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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="#orgdc168b9">1. computeReferencePose</a></li>
<li><a href="#org493ab7f">2. Compute the Sample Position Error w.r.t. the NASS</a></li>
</ul>
</div>
</div>

<div id="outline-container-orgdc168b9" class="outline-2">
<h2 id="orgdc168b9"><span class="section-number-2">1</span> computeReferencePose</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org98cbe6e"></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">[WTr]</span> = <span class="org-function-name">computeReferencePose</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-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 = [1 0 0 0;
         0 1 0 Dy;
         0 0 1 0;
         0 0 0 1];

  <span class="org-matlab-cellbreak"><span class="org-comment">%% Tilt Stage - Pure rotating aligned with Ob</span></span>
  Rry = [ cos(Ry) 0 sin(Ry) 0;
          0       1 0       0;
         <span class="org-type">-</span>sin(Ry) 0 cos(Ry) 0;
          0       0 0       1];

  <span class="org-matlab-cellbreak"><span class="org-comment">%% Spindle - Rotation along the Z axis</span></span>
  Rrz = [cos(Rz) <span class="org-type">-</span>sin(Rz) 0 0 ;
         sin(Rz)  cos(Rz) 0 0 ;
         0        0       1 0 ;
         0        0       0 1 ];


  <span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
  Rhx = [1 0           0;
         0 cos(Dh(4)) <span class="org-type">-</span>sin(Dh(4));
         0 sin(Dh(4))  cos(Dh(4))];

  Rhy = [ cos(Dh(5)) 0 sin(Dh(5));
         0           1 0;
         <span class="org-type">-</span>sin(Dh(5)) 0 cos(Dh(5))];

  Rhz = [cos(Dh(6)) <span class="org-type">-</span>sin(Dh(6)) 0;
         sin(Dh(6))  cos(Dh(6)) 0;
         0           0          1];

  Rh = [1 0 0 Dh(1) ;
        0 1 0 Dh(2) ;
        0 0 1 Dh(3) ;
        0 0 0 1 ];

  Rh(1<span class="org-type">:</span>3, 1<span class="org-type">:</span>3) = 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 = [1 0           0;
         0 cos(Dn(4)) <span class="org-type">-</span>sin(Dn(4));
         0 sin(Dn(4))  cos(Dn(4))];

  Rny = [ cos(Dn(5)) 0 sin(Dn(5));
         0           1 0;
         <span class="org-type">-</span>sin(Dn(5)) 0 cos(Dn(5))];

  Rnz = [cos(Dn(6)) <span class="org-type">-</span>sin(Dn(6)) 0;
         sin(Dn(6))  cos(Dn(6)) 0;
         0           0          1];

  Rn = [1 0 0 Dn(1) ;
        0 1 0 Dn(2) ;
        0 0 1 Dn(3) ;
        0 0 0 1 ];

  Rn(1<span class="org-type">:</span>3, 1<span class="org-type">:</span>3) = Rnz<span class="org-type">*</span>Rny<span class="org-type">*</span>Rnx;

  <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 id="outline-container-org493ab7f" class="outline-2">
<h2 id="org493ab7f"><span class="section-number-2">2</span> Compute the Sample Position Error w.r.t. the NASS</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org6dcd4fb"></a>
</p>

<p>
This Matlab function is accessible <a href="..//src/computeSampleError.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">[MTr]</span> = <span class="org-function-name">computeSampleError</span>(<span class="org-variable-name">WTm</span>, <span class="org-variable-name">WTr</span>)
<span class="org-comment">% computeSampleError -</span>
<span class="org-comment">%</span>
<span class="org-comment">% Syntax: [MTr] = computeSampleError(WTm, WTr)</span>
<span class="org-comment">%</span>
<span class="org-comment">% Inputs:</span>
<span class="org-comment">%    - WTm - Homoegeneous transformation that represent the</span>
<span class="org-comment">%            wanted pose of the sample with respect to the granite</span>
<span class="org-comment">%    - WTr - Homoegeneous transformation that represent the</span>
<span class="org-comment">%            measured pose of the sample with respect to the granite</span>
<span class="org-comment">%</span>
<span class="org-comment">% Outputs:</span>
<span class="org-comment">%    - MTr - Homoegeneous transformation that represent the</span>
<span class="org-comment">%            wanted pose of the sample expressed in a frame</span>
<span class="org-comment">%            attached to the top platform of the nano-hexapod</span>

MTr = zeros(4,4);

MTr = [WTm(1<span class="org-type">:</span>3,1<span class="org-type">:</span>3)<span class="org-type">'</span>, <span class="org-type">-</span>WTm(1<span class="org-type">:</span>3,1<span class="org-type">:</span>3)<span class="org-type">'*</span>WTm(1<span class="org-type">:</span>3,4) ; 0 0 0 1]<span class="org-type">*</span>WTr;
<span class="org-keyword">end</span>
</pre>
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<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-03-17 mar. 17:28</p>
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