||
|
pre.src-org:before { content: 'Org mode'; }
|
||||||
|
pre.src-oz:before { content: 'OZ'; }
|
||||||
|
pre.src-plantuml:before { content: 'Plantuml'; }
|
||||||
|
pre.src-processing:before { content: 'Processing.js'; }
|
||||||
|
pre.src-python:before { content: 'Python'; }
|
||||||
|
pre.src-R:before { content: 'R'; }
|
||||||
|
pre.src-ruby:before { content: 'Ruby'; }
|
||||||
|
pre.src-sass:before { content: 'Sass'; }
|
||||||
|
pre.src-scheme:before { content: 'Scheme'; }
|
||||||
|
pre.src-screen:before { content: 'Gnu Screen'; }
|
||||||
|
pre.src-sed:before { content: 'Sed'; }
|
||||||
|
pre.src-sh:before { content: 'shell'; }
|
||||||
|
pre.src-sql:before { content: 'SQL'; }
|
||||||
|
pre.src-sqlite:before { content: 'SQLite'; }
|
||||||
|
/* additional languages in org.el's org-babel-load-languages alist */
|
||||||
|
pre.src-forth:before { content: 'Forth'; }
|
||||||
|
pre.src-io:before { content: 'IO'; }
|
||||||
|
pre.src-J:before { content: 'J'; }
|
||||||
|
pre.src-makefile:before { content: 'Makefile'; }
|
||||||
|
pre.src-maxima:before { content: 'Maxima'; }
|
||||||
|
pre.src-perl:before { content: 'Perl'; }
|
||||||
|
pre.src-picolisp:before { content: 'Pico Lisp'; }
|
||||||
|
pre.src-scala:before { content: 'Scala'; }
|
||||||
|
pre.src-shell:before { content: 'Shell Script'; }
|
||||||
|
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
|
||||||
|
/* additional language identifiers per "defun org-babel-execute"
|
||||||
|
in ob-*.el */
|
||||||
|
pre.src-cpp:before { content: 'C++'; }
|
||||||
|
pre.src-abc:before { content: 'ABC'; }
|
||||||
|
pre.src-coq:before { content: 'Coq'; }
|
||||||
|
pre.src-groovy:before { content: 'Groovy'; }
|
||||||
|
/* additional language identifiers from org-babel-shell-names in
|
||||||
|
ob-shell.el: ob-shell is the only babel language using a lambda to put
|
||||||
|
the execution function name together. */
|
||||||
|
pre.src-bash:before { content: 'bash'; }
|
||||||
|
pre.src-csh:before { content: 'csh'; }
|
||||||
|
pre.src-ash:before { content: 'ash'; }
|
||||||
|
pre.src-dash:before { content: 'dash'; }
|
||||||
|
pre.src-ksh:before { content: 'ksh'; }
|
||||||
|
pre.src-mksh:before { content: 'mksh'; }
|
||||||
|
pre.src-posh:before { content: 'posh'; }
|
||||||
|
/* Additional Emacs modes also supported by the LaTeX listings package */
|
||||||
|
pre.src-ada:before { content: 'Ada'; }
|
||||||
|
pre.src-asm:before { content: 'Assembler'; }
|
||||||
|
pre.src-caml:before { content: 'Caml'; }
|
||||||
|
pre.src-delphi:before { content: 'Delphi'; }
|
||||||
|
pre.src-html:before { content: 'HTML'; }
|
||||||
|
pre.src-idl:before { content: 'IDL'; }
|
||||||
|
pre.src-mercury:before { content: 'Mercury'; }
|
||||||
|
pre.src-metapost:before { content: 'MetaPost'; }
|
||||||
|
pre.src-modula-2:before { content: 'Modula-2'; }
|
||||||
|
pre.src-pascal:before { content: 'Pascal'; }
|
||||||
|
pre.src-ps:before { content: 'PostScript'; }
|
||||||
|
pre.src-prolog:before { content: 'Prolog'; }
|
||||||
|
pre.src-simula:before { content: 'Simula'; }
|
||||||
|
pre.src-tcl:before { content: 'tcl'; }
|
||||||
|
pre.src-tex:before { content: 'TeX'; }
|
||||||
|
pre.src-plain-tex:before { content: 'Plain TeX'; }
|
||||||
|
pre.src-verilog:before { content: 'Verilog'; }
|
||||||
|
pre.src-vhdl:before { content: 'VHDL'; }
|
||||||
|
pre.src-xml:before { content: 'XML'; }
|
||||||
|
pre.src-nxml:before { content: 'XML'; }
|
||||||
|
/* add a generic configuration mode; LaTeX export needs an additional
|
||||||
|
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
|
||||||
|
pre.src-conf:before { content: 'Configuration File'; }
|
||||||
|
|
||||||
|
table { border-collapse:collapse; }
|
||||||
|
caption.t-above { caption-side: top; }
|
||||||
|
caption.t-bottom { caption-side: bottom; }
|
||||||
|
td, th { vertical-align:top; }
|
||||||
|
th.org-right { text-align: center; }
|
||||||
|
th.org-left { text-align: center; }
|
||||||
|
th.org-center { text-align: center; }
|
||||||
|
td.org-right { text-align: right; }
|
||||||
|
td.org-left { text-align: left; }
|
||||||
|
td.org-center { text-align: center; }
|
||||||
|
dt { font-weight: bold; }
|
||||||
|
.footpara { display: inline; }
|
||||||
|
.footdef { margin-bottom: 1em; }
|
||||||
|
.figure { padding: 1em; }
|
||||||
|
.figure p { text-align: center; }
|
||||||
|
.equation-container {
|
||||||
|
display: table;
|
||||||
|
text-align: center;
|
||||||
|
width: 100%;
|
||||||
|
}
|
||||||
|
.equation {
|
||||||
|
vertical-align: middle;
|
||||||
|
}
|
||||||
|
.equation-label {
|
||||||
|
display: table-cell;
|
||||||
|
text-align: right;
|
||||||
|
vertical-align: middle;
|
||||||
|
}
|
||||||
|
.inlinetask {
|
||||||
|
padding: 10px;
|
||||||
|
border: 2px solid gray;
|
||||||
|
margin: 10px;
|
||||||
|
background: #ffffcc;
|
||||||
|
}
|
||||||
|
#org-div-home-and-up
|
||||||
|
{ text-align: right; font-size: 70%; white-space: nowrap; }
|
||||||
|
textarea { overflow-x: auto; }
|
||||||
|
.linenr { font-size: smaller }
|
||||||
|
.code-highlighted { background-color: #ffff00; }
|
||||||
|
.org-info-js_info-navigation { border-style: none; }
|
||||||
|
#org-info-js_console-label
|
||||||
|
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
|
||||||
|
.org-info-js_search-highlight
|
||||||
|
{ background-color: #ffff00; color: #000000; font-weight: bold; }
|
||||||
|
.org-svg { width: 90%; }
|
||||||
|
/*]]>*/-->
|
||||||
|
</style>
|
||||||
|
<script type="text/javascript">
|
||||||
|
/*
|
||||||
|
@licstart The following is the entire license notice for the
|
||||||
|
JavaScript code in this tag.
|
||||||
|
|
||||||
|
Copyright (C) 2012-2019 Free Software Foundation, Inc.
|
||||||
|
|
||||||
|
The JavaScript code in this tag is free software: you can
|
||||||
|
redistribute it and/or modify it under the terms of the GNU
|
||||||
|
General Public License (GNU GPL) as published by the Free Software
|
||||||
|
Foundation, either version 3 of the License, or (at your option)
|
||||||
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
||||||
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||||
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
||||||
|
|
||||||
|
As additional permission under GNU GPL version 3 section 7, you
|
||||||
|
may distribute non-source (e.g., minimized or compacted) forms of
|
||||||
|
that code without the copy of the GNU GPL normally required by
|
||||||
|
section 4, provided you include this license notice and a URL
|
||||||
|
through which recipients can access the Corresponding Source.
|
||||||
|
|
||||||
|
|
||||||
|
@licend The above is the entire license notice
|
||||||
|
for the JavaScript code in this tag.
|
||||||
|
*/
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
function CodeHighlightOn(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(null != target) {
|
||||||
|
elem.cacheClassElem = elem.className;
|
||||||
|
elem.cacheClassTarget = target.className;
|
||||||
|
target.className = "code-highlighted";
|
||||||
|
elem.className = "code-highlighted";
|
||||||
|
}
|
||||||
|
}
|
||||||
|
function CodeHighlightOff(elem, id)
|
||||||
|
{
|
||||||
|
var target = document.getElementById(id);
|
||||||
|
if(elem.cacheClassElem)
|
||||||
|
elem.className = elem.cacheClassElem;
|
||||||
|
if(elem.cacheClassTarget)
|
||||||
|
target.className = elem.cacheClassTarget;
|
||||||
|
}
|
||||||
|
/*]]>*///-->
|
||||||
|
</script>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="content">
|
||||||
|
<h1 class="title">Stiffness of the Stewart Platform</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org178badc">1. Functions</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org31327cd">1.1. getStiffnessMatrix</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org178badc" class="outline-2">
|
||||||
|
<h2 id="org178badc"><span class="section-number-2">1</span> Functions</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org31327cd" class="outline-3">
|
||||||
|
<h3 id="org31327cd"><span class="section-number-3">1.1</span> getStiffnessMatrix</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">K</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">getStiffnessMatrix</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">k</span>, <span style="color: #DFAF8F;">J</span><span style="color: #DCDCCC;">)</span>
|
||||||
|
<span style="color: #7F9F7F;">% k - leg stiffness</span>
|
||||||
|
<span style="color: #7F9F7F;">% J - Jacobian matrix</span>
|
||||||
|
K = k<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">(</span>J'<span style="color: #7CB8BB;">*</span>J<span style="color: #DCDCCC;">)</span>;
|
||||||
|
<span style="color: #F0DFAF; font-weight: bold;">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Thomas Dehaeze</p>
|
||||||
|
<p class="date">Created: 2019-03-22 ven. 12:03</p>
|
||||||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
20
stiffness-study.org
Normal file
20
stiffness-study.org
Normal file
@ -0,0 +1,20 @@
|
|||||||
|
#+TITLE: Stiffness of the Stewart Platform
|
||||||
|
|
||||||
|
* Functions
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :exports code
|
||||||
|
:HEADER-ARGS:matlab+: :comments no
|
||||||
|
:HEADER-ARGS:matlab+: :mkdir yes
|
||||||
|
:HEADER-ARGS:matlab+: :eval no
|
||||||
|
:END:
|
||||||
|
** getStiffnessMatrix
|
||||||
|
:PROPERTIES:
|
||||||
|
:HEADER-ARGS:matlab+: :tangle src/getStiffnessMatrix.m
|
||||||
|
:END:
|
||||||
|
#+begin_src matlab
|
||||||
|
function [K] = getStiffnessMatrix(k, J)
|
||||||
|
% k - leg stiffness
|
||||||
|
% J - Jacobian matrix
|
||||||
|
K = k*(J'*J);
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
Loading…
Reference in New Issue
Block a user