From 2914d01e8f1a323c5f94a1f9949ed9dcb6db8960 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Fri, 22 Mar 2019 12:03:59 +0100 Subject: [PATCH] Add css and js. Add lots of org mode files. --- css/htmlize.css | 145 +++ css/readtheorg.css | 1095 +++++++++++++++++ figs/stewart_ball_joints.png | Bin 0 -> 5057 bytes figs/stewart_bottom_plate.png | Bin 0 -> 39477 bytes figs/stewart_legs.png | Bin 0 -> 21922 bytes identification.html | 571 +++++++++ identification.org | 242 ++++ index.html | 301 +++++ index.org | 639 +--------- js/bootstrap.min.js | 7 + js/jquery.min.js | 4 + js/jquery.stickytableheaders.min.js | 1 + js/readtheorg.js | 85 ++ js/siunitx.js | 2 + kinematic-study.html | 316 +++++ kinematic-study.org | 49 + mat/G.mat | Bin 16341 -> 0 bytes mat/G_iff.mat | Bin 90985 -> 0 bytes mat/G_jacobian.mat | Bin 132424 -> 0 bytes mat/K_iff.mat | Bin 1030 -> 0 bytes mat/K_iff_sisotool.mat | Bin 2216 -> 0 bytes mat/config.mat | Bin 7928 -> 0 bytes mat/controllers.mat | Bin 21840 -> 0 bytes mat/sample.mat | Bin 286 -> 278 bytes mat/stewart.mat | Bin 1589 -> 1474 bytes .../active_damping}/act_damp_iff_generate.m | 0 .../active_damping}/act_damp_iff_id.m | 0 .../active_damping}/act_damp_iff_plots.m | 0 .../active_damping}/act_damp_main.m | 0 .../analysis}/analysis_stiffness.m | 0 analyze_jacobian.m => old/analyze_jacobian.m | 0 config.m => old/config.m | 0 {identification => old/identification}/id_G.m | 0 .../identification}/id_jacobian.m | 0 .../identification}/id_jacobian_plots.m | 0 .../identification}/id_main.m | 0 .../identification}/id_plot_cart.m | 0 .../identification}/id_plot_db.m | 0 .../identification}/id_plot_iff.m | 0 .../identification}/id_plot_legs.m | 0 main.m => old/main.m | 0 .../plot_max_positions.m | 0 {studies => old/studies}/com.m | 0 {studies => old/studies}/coupling.m | 0 {studies => old/studies}/stiffness_matrix.m | 0 .../study_architecture.m | 0 simscape-model.html | 855 +++++++++++++ simscape-model.org | 503 ++++++++ src/identifyPlant.m | 108 +- src/initializeHexapod.m | 199 ++- src/initializeSample.m | 6 +- stewart.slx | Bin 68491 -> 67479 bytes stiffness-study.html | 284 +++++ stiffness-study.org | 20 + 54 files changed, 4756 insertions(+), 676 deletions(-) create mode 100644 css/htmlize.css create mode 100644 css/readtheorg.css create mode 100644 figs/stewart_ball_joints.png create mode 100644 figs/stewart_bottom_plate.png create mode 100644 figs/stewart_legs.png create mode 100644 identification.html create mode 100644 identification.org create mode 100644 index.html create mode 100644 js/bootstrap.min.js create mode 100644 js/jquery.min.js create mode 100644 js/jquery.stickytableheaders.min.js create mode 100644 js/readtheorg.js create mode 100644 js/siunitx.js create mode 100644 kinematic-study.html create mode 100644 kinematic-study.org delete mode 100644 mat/G.mat delete mode 100644 mat/G_iff.mat delete mode 100644 mat/G_jacobian.mat delete mode 100644 mat/K_iff.mat delete mode 100644 mat/K_iff_sisotool.mat delete mode 100644 mat/config.mat delete mode 100644 mat/controllers.mat rename {active_damping => old/active_damping}/act_damp_iff_generate.m (100%) rename {active_damping => old/active_damping}/act_damp_iff_id.m (100%) rename {active_damping => old/active_damping}/act_damp_iff_plots.m (100%) rename {active_damping => old/active_damping}/act_damp_main.m (100%) rename {analysis => old/analysis}/analysis_stiffness.m (100%) rename analyze_jacobian.m => old/analyze_jacobian.m (100%) rename config.m => old/config.m (100%) rename {identification => old/identification}/id_G.m (100%) rename {identification => old/identification}/id_jacobian.m (100%) rename {identification => old/identification}/id_jacobian_plots.m (100%) rename {identification => old/identification}/id_main.m (100%) rename {identification => old/identification}/id_plot_cart.m (100%) rename {identification => old/identification}/id_plot_db.m (100%) rename {identification => old/identification}/id_plot_iff.m (100%) rename {identification => old/identification}/id_plot_legs.m (100%) rename main.m => old/main.m (100%) rename plot_max_positions.m => old/plot_max_positions.m (100%) rename {studies => old/studies}/com.m (100%) rename {studies => old/studies}/coupling.m (100%) rename {studies => old/studies}/stiffness_matrix.m (100%) rename study_architecture.m => old/study_architecture.m (100%) create mode 100644 simscape-model.html create mode 100644 simscape-model.org create mode 100644 stiffness-study.html create mode 100644 stiffness-study.org diff --git a/css/htmlize.css b/css/htmlize.css new file mode 100644 index 0000000..0b32a03 --- /dev/null +++ b/css/htmlize.css @@ -0,0 +1,145 @@ +.org-bold { /* bold */ font-weight: bold; } +.org-bold-italic { /* bold-italic */ font-weight: bold; font-style: italic; } +.org-buffer-menu-buffer { /* buffer-menu-buffer */ font-weight: bold; } +.org-builtin { /* font-lock-builtin-face */ color: #7a378b; } +.org-button { /* button */ text-decoration: underline; } +.org-calendar-today { /* calendar-today */ text-decoration: underline; } +.org-change-log-acknowledgement { /* change-log-acknowledgement */ color: #b22222; } +.org-change-log-conditionals { /* change-log-conditionals */ color: #a0522d; } +.org-change-log-date { /* change-log-date */ color: #8b2252; } +.org-change-log-email { /* change-log-email */ color: #a0522d; } +.org-change-log-file { /* change-log-file */ color: #0000ff; } +.org-change-log-function { /* change-log-function */ color: #a0522d; } +.org-change-log-list { /* change-log-list */ color: #a020f0; } +.org-change-log-name { /* change-log-name */ color: #008b8b; } +.org-comint-highlight-input { /* comint-highlight-input */ font-weight: bold; } +.org-comint-highlight-prompt { /* comint-highlight-prompt */ color: #00008b; } +.org-comment { /* font-lock-comment-face */ color: #999988; font-style: italic; } +.org-comment-delimiter { /* font-lock-comment-delimiter-face */ color: #999988; font-style: italic; } +.org-completions-annotations { /* completions-annotations */ font-style: italic; } +.org-completions-common-part { /* completions-common-part */ color: #000000; background-color: #ffffff; } +.org-completions-first-difference { /* completions-first-difference */ font-weight: bold; } +.org-constant { /* font-lock-constant-face */ color: #008b8b; } +.org-diary { /* diary */ color: #ff0000; } +.org-diff-context { /* diff-context */ color: #7f7f7f; } +.org-diff-file-header { /* diff-file-header */ background-color: #b3b3b3; font-weight: bold; } +.org-diff-function { /* diff-function */ background-color: #cccccc; } +.org-diff-header { /* diff-header */ background-color: #cccccc; } +.org-diff-hunk-header { /* diff-hunk-header */ background-color: #cccccc; } +.org-diff-index { /* diff-index */ background-color: #b3b3b3; font-weight: bold; } +.org-diff-nonexistent { /* diff-nonexistent */ background-color: #b3b3b3; font-weight: bold; } +.org-diff-refine-change { /* diff-refine-change */ background-color: #d9d9d9; } +.org-dired-directory { /* dired-directory */ color: #0000ff; } +.org-dired-flagged { /* dired-flagged */ color: #ff0000; font-weight: bold; } +.org-dired-header { /* dired-header */ color: #228b22; } +.org-dired-ignored { /* dired-ignored */ color: #7f7f7f; } +.org-dired-mark { /* dired-mark */ color: #008b8b; } +.org-dired-marked { /* dired-marked */ color: #ff0000; font-weight: bold; } +.org-dired-perm-write { /* dired-perm-write */ color: #b22222; } +.org-dired-symlink { /* dired-symlink */ color: #a020f0; } +.org-dired-warning { /* dired-warning */ color: #ff0000; font-weight: bold; } +.org-doc { /* font-lock-doc-face */ color: #8b2252; } +.org-escape-glyph { /* escape-glyph */ color: #a52a2a; } +.org-file-name-shadow { /* file-name-shadow */ color: #7f7f7f; } +.org-flyspell-duplicate { /* flyspell-duplicate */ color: #cdad00; font-weight: bold; text-decoration: underline; } +.org-flyspell-incorrect { /* flyspell-incorrect */ color: #ff4500; font-weight: bold; text-decoration: underline; } +.org-fringe { /* fringe */ background-color: #f2f2f2; } +.org-function-name { /* font-lock-function-name-face */ color: teal; } +.org-header-line { /* header-line */ color: #333333; background-color: #e5e5e5; } +.org-help-argument-name { /* help-argument-name */ font-style: italic; } +.org-highlight { /* highlight */ background-color: #b4eeb4; } +.org-holiday { /* holiday */ background-color: #ffc0cb; } +.org-isearch { /* isearch */ color: #b0e2ff; background-color: #cd00cd; } +.org-isearch-fail { /* isearch-fail */ background-color: #ffc1c1; } +.org-italic { /* italic */ font-style: italic; } +.org-keyword { /* font-lock-keyword-face */ color: #0086b3; } +.org-lazy-highlight { /* lazy-highlight */ background-color: #afeeee; } +.org-link { /* link */ color: #0000ff; text-decoration: underline; } +.org-link-visited { /* link-visited */ color: #8b008b; text-decoration: underline; } +.org-log-edit-header { /* log-edit-header */ color: #a020f0; } +.org-log-edit-summary { /* log-edit-summary */ color: #0000ff; } +.org-log-edit-unknown-header { /* log-edit-unknown-header */ color: #b22222; } +.org-match { /* match */ background-color: #ffff00; } +.org-next-error { /* next-error */ background-color: #eedc82; } +.org-nobreak-space { /* nobreak-space */ color: #a52a2a; text-decoration: underline; } +.org-org-archived { /* org-archived */ color: #7f7f7f; } +.org-org-block { /* org-block */ color: #7f7f7f; } +.org-org-block-begin-line { /* org-block-begin-line */ color: #b22222; } +.org-org-block-end-line { /* org-block-end-line */ color: #b22222; } +.org-org-checkbox { /* org-checkbox */ font-weight: bold; } +.org-org-checkbox-statistics-done { /* org-checkbox-statistics-done */ color: #228b22; font-weight: bold; } +.org-org-checkbox-statistics-todo { /* org-checkbox-statistics-todo */ color: #ff0000; font-weight: bold; } +.org-org-clock-overlay { /* org-clock-overlay */ background-color: #ffff00; } +.org-org-code { /* org-code */ color: #7f7f7f; } +.org-org-column { /* org-column */ background-color: #e5e5e5; } +.org-org-column-title { /* org-column-title */ background-color: #e5e5e5; font-weight: bold; text-decoration: underline; } +.org-org-date { /* org-date */ color: #a020f0; text-decoration: underline; } +.org-org-document-info { /* org-document-info */ color: #191970; } +.org-org-document-info-keyword { /* org-document-info-keyword */ color: #7f7f7f; } +.org-org-document-title { /* org-document-title */ color: #191970; font-size: 144%; font-weight: bold; } +.org-org-done { /* org-done */ color: #228b22; font-weight: bold; } +.org-org-drawer { /* org-drawer */ color: #0000ff; } +.org-org-ellipsis { /* org-ellipsis */ color: #b8860b; text-decoration: underline; } +.org-org-footnote { /* org-footnote */ color: #a020f0; text-decoration: underline; } +.org-org-formula { /* org-formula */ color: #b22222; } +.org-org-headline-done { /* org-headline-done */ color: #bc8f8f; } +.org-org-hide { /* org-hide */ color: #ffffff; } +.org-org-latex-and-export-specials { /* org-latex-and-export-specials */ color: #8b4513; } +.org-org-level-1 { /* org-level-1 */ color: #0000ff; } +.org-org-level-2 { /* org-level-2 */ color: #a0522d; } +.org-org-level-3 { /* org-level-3 */ color: #a020f0; } +.org-org-level-4 { /* org-level-4 */ color: #b22222; } +.org-org-level-5 { /* org-level-5 */ color: #228b22; } +.org-org-level-6 { /* org-level-6 */ color: #008b8b; } +.org-org-level-7 { /* org-level-7 */ color: #7a378b; } +.org-org-level-8 { /* org-level-8 */ color: #8b2252; } +.org-org-link { /* org-link */ color: #0000ff; text-decoration: underline; } +.org-org-meta-line { /* org-meta-line */ color: #b22222; } +.org-org-mode-line-clock { /* org-mode-line-clock */ color: #000000; background-color: #bfbfbf; } +.org-org-mode-line-clock-overrun { /* org-mode-line-clock-overrun */ color: #000000; background-color: #ff0000; } +.org-org-quote { /* org-quote */ color: #7f7f7f; } +.org-org-scheduled { /* org-scheduled */ color: #006400; } +.org-org-scheduled-previously { /* org-scheduled-previously */ color: #b22222; } +.org-org-scheduled-today { /* org-scheduled-today */ color: #006400; } +.org-org-sexp-date { /* org-sexp-date */ color: #a020f0; } +.org-org-special-keyword { /* org-special-keyword */ color: #a020f0; } +.org-org-table { /* org-table */ color: #0000ff; } +.org-org-tag { /* org-tag */ font-weight: bold; } +.org-org-target { /* org-target */ text-decoration: underline; } +.org-org-time-grid { /* org-time-grid */ color: #b8860b; } +.org-org-todo { /* org-todo */ color: #ff0000; font-weight: bold; } +.org-org-upcoming-deadline { /* org-upcoming-deadline */ color: #b22222; } +.org-org-verbatim { /* org-verbatim */ color: #7f7f7f; } +.org-org-verse { /* org-verse */ color: #7f7f7f; } +.org-org-warning { /* org-warning */ color: #ff0000; font-weight: bold; } +.org-outline-1 { /* outline-1 */ color: #0000ff; } +.org-outline-2 { /* outline-2 */ color: #a0522d; } +.org-outline-3 { /* outline-3 */ color: #a020f0; } +.org-outline-4 { /* outline-4 */ color: #b22222; } 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{ /* tool-bar */ color: #000000; background-color: #bfbfbf; } +.org-tooltip { /* tooltip */ color: #000000; background-color: #ffffe0; } +.org-trailing-whitespace { /* trailing-whitespace */ background-color: #ff0000; } +.org-type { /* font-lock-type-face */ color: #228b22; } +.org-underline { /* underline */ text-decoration: underline; } +.org-variable-name { /* font-lock-variable-name-face */ color: teal; } +.org-warning { /* font-lock-warning-face */ color: #ff0000; font-weight: bold; } +.org-widget-button { /* widget-button */ font-weight: bold; } +.org-widget-button-pressed { /* widget-button-pressed */ color: #ff0000; } +.org-widget-documentation { /* widget-documentation */ color: #006400; } +.org-widget-field { /* widget-field */ background-color: #d9d9d9; } +.org-widget-inactive { /* widget-inactive */ color: #7f7f7f; } +.org-widget-single-line-field { /* widget-single-line-field */ background-color: #d9d9d9; } diff --git a/css/readtheorg.css b/css/readtheorg.css new file mode 100644 index 0000000..1690bd0 --- /dev/null +++ b/css/readtheorg.css @@ -0,0 +1,1095 @@ +@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic|Roboto+Slab:400,700|Inconsolata:400,700); +@import url(https://maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css); + +h1,h2,h3,h4,h5,h6,legend{ + font-family:"Roboto Slab","ff-tisa-web-pro","Georgia",Arial,sans-serif; + font-weight:700; + margin-top:0; +} + +h1{ + font-size:175%; +} + +.subtitle{ + font-size:95%; /* of h1 */ +} + +h2{ + font-size:150%; +} + +h3{ + font-size:125%; +} + +h4{ + font-size:115%; +} + +h5{ + font-size:110%; +} + +h6{ + font-size:100%; +} + +h4,h5,h6{ + color:#2980B9; + font-weight:300; +} + +html{ + -ms-text-size-adjust:100%; + -webkit-text-size-adjust:100%; + font-size:100%; + height:100%; + overflow-x:hidden; +} + +body{ + background:#edf0f2; + color:#404040; + font-family:"Lato","proxima-nova","Helvetica Neue",Arial,sans-serif; + font-weight:normal; + margin:0; + min-height:100%; + overflow-x:hidden; +} + +#content{ + background:#fcfcfc; + height:100%; + margin-left:300px; + /* margin:auto; */ + max-width:1200px; + min-height:100%; + padding:1.618em 3.236em; +} + +p{ + font-size:16px; + line-height:24px; + margin:0px 0px 24px 0px; +} + +b,strong{ + font-weight:bold} + +blockquote{ + background-color: #F0F0F0; + border-left:5px solid #CCCCCC; + font-style:italic; + line-height:24px; + margin:0px 0px 24px 0px; + /* margin-left:24px; */ + padding: 6px 20px; +} + +ul,ol,dl{ + line-height:24px; + list-style-image:none; + /* list-style:none; */ + margin:0px 0px 24px 0px; + padding:0; +} + +li{ + margin-left: 24px; +} + +dd{ + margin:0; +} + +#content .section ul,#content .toctree-wrapper ul,article ul{ + list-style:disc; + line-height:24px; + margin-bottom:24px} + +#content .section ul li,#content .toctree-wrapper ul li,article ul li{ + list-style:disc; + margin-left:24px} + +#content .section ul li p:last-child,#content .toctree-wrapper ul li p:last-child,article ul li p:last-child{ + margin-bottom:0} + +#content .section ul li ul,#content .toctree-wrapper ul li ul,article ul li ul{ + margin-bottom:0} + +#content .section ul li li,#content .toctree-wrapper ul li li,article ul li li{ + list-style:circle} + +#content .section ul li li li,#content .toctree-wrapper ul li li li,article ul li li li{ + list-style:square} + +#content .section ul li ol li,#content .toctree-wrapper ul li ol li,article ul li ol li{ + list-style:decimal} + +#content .section ol,#content ol,article ol{ + list-style:decimal; + line-height:24px; + margin-bottom:24px} + +#content .section ol li,#content ol li,article ol li{ + list-style:decimal; + margin-left:24px} + +#content .section ol li p:last-child,#content ol li p:last-child,article ol li p:last-child{ + margin-bottom:0} + +#content .section ol li ul,#content ol li ul,article ol li ul{ + margin-bottom:0} + +#content .section ol li ul li,#content ol li ul li,article ol li ul li{ + list-style:disc} + +dl dt{ + font-weight:bold; +} + +dl p,dl table,dl ul,dl ol{ + margin-bottom:12px !important; +} + +dl dd{ + margin:0 0 12px 24px; +} + +@media print{ + .codeblock,pre.src{ + white-space:pre.src-wrap} +} + +@media print{ + html,body,section{ + background:none !important} + + *{ + box-shadow:none !important; + text-shadow:none !important; + filter:none !important; + -ms-filter:none !important} + + a,a:visited{ + text-decoration:underline} + + pre.src,blockquote{ + page-break-inside:avoid} + + thead{ + display:table-header-group} + + tr,img{ + page-break-inside:avoid} + + img{ + max-width:100% !important} + + @page{ + margin:0.5cm} + + p,h2,h3{ + orphans:3; + widows:3} + + h2,h3{ + page-break-after:avoid} +} + +@media print{ + #postamble{ + display:none} + + #content{ + margin-left:0} +} + +@media print{ + #table-of-contents{ + display:none} + + @page{ + size: auto; + margin: 25mm 25mm 25mm 25mm;} + + body { + margin: 0px;} +} + +@media screen and (max-width: 768px){ +} + +@media only screen and (max-width: 480px){ +} + +@media screen and (max-width: 768px){ + .tablet-hide{ + display:none} +} + +@media screen and (max-width: 480px){ + .mobile-hide{ + display:none} +} + +@media screen and (max-width: 480px){ +} + +@media screen and (max-width: 768px){ + #content{ + margin-left:0} + + #content #content{ + padding:1.618em} + + #content.shift{ + position:fixed; + min-width:100%; + left:85%; + top:0; + height:100%; + overflow:hidden} +} + +@media screen and (min-width: 1400px){ + #content{ + background:rgba(0,0,0,0.05)} + + #content{ + background:#fcfcfc} +} + +@media screen and (max-width: 768px){ + #copyright{ + width:85%; + display:none} + + #copyright.shift{ + display:block} + + img{ + width:100%; + height:auto} +} + +@media screen and (max-width: 480px){ + #content .sidebar{ + width:100%} +} + +code{ + background:#fff; + border:solid 1px #e1e4e5; + /* color:#000; for clickable code */ + font-family:Consolas,"Andale Mono WT","Andale Mono","Lucida Console","Lucida 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+

Identification of the Stewart Platform using Simscape

+ + +
+

1 Identification

+
+

+The hexapod structure and Sample structure are initialized. +

+
+
initializeHexapod();
+initializeSample();
+
+
+ +
+
G = identifyPlant();
+
+
+
+
+ +
+

2 Cartesian Plot

+
+

+From a force applied in the Cartesian frame to a displacement in the Cartesian frame. +

+
+
figure;
+hold on;
+bode(G.G_cart(1, 1));
+bode(G.G_cart(3, 3));
+hold off;
+
+
+
+
+ +
+

3 From a force to force sensor

+
+
+
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;
+
+
+ +
+
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;
+
+
+
+
+ +
+

4 From a force applied in the leg to the displacement of the leg

+
+
+
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;
+
+
+ +
+
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;
+
+
+
+
+ +
+

5 Transmissibility

+
+
+
figure;
+hold on;
+bode(G.G_tran(1, 1));
+bode(G.G_tran(2, 2));
+bode(G.G_tran(3, 3));
+hold off;
+
+
+ +
+
figure;
+hold on;
+bode(G.G_tran(4, 4));
+bode(G.G_tran(5, 5));
+bode(G.G_tran(6, 6));
+hold off;
+
+
+ +
+
figure;
+hold on;
+bode(G.G_tran(1, 1));
+bode(G.G_tran(2, 1));
+bode(G.G_tran(3, 1));
+hold off;
+
+
+
+
+ +
+

6 Compliance

+
+

+From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base. +

+ +
+
figure;
+hold on;
+bode(G.G_comp(1, 1));
+bode(G.G_comp(2, 2));
+bode(G.G_comp(3, 3));
+hold off;
+
+
+
+
+ +
+

7 Inertial

+
+

+From a force applied on the Cartesian frame to the absolute displacement of the mobile platform. +

+ +
+
figure;
+hold on;
+bode(G.G_iner(1, 1));
+bode(G.G_iner(2, 2));
+bode(G.G_iner(3, 3));
+hold off;
+
+
+
+
+ +
+

8 identifyPlant

+
+
+
function [sys] = identifyPlant(opts_param)
+
+
+ +

+We use this code block to pass optional parameters. +

+
+
%% 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
+
+
+ +

+We defined the options for the linearize command. +Here, we just identify the system at time \(t = 0\). +

+
+
options = linearizeOptions;
+options.SampleTime = 0;
+
+
+ +

+We define the name of the Simulink File used to identification. +

+
+
mdl = 'stewart';
+
+
+ +

+Then we defined the input/output of the transfer function we want to identify. +

+
+
%% 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
+
+
+ +

+The linearization is run. +

+
+
G = linearize(mdl, io, 0);
+
+
+ +

+We defined all the Input/Output names of the identified transfer function. +

+
+
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'};
+
+
+ +

+We split the transfer function into sub transfer functions and we compute their minimum realization. +

+
+
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
+
+
+
+
+
+
+

Author: Thomas Dehaeze

+

Created: 2019-03-22 ven. 12:03

+

Validate

+
+ + diff --git a/identification.org b/identification.org new file mode 100644 index 0000000..d9a291b --- /dev/null +++ b/identification.org @@ -0,0 +1,242 @@ +#+TITLE: Identification of the Stewart Platform using Simscape +:DRAWER: +#+STARTUP: overview + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+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 + <> + 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 diff --git a/index.html b/index.html new file mode 100644 index 0000000..1337f4b --- /dev/null +++ b/index.html @@ -0,0 +1,301 @@ + + + + + + + +Stewart Platform Studies + + + + + + + + + + + + +
+

Stewart Platform Studies

+ + +
+

1 Simscape Model

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+ +
+

2 Architecture Study

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+ +
+
+ +
+

3 Motion Control

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  • Active Damping
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  • Inertial Control
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  • Decentralized Control
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+

Author: Thomas Dehaeze

+

Created: 2019-03-22 ven. 12:03

+

Validate

+
+ + diff --git a/index.org b/index.org index 854377d..5e25b0f 100644 --- a/index.org +++ b/index.org @@ -1,4 +1,4 @@ -#+TITLE: Stewart Platform with Simscape +#+TITLE: Stewart Platform Studies :DRAWER: #+STARTUP: overview @@ -11,6 +11,7 @@ #+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} @@ -23,626 +24,16 @@ #+PROPERTY: header-args:matlab+ :mkdirp yes :END: -#+begin_src matlab :results none - <> - addpath('src'); - addpath('library'); -#+end_src - -#+begin_src matlab :results none - open stewart -#+end_src - -#+begin_src matlab - hexapod = initializeHexapod(); -#+end_src - -#+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 +* Simscape Model +- [[file:simscape-model.org][Model of the Stewart Platform]] +- [[file:identification.org][Identification]] + +* Architecture Study +- [[file:kinematic-study.org][Kinematic Study]] +- [[file:stiffness-study.org][Stiffness Matrix Study]] +- Jacobian Study + +* Motion Control +- Active Damping +- Inertial Control +- Decentralized Control diff --git a/js/bootstrap.min.js b/js/bootstrap.min.js new file mode 100644 index 0000000..c8f82e5 --- /dev/null +++ b/js/bootstrap.min.js @@ -0,0 +1,7 @@ +/*! + * Bootstrap v3.3.4 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