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@ -4,7 +4,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-02-12 mer. 18:26 --> <!-- 2020-02-13 jeu. 15:01 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Cubic configuration for the Stewart Platform</title> <title>Cubic configuration for the Stewart Platform</title>
@ -274,33 +274,33 @@ for the JavaScript code in this tag.
<li><a href="#orga88e79a">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li> <li><a href="#orga88e79a">1.2. Cubic Stewart platform centered with the cube center - Jacobian not estimated at the cube center</a></li>
<li><a href="#orge02ec88">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li> <li><a href="#orge02ec88">1.3. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the cube center</a></li>
<li><a href="#org43fd7e4">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li> <li><a href="#org43fd7e4">1.4. Cubic Stewart platform not centered with the cube center - Jacobian estimated at the Stewart platform center</a></li>
<li><a href="#org778aab3">1.5. Conclusion</a></li> <li><a href="#org510da86">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd70418b">2. Configuration with the Cube&rsquo;s center above the mobile platform</a> <li><a href="#orgd70418b">2. Configuration with the Cube&rsquo;s center above the mobile platform</a>
<ul> <ul>
<li><a href="#org8afa645">2.1. Having Cube&rsquo;s center above the top platform</a></li> <li><a href="#org8afa645">2.1. Having Cube&rsquo;s center above the top platform</a></li>
<li><a href="#org8e940b8">2.2. Conclusion</a></li> <li><a href="#org949a403">2.2. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgcc4ecce">3. Cubic size analysis</a> <li><a href="#orgcc4ecce">3. Cubic size analysis</a>
<ul> <ul>
<li><a href="#org0029d8c">3.1. Analysis</a></li> <li><a href="#org0029d8c">3.1. Analysis</a></li>
<li><a href="#org9d42e84">3.2. Conclusion</a></li> <li><a href="#orgfc7135f">3.2. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf09da67">4. Dynamic Coupling in the Cartesian Frame</a> <li><a href="#orgf09da67">4. Dynamic Coupling in the Cartesian Frame</a>
<ul> <ul>
<li><a href="#org5fe01ec">4.1. Cube&rsquo;s center at the Center of Mass of the mobile platform</a></li> <li><a href="#org5fe01ec">4.1. Cube&rsquo;s center at the Center of Mass of the mobile platform</a></li>
<li><a href="#org4cb2a36">4.2. Cube&rsquo;s center not coincident with the Mass of the Mobile platform</a></li> <li><a href="#org4cb2a36">4.2. Cube&rsquo;s center not coincident with the Mass of the Mobile platform</a></li>
<li><a href="#org5214dec">4.3. Conclusion</a></li> <li><a href="#org2e09bcb">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8f26dc0">5. Dynamic Coupling between actuators and sensors of each strut</a> <li><a href="#org8f26dc0">5. Dynamic Coupling between actuators and sensors of each strut</a>
<ul> <ul>
<li><a href="#org6e391c9">5.1. Coupling between the actuators and sensors - Cubic Architecture</a></li> <li><a href="#org6e391c9">5.1. Coupling between the actuators and sensors - Cubic Architecture</a></li>
<li><a href="#orgafd808d">5.2. Coupling between the actuators and sensors - Non-Cubic Architecture</a></li> <li><a href="#orgafd808d">5.2. Coupling between the actuators and sensors - Non-Cubic Architecture</a></li>
<li><a href="#org0936a8a">5.3. Conclusion</a></li> <li><a href="#org8c1a310">5.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3044455">6. Functions</a> <li><a href="#org3044455">6. Functions</a>
@ -836,8 +836,8 @@ stewart = initializeCylindricalPlatforms(stewart, <span class="org-string">'Fpr'
</div> </div>
</div> </div>
<div id="outline-container-org778aab3" class="outline-3"> <div id="outline-container-org510da86" class="outline-3">
<h3 id="org778aab3"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="org510da86"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important">
<p> <p>
@ -1162,8 +1162,8 @@ FOc = H <span class="org-type">+</span> MO_B; <span class="org-comment">% Cente
</div> </div>
</div> </div>
<div id="outline-container-org8e940b8" class="outline-3"> <div id="outline-container-org949a403" class="outline-3">
<h3 id="org8e940b8"><span class="section-number-3">2.2</span> Conclusion</h3> <h3 id="org949a403"><span class="section-number-3">2.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="important"> <div class="important">
<p> <p>
@ -1237,8 +1237,8 @@ We also find that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) are varyi
</div> </div>
</div> </div>
<div id="outline-container-org9d42e84" class="outline-3"> <div id="outline-container-orgfc7135f" class="outline-3">
<h3 id="org9d42e84"><span class="section-number-3">3.2</span> Conclusion</h3> <h3 id="orgfc7135f"><span class="section-number-3">3.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size. We observe that \(k_{\theta_x} = k_{\theta_y}\) and \(k_{\theta_z}\) increase linearly with the cube size.
@ -1373,6 +1373,15 @@ stewart = initializeInertialSensor(stewart);
</pre> </pre>
</div> </div>
<p>
No flexibility below the Stewart platform and no payload.
</p>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<p> <p>
The obtain geometry is shown in figure <a href="#orgc92a65b">10</a>. The obtain geometry is shown in figure <a href="#orgc92a65b">10</a>.
</p> </p>
@ -1388,19 +1397,19 @@ The obtain geometry is shown in figure <a href="#orgc92a65b">10</a>.
We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\). We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">open(<span class="org-string">'simulink/stewart_active_damping.slx'</span>) <pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
options = linearizeOptions; options = linearizeOptions;
options.SampleTime = 0; options.SampleTime = 0;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'stewart_active_damping'</span>; mdl = <span class="org-string">'stewart_platform_model'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span> io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
io(io_i) = linio([mdl, <span class="org-string">'/Dm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Displacement of each leg [m]</span> io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1508,6 +1517,15 @@ stewart = initializeInertialSensor(stewart);
</pre> </pre>
</div> </div>
<p>
No flexibility below the Stewart platform and no payload.
</p>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<p> <p>
The obtain geometry is shown in figure <a href="#orgfce7805">12</a>. The obtain geometry is shown in figure <a href="#orgfce7805">12</a>.
</p> </p>
@ -1522,19 +1540,19 @@ The obtain geometry is shown in figure <a href="#orgfce7805">12</a>.
We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\). We now identify the dynamics from forces applied in each strut \(\bm{\tau}\) to the displacement of each strut \(d \bm{\mathcal{L}}\).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">open(<span class="org-string">'simulink/stewart_active_damping.slx'</span>) <pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
<span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
options = linearizeOptions; options = linearizeOptions;
options.SampleTime = 0; options.SampleTime = 0;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'stewart_active_damping'</span>; mdl = <span class="org-string">'stewart_platform_model'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span> io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
io(io_i) = linio([mdl, <span class="org-string">'/Dm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Displacement of each leg [m]</span> io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1577,8 +1595,8 @@ This was expected as the mass matrix is not diagonal (the Center of Mass of the
</div> </div>
</div> </div>
<div id="outline-container-org5214dec" class="outline-3"> <div id="outline-container-org2e09bcb" class="outline-3">
<h3 id="org5214dec"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="org2e09bcb"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div class="important"> <div class="important">
<p> <p>
@ -1645,6 +1663,15 @@ stewart = initializeInertialSensor(stewart);
</pre> </pre>
</div> </div>
<p>
No flexibility below the Stewart platform and no payload.
</p>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<div id="org67d7284" class="figure"> <div id="org67d7284" class="figure">
<p><img src="figs/stewart_architecture_coupling_struts_cubic.png" alt="stewart_architecture_coupling_struts_cubic.png" /> <p><img src="figs/stewart_architecture_coupling_struts_cubic.png" alt="stewart_architecture_coupling_struts_cubic.png" />
@ -1703,6 +1730,15 @@ stewart = initializeInertialSensor(stewart);
</pre> </pre>
</div> </div>
<p>
No flexibility below the Stewart platform and no payload.
</p>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<div id="org14d3492" class="figure"> <div id="org14d3492" class="figure">
<p><img src="figs/stewart_architecture_coupling_struts_non_cubic.png" alt="stewart_architecture_coupling_struts_non_cubic.png" /> <p><img src="figs/stewart_architecture_coupling_struts_non_cubic.png" alt="stewart_architecture_coupling_struts_non_cubic.png" />
@ -1730,12 +1766,12 @@ And we identify the dynamics from the actuator forces \(\tau_{i}\) to the relati
</div> </div>
</div> </div>
<div id="outline-container-org0936a8a" class="outline-3"> <div id="outline-container-org8c1a310" class="outline-3">
<h3 id="org0936a8a"><span class="section-number-3">5.3</span> Conclusion</h3> <h3 id="org8c1a310"><span class="section-number-3">5.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div class="important"> <div class="important">
<p> <p>
The Cubic architecture seems to not have any significant effect on the coupling between actuator and sensors of each strut. The Cubic architecture seems to not have any significant effect on the coupling between actuator and sensors of each strut and thus provides no advantages for decentralized control.
</p> </p>
</div> </div>
@ -1902,7 +1938,7 @@ stewart.platform_M.Mb = Mb;
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-12 mer. 18:26</p> <p class="date">Created: 2020-02-13 jeu. 15:01</p>
</div> </div>
</body> </body>
</html> </html>

66
org/cubic-configuration.org
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@ -647,6 +647,12 @@ And we set small mass for the struts.
stewart = initializeInertialSensor(stewart); stewart = initializeInertialSensor(stewart);
#+end_src #+end_src
No flexibility below the Stewart platform and no payload.
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
The obtain geometry is shown in figure [[fig:stewart_cubic_conf_decouple_dynamics]]. The obtain geometry is shown in figure [[fig:stewart_cubic_conf_decouple_dynamics]].
#+begin_src matlab :exports none #+begin_src matlab :exports none
@ -664,19 +670,19 @@ The obtain geometry is shown in figure [[fig:stewart_cubic_conf_decouple_dynamic
We now identify the dynamics from forces applied in each strut $\bm{\tau}$ to the displacement of each strut $d \bm{\mathcal{L}}$. We now identify the dynamics from forces applied in each strut $\bm{\tau}$ to the displacement of each strut $d \bm{\mathcal{L}}$.
#+begin_src matlab #+begin_src matlab
open('simulink/stewart_active_damping.slx') open('stewart_platform_model.slx')
%% Options for Linearized %% Options for Linearized
options = linearizeOptions; options = linearizeOptions;
options.SampleTime = 0; options.SampleTime = 0;
%% Name of the Simulink File %% Name of the Simulink File
mdl = 'stewart_active_damping'; mdl = 'stewart_platform_model';
%% Input/Output definition %% Input/Output definition
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N] io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Dm'], 1, 'openoutput'); io_i = io_i + 1; % Displacement of each leg [m] io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization %% Run the linearization
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -826,6 +832,12 @@ And we set small mass for the struts.
stewart = initializeInertialSensor(stewart); stewart = initializeInertialSensor(stewart);
#+end_src #+end_src
No flexibility below the Stewart platform and no payload.
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
The obtain geometry is shown in figure [[fig:stewart_cubic_conf_mass_above]]. The obtain geometry is shown in figure [[fig:stewart_cubic_conf_mass_above]].
#+begin_src matlab :exports none #+begin_src matlab :exports none
displayArchitecture(stewart, 'labels', false, 'view', 'all'); displayArchitecture(stewart, 'labels', false, 'view', 'all');
@ -842,19 +854,19 @@ The obtain geometry is shown in figure [[fig:stewart_cubic_conf_mass_above]].
We now identify the dynamics from forces applied in each strut $\bm{\tau}$ to the displacement of each strut $d \bm{\mathcal{L}}$. We now identify the dynamics from forces applied in each strut $\bm{\tau}$ to the displacement of each strut $d \bm{\mathcal{L}}$.
#+begin_src matlab #+begin_src matlab
open('simulink/stewart_active_damping.slx') open('stewart_platform_model.slx')
%% Options for Linearized %% Options for Linearized
options = linearizeOptions; options = linearizeOptions;
options.SampleTime = 0; options.SampleTime = 0;
%% Name of the Simulink File %% Name of the Simulink File
mdl = 'stewart_active_damping'; mdl = 'stewart_platform_model';
%% Input/Output definition %% Input/Output definition
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N] io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Dm'], 1, 'openoutput'); io_i = io_i + 1; % Displacement of each leg [m] io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization %% Run the linearization
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1016,6 +1028,12 @@ Let's generate a Cubic architecture where the cube's center and the frames $\{A\
stewart = initializeInertialSensor(stewart); stewart = initializeInertialSensor(stewart);
#+end_src #+end_src
No flexibility below the Stewart platform and no payload.
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
displayArchitecture(stewart, 'labels', false, 'view', 'all'); displayArchitecture(stewart, 'labels', false, 'view', 'all');
#+end_src #+end_src
@ -1032,19 +1050,19 @@ Let's generate a Cubic architecture where the cube's center and the frames $\{A\
And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative motion sensors $\delta \mathcal{L}_{i}$ (Figure [[fig:coupling_struts_relative_sensor_cubic]]) and to the force sensors $\tau_{m,i}$ (Figure [[fig:coupling_struts_force_sensor_cubic]]). And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative motion sensors $\delta \mathcal{L}_{i}$ (Figure [[fig:coupling_struts_relative_sensor_cubic]]) and to the force sensors $\tau_{m,i}$ (Figure [[fig:coupling_struts_force_sensor_cubic]]).
#+begin_src matlab :exports none #+begin_src matlab :exports none
open('simulink/stewart_active_damping.slx') open('stewart_platform_model.slx')
%% Options for Linearized %% Options for Linearized
options = linearizeOptions; options = linearizeOptions;
options.SampleTime = 0; options.SampleTime = 0;
%% Name of the Simulink File %% Name of the Simulink File
mdl = 'stewart_active_damping'; mdl = 'stewart_platform_model';
%% Input/Output definition %% Input/Output definition
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N] io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Dm'], 1, 'openoutput'); io_i = io_i + 1; % Displacement of each leg [m] io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization %% Run the linearization
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1101,8 +1119,8 @@ And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative
#+begin_src matlab :exports none #+begin_src matlab :exports none
%% Input/Output definition %% Input/Output definition
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N] io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Displacement of each leg [m] io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
%% Run the linearization %% Run the linearization
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1181,6 +1199,12 @@ Now we generate a Stewart platform which is not cubic but with approximately the
stewart = initializeInertialSensor(stewart); stewart = initializeInertialSensor(stewart);
#+end_src #+end_src
No flexibility below the Stewart platform and no payload.
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
displayArchitecture(stewart, 'labels', false, 'view', 'all'); displayArchitecture(stewart, 'labels', false, 'view', 'all');
#+end_src #+end_src
@ -1197,19 +1221,19 @@ Now we generate a Stewart platform which is not cubic but with approximately the
And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative motion sensors $\delta \mathcal{L}_{i}$ (Figure [[fig:coupling_struts_relative_sensor_non_cubic]]) and to the force sensors $\tau_{m,i}$ (Figure [[fig:coupling_struts_force_sensor_non_cubic]]). And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative motion sensors $\delta \mathcal{L}_{i}$ (Figure [[fig:coupling_struts_relative_sensor_non_cubic]]) and to the force sensors $\tau_{m,i}$ (Figure [[fig:coupling_struts_force_sensor_non_cubic]]).
#+begin_src matlab :exports none #+begin_src matlab :exports none
open('simulink/stewart_active_damping.slx') open('stewart_platform_model.slx')
%% Options for Linearized %% Options for Linearized
options = linearizeOptions; options = linearizeOptions;
options.SampleTime = 0; options.SampleTime = 0;
%% Name of the Simulink File %% Name of the Simulink File
mdl = 'stewart_active_damping'; mdl = 'stewart_platform_model';
%% Input/Output definition %% Input/Output definition
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N] io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Dm'], 1, 'openoutput'); io_i = io_i + 1; % Displacement of each leg [m] io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization %% Run the linearization
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1266,8 +1290,8 @@ And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative
#+begin_src matlab :exports none #+begin_src matlab :exports none
%% Input/Output definition %% Input/Output definition
clear io; io_i = 1; clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N] io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Displacement of each leg [m] io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
%% Run the linearization %% Run the linearization
G = linearize(mdl, io, options); G = linearize(mdl, io, options);
@ -1323,7 +1347,7 @@ And we identify the dynamics from the actuator forces $\tau_{i}$ to the relative
** Conclusion ** Conclusion
#+begin_important #+begin_important
The Cubic architecture seems to not have any significant effect on the coupling between actuator and sensors of each strut. The Cubic architecture seems to not have any significant effect on the coupling between actuator and sensors of each strut and thus provides no advantages for decentralized control.
#+end_important #+end_important
* Functions * Functions