808 lines
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808 lines
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Tomography Experiment</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgc1ba6cb">1. Simscape Model</a></li>
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<li><a href="#orgf0c34e6">2. Tomography Experiment with no disturbances</a>
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<ul>
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<li><a href="#orge470384">2.1. Simulation Setup</a></li>
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<li><a href="#orgf23b2a2">2.2. Analysis</a></li>
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<li><a href="#orged24ea9">2.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgbdf5d41">3. Tomography Experiment with included perturbations</a>
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<ul>
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<li><a href="#org896f3ab">3.1. Simulation Setup</a></li>
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<li><a href="#org5021a67">3.2. Analysis</a></li>
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<li><a href="#org449c206">3.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org76d45ac">4. Tomography when the micro-hexapod is not centered</a>
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<ul>
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<li><a href="#org9dfa994">4.1. Simulation Setup</a></li>
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<li><a href="#org53a566e">4.2. Analysis</a></li>
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<li><a href="#org626ad53">4.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org7f867ad">5. Raster Scans with the translation stage</a>
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<ul>
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<li><a href="#org957d49b">5.1. Simulation Setup</a></li>
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<li><a href="#org7c493c6">5.2. Analysis</a></li>
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<li><a href="#org6d754cb">5.3. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<p>
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The goal here is to simulate some scientific experiments with the tuned Simscape model when no control is applied to the nano-hexapod.
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</p>
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<p>
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This has several goals:
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</p>
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<ul class="org-ul">
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<li>Validate the model</li>
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<li>Estimate the expected error motion for the experiments</li>
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<li>Estimate the stroke that we may need for the nano-hexapod</li>
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</ul>
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<p>
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The document in organized as follow:
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</p>
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<ul class="org-ul">
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<li>In section <a href="#org62942ec">1</a> the Simscape model is initialized</li>
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<li>In section <a href="#orgc810276">2</a> a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included</li>
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<li>In section <a href="#org9cd3ace">3</a>, the same is done but with disturbance included</li>
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<li>In section <a href="#orgc5d1986">4</a> the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included</li>
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<li>In section <a href="#org0e3c219">5</a>, scans with the translation stage are simulated with no perturbation included</li>
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</ul>
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<div id="outline-container-orgc1ba6cb" class="outline-2">
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<h2 id="orgc1ba6cb"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org62942ec"></a>
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</p>
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<p>
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The simulink file to do tomography experiments is <code>sim_nano_station_tomo.slx</code>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">open<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/matlab/sim_nano_station_tomo.slx'</span><span class="org-rainbow-delimiters-depth-1">)</span>
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</pre>
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</div>
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<p>
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We load the shared simulink configuration and we set the <code>StopTime</code>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/conf_simscape.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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<span class="org-matlab-simulink-keyword">set_param</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, '<span class="org-highlight-numbers-number">5</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<p>
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We first initialize all the stages.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
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initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</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>;
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</pre>
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</div>
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<p>
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We initialize the reference path for all the stages.
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All stage is set to its zero position except the Spindle which is rotating at 60rpm.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeReferences<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</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>;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf0c34e6" class="outline-2">
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<h2 id="orgf0c34e6"><span class="section-number-2">2</span> Tomography Experiment with no disturbances</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="orgc810276"></a>
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</p>
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</div>
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<div id="outline-container-orge470384" class="outline-3">
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<h3 id="orge470384"><span class="section-number-3">2.1</span> Simulation Setup</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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And we initialize the disturbances to be equal to zero.
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</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
|
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
initDisturbances<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'sim_nano_station_tomo'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">tomo_align_no_dist = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf23b2a2" class="outline-3">
|
|
<h3 id="orgf23b2a2"><span class="section-number-3">2.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
t = tomo_align_no_dist.t;
|
|
MTr = tomo_align_no_dist.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edy = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edz = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2<span class="org-rainbow-delimiters-depth-1">(</span> squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</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>;
|
|
Erx = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Erz = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org5d578cf" class="figure">
|
|
<p><img src="figs/exp_tomo_without_dist_trans.png" alt="exp_tomo_without_dist_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist_trans.png">png</a>, <a href="./figs/exp_tomo_without_dist_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8a4881b" class="figure">
|
|
<p><img src="figs/exp_tomo_without_dist_rot.png" alt="exp_tomo_without_dist_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist_rot.png">png</a>, <a href="./figs/exp_tomo_without_dist_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orged24ea9" class="outline-3">
|
|
<h3 id="orged24ea9"><span class="section-number-3">2.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<div class="important">
|
|
<p>
|
|
When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included.
|
|
This residual error motion probably comes from a small misalignment somewhere.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgbdf5d41" class="outline-2">
|
|
<h2 id="orgbdf5d41"><span class="section-number-2">3</span> Tomography Experiment with included perturbations</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="org9cd3ace"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org896f3ab" class="outline-3">
|
|
<h3 id="org896f3ab"><span class="section-number-3">3.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
We now activate the disturbances.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
|
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
initDisturbances<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'sim_nano_station_tomo'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">tomo_align_dist = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5021a67" class="outline-3">
|
|
<h3 id="org5021a67"><span class="section-number-3">3.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_dist'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
t = tomo_align_dist.t;
|
|
MTr = tomo_align_dist.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edy = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edz = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2<span class="org-rainbow-delimiters-depth-1">(</span> squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</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>;
|
|
Erx = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Erz = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgfe30b96" class="figure">
|
|
<p><img src="figs/exp_tomo_dist_trans.png" alt="exp_tomo_dist_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist_trans.png">png</a>, <a href="./figs/exp_tomo_dist_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org36e30c6" class="figure">
|
|
<p><img src="figs/exp_tomo_dist_rot.png" alt="exp_tomo_dist_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>X-Y-Z rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist_rot.png">png</a>, <a href="./figs/exp_tomo_dist_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org449c206" class="outline-3">
|
|
<h3 id="org449c206"><span class="section-number-3">3.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="important">
|
|
<p>
|
|
Error motion is what expected from the disturbance measurements.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org76d45ac" class="outline-2">
|
|
<h2 id="org76d45ac"><span class="section-number-2">4</span> Tomography when the micro-hexapod is not centered</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="orgc5d1986"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org9dfa994" class="outline-3">
|
|
<h3 id="org9dfa994"><span class="section-number-3">4.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
We first set the wanted translation of the Micro Hexapod.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">P_micro_hexapod = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">01</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>; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We initialize the reference path.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'Dh_pos'</span>, <span class="org-rainbow-delimiters-depth-3">[</span>P_micro_hexapod; <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-3">]</span>, <span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</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>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We initialize the stages.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'AP'</span>, P_micro_hexapod<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we initialize the disturbances to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
|
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
initDisturbances<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'sim_nano_station_tomo'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">tomo_not_align = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org53a566e" class="outline-3">
|
|
<h3 id="org53a566e"><span class="section-number-3">4.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_not_align'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
t = tomo_not_align.t;
|
|
MTr = tomo_not_align.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edy = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edz = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2<span class="org-rainbow-delimiters-depth-1">(</span> squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</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>;
|
|
Erx = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Erz = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org3ef6891" class="figure">
|
|
<p><img src="figs/exp_tomo_offset_trans.png" alt="exp_tomo_offset_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset_trans.png">png</a>, <a href="./figs/exp_tomo_offset_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8a6932c" class="figure">
|
|
<p><img src="figs/exp_tomo_offset_rot.png" alt="exp_tomo_offset_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset_rot.png">png</a>, <a href="./figs/exp_tomo_offset_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org626ad53" class="outline-3">
|
|
<h3 id="org626ad53"><span class="section-number-3">4.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<div class="important">
|
|
<p>
|
|
The main motions are translations in the X direction of the mobile platform (corresponds to the eccentricity of the micro-hexapod) and rotations along the rotating Y axis.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7f867ad" class="outline-2">
|
|
<h2 id="org7f867ad"><span class="section-number-2">5</span> Raster Scans with the translation stage</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org0e3c219"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org957d49b" class="outline-3">
|
|
<h3 id="org957d49b"><span class="section-number-3">5.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<p>
|
|
We set the reference path.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'Dy_type'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'Dy_amplitude'</span>, <span class="org-highlight-numbers-number">10e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span>, <span class="org-string">'Dy_period'</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>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We initialize the stages.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</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>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we initialize the disturbances to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">(</span>...
|
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
|
|
<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
|
|
<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
|
<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
initDisturbances<span class="org-rainbow-delimiters-depth-1">(</span>opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'sim_nano_station_tomo'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty_scan = struct<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'ty_scan'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7c493c6" class="outline-3">
|
|
<h3 id="org7c493c6"><span class="section-number-3">5.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'ty_scan'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
t = ty_scan.t;
|
|
MTr = ty_scan.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edy = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Edz = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>MTr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2<span class="org-rainbow-delimiters-depth-1">(</span> squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> MTr<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</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>;
|
|
Erx = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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Erz = atan2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">-</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span>, squeeze<span class="org-rainbow-delimiters-depth-2">(</span>MTr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>cos<span class="org-rainbow-delimiters-depth-2">(</span>Ery<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<div id="org96b63df" class="figure">
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<p><img src="figs/exp_ty_scan_trans.png" alt="exp_ty_scan_trans.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan_trans.png">png</a>, <a href="./figs/exp_ty_scan_trans.pdf">pdf</a>)</p>
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</div>
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<div id="org4748377" class="figure">
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<p><img src="figs/exp_ty_scan_rot.png" alt="exp_ty_scan_rot.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan_rot.png">png</a>, <a href="./figs/exp_ty_scan_rot.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org6d754cb" class="outline-3">
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<h3 id="org6d754cb"><span class="section-number-3">5.3</span> Conclusion</h3>
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<div class="outline-text-3" id="text-5-3">
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<div class="important">
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<p>
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This is logic that the main error moving is translation along the Y axis and rotation along the X axis.
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In order to reduce the errors, we can make a smoother reference path for the translation stage.
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</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2019-12-19 jeu. 12:47</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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