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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>
<li><a href="#orgac71426">1. Functions</a>
<ul>
<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>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgac71426" class="outline-2">
<h2 id="orgac71426"><span class="section-number-2">1</span> Functions</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org8643823"></a>
</p>
</div>
<div id="outline-container-orga30ed3e" class="outline-3">
<h3 id="orga30ed3e"><span class="section-number-3">1.1</span> computePsdDispl</h3>
<div class="outline-text-3" id="text-1-1">
<p>
<a id="orgeb6170e"></a>
</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>
</div>
</div>
</div>
<div id="outline-container-org164599d" class="outline-3">
<h3 id="org164599d"><span class="section-number-3">1.2</span> computeSetpoint</h3>
<div class="outline-text-3" id="text-1-2">
<p>
<a id="org5f98a47"></a>
</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>
<div id="outline-container-org0d7c91f" class="outline-3">
<h3 id="org0d7c91f"><span class="section-number-3">1.3</span> converErrorBasis</h3>
<div class="outline-text-3" id="text-1-3">
<p>
<a id="orgdf67397"></a>
</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>
<div id="outline-container-orge57e769" class="outline-3">
<h3 id="orge57e769"><span class="section-number-3">1.4</span> generateDiagPidControl</h3>
<div class="outline-text-3" id="text-1-4">
<p>
<a id="org94ba4ce"></a>
</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>
<div id="outline-container-orgb953a5b" class="outline-3">
<h3 id="orgb953a5b"><span class="section-number-3">1.5</span> identifyPlant</h3>
<div class="outline-text-3" id="text-1-5">
<p>
<a id="org2662524"></a>
</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>
<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>
<div class="outline-text-3" id="text-1-6">
<p>
<a id="org7102666"></a>
</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>
<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">
<p>
<a id="org11721fe"></a>
</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>
<p class="date">Created: 2019-12-12 jeu. 11:25</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>