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< h1 class = "title" > Matlab Functions used for the NASS Project< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#orgac71426" > 1. Functions< / a >
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< ul >
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< li > < a href = "#orga30ed3e" > 1.1. computePsdDispl< / a > < / li >
< li > < a href = "#org164599d" > 1.2. computeSetpoint< / a > < / li >
< li > < a href = "#org0d7c91f" > 1.3. converErrorBasis< / a > < / li >
< li > < a href = "#orge57e769" > 1.4. generateDiagPidControl< / a > < / li >
< li > < a href = "#orgb953a5b" > 1.5. identifyPlant< / a > < / li >
< li > < a href = "#org442df30" > 1.6. Inverse Kinematics of the Hexapod< / a > < / li >
< li > < a href = "#orgce14673" > 1.7. computeReferencePose< / a > < / li >
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< div id = "outline-container-orgac71426" class = "outline-2" >
< h2 id = "orgac71426" > < span class = "section-number-2" > 1< / span > Functions< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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< a id = "org8643823" > < / a >
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< / p >
< / div >
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< div id = "outline-container-orga30ed3e" class = "outline-3" >
< h3 id = "orga30ed3e" > < span class = "section-number-3" > 1.1< / span > computePsdDispl< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
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< a id = "orgeb6170e" > < / a >
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< / p >
< p >
This Matlab function is accessible < a href = "../src/computePsdDispl.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > psd_object< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > computePsdDispl< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > sys_data< / span > , < span class = "org-variable-name" > t_init< / span > , < span class = "org-variable-name" > n_av< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
i_init = find< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.time < span class = "org-type" > > < / span > t_init, < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
han_win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > length< span class = "org-rainbow-delimiters-depth-3" > (< / span > sys_data.Dx< span class = "org-rainbow-delimiters-depth-4" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > /< / span > n_av< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > sys_data.time< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pdx, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.Dx< span class = "org-rainbow-delimiters-depth-2" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , han_win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pdy, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.Dy< span class = "org-rainbow-delimiters-depth-2" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , han_win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pdz, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.Dz< span class = "org-rainbow-delimiters-depth-2" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , han_win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > prx, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.Rx< span class = "org-rainbow-delimiters-depth-2" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , han_win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pry, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.Ry< span class = "org-rainbow-delimiters-depth-2" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , han_win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > prz, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys_data.Rz< span class = "org-rainbow-delimiters-depth-2" > (< / span > i_init< span class = "org-type" > :< / span > end, < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , han_win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
psd_object = struct< span class = "org-rainbow-delimiters-depth-1" > (< / span > ...
< span class = "org-string" > 'f'< / span > , f, ...
< span class = "org-string" > 'dx'< / span > , pdx, ...
< span class = "org-string" > 'dy'< / span > , pdy, ...
< span class = "org-string" > 'dz'< / span > , pdz, ...
< span class = "org-string" > 'rx'< / span > , prx, ...
< span class = "org-string" > 'ry'< / span > , pry, ...
< span class = "org-string" > 'rz'< / span > , prz< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
< / pre >
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< div id = "outline-container-org164599d" class = "outline-3" >
< h3 id = "org164599d" > < span class = "section-number-3" > 1.2< / span > computeSetpoint< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
< p >
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< a id = "org5f98a47" > < / a >
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< / p >
< p >
This Matlab function is accessible < a href = "../src/computeSetpoint.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > setpoint< / span > = < span class = "org-function-name" > computeSetpoint< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > ty< / span > , < span class = "org-variable-name" > ry< / span > , < span class = "org-variable-name" > rz< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %%< / span > < / span >
setpoint = zeros< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Ty< / span > < / span >
Ty = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ty ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
% Tyinv = [< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
% < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-type" > -< / span > ty ;
% < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
% < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > ];
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Ry< / span > < / span >
Ry = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-comment" > % TMry = Ty*Ry*Tyinv;< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Rz< / span > < / span >
Rz = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-comment" > % TMrz = Ty*TMry*Rz*TMry'*Tyinv;< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% All stages< / span > < / span >
< span class = "org-comment" > % < / span > < span class = "org-comment" > < span class = "org-constant" > TM < / span > < / span > < span class = "org-comment" > = TMrz*TMry*Ty;< / span >
TM = Ty< span class = "org-type" > *< / span > Ry< span class = "org-type" > *< / span > Rz;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > thetax, thetay, thetaz< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = RM2angle< span class = "org-rainbow-delimiters-depth-1" > (< / span > TM< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
setpoint< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = TM< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
setpoint< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = < span class = "org-rainbow-delimiters-depth-1" > [< / span > thetax, thetay, thetaz< span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Custom Functions< / span > < / span >
< span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > thetax, thetay, thetaz< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > RM2angle< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > R< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-keyword" > if< / span > abs< span class = "org-rainbow-delimiters-depth-1" > (< / span > abs< span class = "org-rainbow-delimiters-depth-2" > (< / span > R< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > > < / span > < span class = "org-highlight-numbers-number" > 1e< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6< / span > % R31 < span class = "org-type" > !< / span > = < span class = "org-highlight-numbers-number" > 1< / span > and R31 < span class = "org-type" > !< / span > = < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span >
thetay = < span class = "org-type" > -< / span > asin< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
thetax = atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > , R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
thetaz = atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > , R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > else< / span >
thetaz = < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-keyword" > if< / span > abs< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > +< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > < < / span > < span class = "org-highlight-numbers-number" > 1e< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6< / span > % R31 = < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span >
thetay = < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
thetax = thetaz < span class = "org-type" > +< / span > atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > else< / span >
thetay = < span class = "org-type" > -< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
thetax = < span class = "org-type" > -< / span > thetaz < span class = "org-type" > +< / span > atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > -< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-type" > -< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
2019-12-12 11:26:27 +01:00
< div id = "outline-container-org0d7c91f" class = "outline-3" >
< h3 id = "org0d7c91f" > < span class = "section-number-3" > 1.3< / span > converErrorBasis< / h3 >
2019-12-11 17:33:45 +01:00
< div class = "outline-text-3" id = "text-1-3" >
< p >
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< a id = "orgdf67397" > < / a >
2019-12-11 17:33:45 +01:00
< / p >
< p >
This Matlab function is accessible < a href = "../src/converErrorBasis.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > error_nass< / span > = < span class = "org-function-name" > convertErrorBasis< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > pos< / span > , < span class = "org-variable-name" > setpoint< / span > , < span class = "org-variable-name" > ty< / span > , < span class = "org-variable-name" > ry< / span > , < span class = "org-variable-name" > rz< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-comment" > % convertErrorBasis -< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Syntax: convertErrorBasis(p_error, ty, ry, rz)< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Inputs:< / span >
< span class = "org-comment" > % - p_error - Position error of the sample w.r.t. the granite [m, rad]< / span >
< span class = "org-comment" > % - ty - Measured translation of the Ty stage [m]< / span >
< span class = "org-comment" > % - ry - Measured rotation of the Ry stage [rad]< / span >
< span class = "org-comment" > % - rz - Measured rotation of the Rz stage [rad]< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Outputs:< / span >
< span class = "org-comment" > % - P_nass - Position error of the sample w.r.t. the NASS base [m]< / span >
< span class = "org-comment" > % - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Example:< / span >
< span class = "org-comment" > %< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% If line vector => column vector< / span > < / span >
< span class = "org-keyword" > if< / span > size< span class = "org-rainbow-delimiters-depth-1" > (< / span > pos, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-highlight-numbers-number" > 6< / span >
pos = pos< span class = "org-type" > '< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > if< / span > size< span class = "org-rainbow-delimiters-depth-1" > (< / span > setpoint, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-highlight-numbers-number" > 6< / span >
setpoint = setpoint< span class = "org-type" > '< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Position of the sample in the frame fixed to the Granite< / span > < / span >
P_granite = < span class = "org-rainbow-delimiters-depth-1" > [< / span > pos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ; < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ; < span class = "org-comment" > % Position [m]< / span >
R_granite = < span class = "org-rainbow-delimiters-depth-1" > [< / span > setpoint< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ; < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ; < span class = "org-comment" > % Reference [m]< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Transformation matrices of the stages< / span > < / span >
< span class = "org-comment" > % T-y< / span >
TMty = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ty ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-comment" > % R-y< / span >
TMry = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-comment" > % R-z< / span >
TMrz = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Compute Point coordinates in the new reference fixed to the NASS base< / span > < / span >
< span class = "org-comment" > % P_nass = TMrz*TMry*TMty*P_granite;< / span >
P_nass = TMrz< span class = "org-type" > \< / span > TMry< span class = "org-type" > \< / span > TMty< span class = "org-type" > \< / span > P_granite;
R_nass = TMrz< span class = "org-type" > \< / span > TMry< span class = "org-type" > \< / span > TMty< span class = "org-type" > \< / span > R_granite;
dx = R_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > P_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
dy = R_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > P_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
dz = R_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > P_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Compute new basis vectors linked to the NASS base< / span > < / span >
% ux_nass = TMrz< span class = "org-type" > *< / span > TMry< span class = "org-type" > *< / span > TMty< span class = "org-type" > *< / span > [< span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ];
% ux_nass = ux_nass(< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > );
% uy_nass = TMrz< span class = "org-type" > *< / span > TMry< span class = "org-type" > *< / span > TMty< span class = "org-type" > *< / span > [< span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ];
% uy_nass = uy_nass(< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > );
% uz_nass = TMrz< span class = "org-type" > *< / span > TMry< span class = "org-type" > *< / span > TMty< span class = "org-type" > *< / span > [< span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ];
% uz_nass = uz_nass(< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > );
ux_nass = TMrz< span class = "org-type" > \< / span > TMry< span class = "org-type" > \< / span > TMty< span class = "org-type" > \< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
ux_nass = ux_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
uy_nass = TMrz< span class = "org-type" > \< / span > TMry< span class = "org-type" > \< / span > TMty< span class = "org-type" > \< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
uy_nass = uy_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
uz_nass = TMrz< span class = "org-type" > \< / span > TMry< span class = "org-type" > \< / span > TMty< span class = "org-type" > \< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
uz_nass = uz_nass< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Rotations error w.r.t. granite Frame< / span > < / span >
< span class = "org-comment" > % Rotations error w.r.t. granite Frame< / span >
rx_nass = pos< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ry_nass = pos< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
rz_nass = pos< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % Rotation matrices of the Sample w.r.t. the Granite< / span >
Mrx_error = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rx_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rx_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rx_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rx_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Mry_error = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > ry_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > ry_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > ry_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > ry_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Mrz_error = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rz_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rz_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rz_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > -< / span > rz_nass< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-comment" > % Rotation matrix of the Sample w.r.t. the Granite< / span >
Mr_error = Mrz_error< span class = "org-type" > *< / span > Mry_error< span class = "org-type" > *< / span > Mrx_error;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Use matrix to solve< / span > < / span >
R = Mr_error< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > ux_nass, uy_nass, uz_nass< span class = "org-rainbow-delimiters-depth-1" > ]< / span > ; < span class = "org-comment" > % Rotation matrix from NASS base to Sample< / span >
< span class = "org-rainbow-delimiters-depth-1" > [< / span > thetax, thetay, thetaz< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = RM2angle< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
error_nass = < span class = "org-rainbow-delimiters-depth-1" > [< / span > dx; dy; dz; thetax; thetay; thetaz< span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Custom Functions< / span > < / span >
< span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > thetax, thetay, thetaz< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > RM2angle< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > R< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-keyword" > if< / span > abs< span class = "org-rainbow-delimiters-depth-1" > (< / span > abs< span class = "org-rainbow-delimiters-depth-2" > (< / span > R< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > > < / span > < span class = "org-highlight-numbers-number" > 1e< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6< / span > % R31 < span class = "org-type" > !< / span > = < span class = "org-highlight-numbers-number" > 1< / span > and R31 < span class = "org-type" > !< / span > = < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span >
thetay = < span class = "org-type" > -< / span > asin< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % thetaybis = pi-thetay;< / span >
thetax = atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > , R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
% thetaxbis = atan2(R(< span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 2< / span > )< span class = "org-type" > /< / span > cos(thetaybis), R(< span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 3< / span > )< span class = "org-type" > /< / span > cos(thetaybis));
thetaz = atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > , R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > thetay< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
% thetazbis = atan2(R(< span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > )< span class = "org-type" > /< / span > cos(thetaybis), R(< span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 1< / span > )< span class = "org-type" > /< / span > cos(thetaybis));
< span class = "org-keyword" > else< / span >
thetaz = < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-keyword" > if< / span > abs< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > +< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > < < / span > < span class = "org-highlight-numbers-number" > 1e< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6< / span > % R31 = < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span >
thetay = < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
thetax = thetaz < span class = "org-type" > +< / span > atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > else< / span >
thetay = < span class = "org-type" > -< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
thetax = < span class = "org-type" > -< / span > thetaz < span class = "org-type" > +< / span > atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > -< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-type" > -< / span > R< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
2019-12-12 11:26:27 +01:00
< div id = "outline-container-orge57e769" class = "outline-3" >
< h3 id = "orge57e769" > < span class = "section-number-3" > 1.4< / span > generateDiagPidControl< / h3 >
2019-12-11 17:33:45 +01:00
< div class = "outline-text-3" id = "text-1-4" >
< p >
2019-12-12 11:26:27 +01:00
< a id = "org94ba4ce" > < / a >
2019-12-11 17:33:45 +01:00
< / p >
< p >
This Matlab function is accessible < a href = "../src/generateDiagPidControl.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > K< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > generateDiagPidControl< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > G< / span > , < span class = "org-variable-name" > fs< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %%< / span > < / span >
pid_opts = pidtuneOptions< span class = "org-rainbow-delimiters-depth-1" > (< / span > ...
< span class = "org-string" > 'PhaseMargin'< / span > , < span class = "org-highlight-numbers-number" > 50< / span > , ...
< span class = "org-string" > 'DesignFocus'< / span > , < span class = "org-string" > 'disturbance-rejection'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %%< / span > < / span >
K = tf< span class = "org-rainbow-delimiters-depth-1" > (< / span > zeros< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > :< / span > < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 6< / span > < / span >
input_name = G.InputName< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
output_name = G.OutputName< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
K< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > , < span class = "org-constant" > i< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = tf< span class = "org-rainbow-delimiters-depth-1" > (< / span > pidtune< span class = "org-rainbow-delimiters-depth-2" > (< / span > minreal< span class = "org-rainbow-delimiters-depth-3" > (< / span > G< span class = "org-rainbow-delimiters-depth-4" > (< / span > output_name, input_name< span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > , < span class = "org-string" > 'PIDF'< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > fs, pid_opts< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
K.InputName = G.OutputName;
K.OutputName = G.InputName;
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgb953a5b" class = "outline-3" >
< h3 id = "orgb953a5b" > < span class = "section-number-3" > 1.5< / span > identifyPlant< / h3 >
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< div class = "outline-text-3" id = "text-1-5" >
< p >
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< a id = "org2662524" > < / a >
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< / p >
< p >
This Matlab function is accessible < a href = "../src/identifyPlant.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > sys< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > identifyPlant< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > opts_param< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Default values for opts< / span > < / span >
opts = struct< span class = "org-rainbow-delimiters-depth-1" > ()< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Populate opts with input parameters< / span > < / span >
< span class = "org-keyword" > if< / span > exist< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'opts_param'< / span > ,< span class = "org-string" > 'var'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > opt< / span > = < span class = "org-constant" > fieldnames< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-constant" > opts_param< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-constant" > '< / span >
opts.< span class = "org-rainbow-delimiters-depth-1" > (< / span > opt< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = opts_param.< span class = "org-rainbow-delimiters-depth-1" > (< / span > opt< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'sim_nano_station_id'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fn'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Cartesian forces applied by NASS< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dw'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Ground Motion< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fs'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % External forces on the sample< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fnl'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Forces applied on the NASS's legs< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fd'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Disturbance Forces< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dsm'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Displacement of the sample< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 7< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fnlm'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Force sensor in NASS's legs< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 8< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dnlm'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Displacement of NASS's legs< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 9< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Es'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Position Error w.r.t. NASS base< / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Vlm'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Measured absolute velocity of the legs< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize< span class = "org-rainbow-delimiters-depth-1" > (< / span > mdl, io, options< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
G.InputName = < span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > , ...
< span class = "org-string" > 'Dgx'< / span > , < span class = "org-string" > 'Dgy'< / span > , < span class = "org-string" > 'Dgz'< / span > , ...
< span class = "org-string" > 'Fsx'< / span > , < span class = "org-string" > 'Fsy'< / span > , < span class = "org-string" > 'Fsz'< / span > , < span class = "org-string" > 'Msx'< / span > , < span class = "org-string" > 'Msy'< / span > , < span class = "org-string" > 'Msz'< / span > , ...
< span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > , ...
< span class = "org-string" > 'Frzz'< / span > , < span class = "org-string" > 'Ftyx'< / span > , < span class = "org-string" > 'Ftyz'< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > ;
G.OutputName = < span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-string" > 'Dx'< / span > , < span class = "org-string" > 'Dy'< / span > , < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Rx'< / span > , < span class = "org-string" > 'Ry'< / span > , < span class = "org-string" > 'Rz'< / span > , ...
< span class = "org-string" > 'Fm1'< / span > , < span class = "org-string" > 'Fm2'< / span > , < span class = "org-string" > 'Fm3'< / span > , < span class = "org-string" > 'Fm4'< / span > , < span class = "org-string" > 'Fm5'< / span > , < span class = "org-string" > 'Fm6'< / span > , ...
< span class = "org-string" > 'Dm1'< / span > , < span class = "org-string" > 'Dm2'< / span > , < span class = "org-string" > 'Dm3'< / span > , < span class = "org-string" > 'Dm4'< / span > , < span class = "org-string" > 'Dm5'< / span > , < span class = "org-string" > 'Dm6'< / span > , ...
< span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > , ...
< span class = "org-string" > 'Vm1'< / span > , < span class = "org-string" > 'Vm2'< / span > , < span class = "org-string" > 'Vm3'< / span > , < span class = "org-string" > 'Vm4'< / span > , < span class = "org-string" > 'Vm5'< / span > , < span class = "org-string" > 'Vm6'< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Create the sub transfer functions< / span > < / span >
minreal_tol = sqrt< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > eps< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From forces applied in the cartesian frame to displacement of the sample in the cartesian frame< / span >
sys.G_cart = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Dx'< / span > , < span class = "org-string" > 'Dy'< / span > , < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Rx'< / span > , < span class = "org-string" > 'Ry'< / span > , < span class = "org-string" > 'Rz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From ground motion to Sample displacement< / span >
sys.G_gm = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Dx'< / span > , < span class = "org-string" > 'Dy'< / span > , < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Rx'< / span > , < span class = "org-string" > 'Ry'< / span > , < span class = "org-string" > 'Rz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Dgx'< / span > , < span class = "org-string" > 'Dgy'< / span > , < span class = "org-string" > 'Dgz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From direct forces applied on the sample to displacement of the sample< / span >
sys.G_fs = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Dx'< / span > , < span class = "org-string" > 'Dy'< / span > , < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Rx'< / span > , < span class = "org-string" > 'Ry'< / span > , < span class = "org-string" > 'Rz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Fsx'< / span > , < span class = "org-string" > 'Fsy'< / span > , < span class = "org-string" > 'Fsz'< / span > , < span class = "org-string" > 'Msx'< / span > , < span class = "org-string" > 'Msy'< / span > , < span class = "org-string" > 'Msz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From forces applied on NASS's legs to force sensor in each leg< / span >
sys.G_iff = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Fm1'< / span > , < span class = "org-string" > 'Fm2'< / span > , < span class = "org-string" > 'Fm3'< / span > , < span class = "org-string" > 'Fm4'< / span > , < span class = "org-string" > 'Fm5'< / span > , < span class = "org-string" > 'Fm6'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From forces applied on NASS's legs to displacement of each leg< / span >
sys.G_dleg = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Dm1'< / span > , < span class = "org-string" > 'Dm2'< / span > , < span class = "org-string" > 'Dm3'< / span > , < span class = "org-string" > 'Dm4'< / span > , < span class = "org-string" > 'Dm5'< / span > , < span class = "org-string" > 'Dm6'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From forces/torques applied by the NASS to position error< / span >
sys.G_plant = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Edx'< / span > , < span class = "org-string" > 'Edy'< / span > , < span class = "org-string" > 'Edz'< / span > , < span class = "org-string" > 'Erx'< / span > , < span class = "org-string" > 'Ery'< / span > , < span class = "org-string" > 'Erz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Fnx'< / span > , < span class = "org-string" > 'Fny'< / span > , < span class = "org-string" > 'Fnz'< / span > , < span class = "org-string" > 'Mnx'< / span > , < span class = "org-string" > 'Mny'< / span > , < span class = "org-string" > 'Mnz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From forces/torques applied by the NASS to velocity of the actuator< / span >
sys.G_geoph = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Vm1'< / span > , < span class = "org-string" > 'Vm2'< / span > , < span class = "org-string" > 'Vm3'< / span > , < span class = "org-string" > 'Vm4'< / span > , < span class = "org-string" > 'Vm5'< / span > , < span class = "org-string" > 'Vm6'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'F1'< / span > , < span class = "org-string" > 'F2'< / span > , < span class = "org-string" > 'F3'< / span > , < span class = "org-string" > 'F4'< / span > , < span class = "org-string" > 'F5'< / span > , < span class = "org-string" > 'F6'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % From various disturbance forces to position error< / span >
sys.G_dist = minreal< span class = "org-rainbow-delimiters-depth-1" > (< / span > G< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Dx'< / span > , < span class = "org-string" > 'Dy'< / span > , < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Rx'< / span > , < span class = "org-string" > 'Ry'< / span > , < span class = "org-string" > 'Rz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > , < span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-string" > 'Frzz'< / span > , < span class = "org-string" > 'Ftyx'< / span > , < span class = "org-string" > 'Ftyz'< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , minreal_tol, < span class = "org-constant" > false< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% We remove low frequency and high frequency dynamics that are usually unstable< / span > < / span >
< span class = "org-comment" > % using =freqsep= is risky as it may change the shape of the transfer functions< / span >
% f_min = < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > ; % [Hz]
% f_max = < span class = "org-highlight-numbers-number" > 1e4< / span > ; % [Hz]
% [< span class = "org-type" > ~< / span > , sys.G_cart] = freqsep(freqsep(sys.G_cart, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_max), < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_min);
% [< span class = "org-type" > ~< / span > , sys.G_gm] = freqsep(freqsep(sys.G_gm, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_max), < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_min);
% [< span class = "org-type" > ~< / span > , sys.G_fs] = freqsep(freqsep(sys.G_fs, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_max), < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_min);
% [< span class = "org-type" > ~< / span > , sys.G_iff] = freqsep(freqsep(sys.G_iff, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_max), < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_min);
% [< span class = "org-type" > ~< / span > , sys.G_dleg] = freqsep(freqsep(sys.G_dleg, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_max), < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_min);
% [< span class = "org-type" > ~< / span > , sys.G_plant] = freqsep(freqsep(sys.G_plant, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_max), < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f_min);
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% We finally verify that the system is stable< / span > < / span >
< span class = "org-keyword" > if< / span > < span class = "org-type" > ~< / span > isstable< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys.G_cart< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ||< / span > < span class = "org-type" > ~< / span > isstable< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys.G_gm< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ||< / span > < span class = "org-type" > ~< / span > isstable< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys.G_fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ||< / span > < span class = "org-type" > ~< / span > isstable< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys.G_iff< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ||< / span > < span class = "org-type" > ~< / span > isstable< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys.G_dleg< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ||< / span > < span class = "org-type" > ~< / span > isstable< span class = "org-rainbow-delimiters-depth-1" > (< / span > sys.G_plant< span class = "org-rainbow-delimiters-depth-1" > )< / span >
warning< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'One of the identified system is unstable'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org442df30" class = "outline-3" >
< h3 id = "org442df30" > < span class = "section-number-3" > 1.6< / span > Inverse Kinematics of the Hexapod< / h3 >
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< div class = "outline-text-3" id = "text-1-6" >
< p >
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< a id = "org7102666" > < / a >
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< / p >
< p >
This Matlab function is accessible < a href = "src/inverseKinematicsHexapod.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > L< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > inverseKinematicsHexapod< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > hexapod< / span > , < span class = "org-variable-name" > AP< / span > , < span class = "org-variable-name" > ARB< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-comment" > % inverseKinematicsHexapod - Compute the initial position of each leg to have the wanted Hexapod's position< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Syntax: inverseKinematicsHexapod(hexapod, AP, ARB)< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Inputs:< / span >
< span class = "org-comment" > % - hexapod - Hexapod object containing the geometry of the hexapod< / span >
< span class = "org-comment" > % - AP - Position vector of point OB expressed in frame {A} in [m]< / span >
< span class = "org-comment" > % - ARB - Rotation Matrix expressed in frame {A}< / span >
< span class = "org-comment" > % Wanted Length of the hexapod's legs [m]< / span >
L = zeros< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > :length< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-constant" > L< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span >
Bbi = hexapod.pos_top_tranform< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > , < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > '< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1e< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; hexapod.TP.thickness< span class = "org-type" > +< / span > hexapod.Leg.sphere.top< span class = "org-type" > +< / span > hexapod.SP.thickness.top< span class = "org-type" > +< / span > hexapod.jacobian< span class = "org-rainbow-delimiters-depth-1" > ]< / span > ; < span class = "org-comment" > % [m]< / span >
Aai = hexapod.pos_base< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > , < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > '< / span > < span class = "org-type" > +< / span > < span class = "org-highlight-numbers-number" > 1e< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > ; < span class = "org-highlight-numbers-number" > 0< / span > ; hexapod.BP.thickness< span class = "org-type" > +< / span > hexapod.Leg.sphere.bottom< span class = "org-type" > +< / span > hexapod.SP.thickness.bottom< span class = "org-type" > -< / span > hexapod.h< span class = "org-type" > -< / span > hexapod.jacobian< span class = "org-rainbow-delimiters-depth-1" > ]< / span > ; < span class = "org-comment" > % [m]< / span >
L< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = sqrt< span class = "org-rainbow-delimiters-depth-1" > (< / span > AP< span class = "org-type" > '*< / span > AP < span class = "org-type" > +< / span > Bbi< span class = "org-type" > '*< / span > Bbi < span class = "org-type" > +< / span > Aai< span class = "org-type" > '*< / span > Aai < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > AP< span class = "org-type" > '*< / span > Aai < span class = "org-type" > +< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > AP< span class = "org-type" > '*< / span > < span class = "org-rainbow-delimiters-depth-2" > (< / span > ARB< span class = "org-type" > *< / span > Bbi< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-2" > (< / span > ARB< span class = "org-type" > *< / span > Bbi< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > '*< / span > Aai< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgce14673" class = "outline-3" >
< h3 id = "orgce14673" > < span class = "section-number-3" > 1.7< / span > computeReferencePose< / h3 >
< div class = "outline-text-3" id = "text-1-7" >
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< p >
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< a id = "org11721fe" > < / a >
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< / p >
< p >
This Matlab function is accessible < a href = "src/computeReferencePose.m" > here< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > function< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < / span > < span class = "org-variable-name" > WTr< / span > < span class = "org-variable-name" > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > < / span > = < span class = "org-function-name" > computeReferencePose< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > Dy< / span > , < span class = "org-variable-name" > Ry< / span > , < span class = "org-variable-name" > Rz< / span > , < span class = "org-variable-name" > Dh< / span > , < span class = "org-variable-name" > Dn< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< span class = "org-comment" > % computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Inputs:< / span >
< span class = "org-comment" > % - Dy - Reference of the Translation Stage [m]< / span >
< span class = "org-comment" > % - Ry - Reference of the Tilt Stage [rad]< / span >
< span class = "org-comment" > % - Rz - Reference of the Spindle [rad]< / span >
< span class = "org-comment" > % - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad]< / span >
< span class = "org-comment" > % - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad]< / span >
< span class = "org-comment" > %< / span >
< span class = "org-comment" > % Outputs:< / span >
< span class = "org-comment" > % - WTr -< / span >
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Translation Stage< / span > < / span >
Rty = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > Dy;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Tilt Stage - Pure rotating aligned with Ob< / span > < / span >
Rry = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Ry< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Spindle - Rotation along the Z axis< / span > < / span >
Rrz = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Rz< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Micro-Hexapod< / span > < / span >
Rhx = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rhy = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rhz = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dh< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rh = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > Dh< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > Dh< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > Dh< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rh< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = Rhz< span class = "org-type" > *< / span > Rhy< span class = "org-type" > *< / span > Rhx;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Nano-Hexapod< / span > < / span >
Rnx = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rny = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rnz = < span class = "org-rainbow-delimiters-depth-1" > [< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
sin< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > cos< span class = "org-rainbow-delimiters-depth-2" > (< / span > Dn< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 6< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rn = < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > Dn< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-highlight-numbers-number" > 0< / span > Dn< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > Dn< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > ;
< span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
Rn< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = Rnx< span class = "org-type" > *< / span > Rny< span class = "org-type" > *< / span > Rnz;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Total Homogeneous transformation< / span > < / span >
WTr = Rty< span class = "org-type" > *< / span > Rry< span class = "org-type" > *< / span > Rrz< span class = "org-type" > *< / span > Rh< span class = "org-type" > *< / span > Rn;
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2019-12-12 11:26:27 +01:00
< p class = "date" > Created: 2019-12-12 jeu. 11:25< / p >
2019-12-11 17:33:45 +01:00
< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
