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Initialize Stewart platform in the wanted position

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Thomas Dehaeze 2020-01-22 18:19:40 +01:00
parent 99f9e46046
commit 0833009e48
11 changed files with 171 additions and 420 deletions
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2
.SimulinkProject/Root.type.EnvironmentCustomizations/environment.loadSimulink.type.Command.xml
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@ -1,2 +1,2 @@
<?xml version='1.0' encoding='UTF-8'?> <?xml version='1.0' encoding='UTF-8'?>
<Info Value="true" /> <Info Value="false" />

3
active-damping.org
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@ -45,7 +45,10 @@
stewart = generateCubicConfiguration(stewart, 'Hc', 40e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); stewart = generateCubicConfiguration(stewart, 'Hc', 40e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1));
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
#+end_src #+end_src
** Identification of the Dynamics ** Identification of the Dynamics

13
control-study.org
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@ -69,17 +69,14 @@
** Initialize the Stewart platform ** Initialize the Stewart platform
#+begin_src matlab #+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); stewart = initializeFramesPositions();
% stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = generateGeneralConfiguration(stewart); stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
#+end_src stewart = initializeStewartPose(stewart);
** Initialize the Simulation
#+begin_src matlab
load('mat/conf_simscape.mat');
#+end_src #+end_src
** Identification of the plant ** Identification of the plant

22
cubic-configuration.org
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@ -53,7 +53,7 @@ The goal is to study the benefits of using a cubic configuration:
- No coupling between the actuators? - No coupling between the actuators?
- Is the center of the cube an important point? - Is the center of the cube an important point?
* Configuration Analysis - Stiffness Matrix * TODO Configuration Analysis - Stiffness Matrix
** Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center ** Cubic Stewart platform centered with the cube center - Jacobian estimated at the cube center
We create a cubic Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot). We create a cubic Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]) in such a way that the center of the cube (black dot) is located at the center of the Stewart platform (blue dot).
The Jacobian matrix is estimated at the location of the center of the cube. The Jacobian matrix is estimated at the location of the center of the cube.
@ -228,7 +228,7 @@ We obtain $k_x = k_y = k_z$ and $k_{\theta_x} = k_{\theta_y}$, but the Stiffness
- The stiffness matrix $K$ is diagonal for the cubic configuration if the Stewart platform and the cube are centered *and* the Jacobian is estimated at the cube center - The stiffness matrix $K$ is diagonal for the cubic configuration if the Stewart platform and the cube are centered *and* the Jacobian is estimated at the cube center
#+end_important #+end_important
* Cubic size analysis * TODO Cubic size analysis
We here study the effect of the size of the cube used for the Stewart configuration. We here study the effect of the size of the cube used for the Stewart configuration.
We fix the height of the Stewart platform, the center of the cube is at the center of the Stewart platform. We fix the height of the Stewart platform, the center of the cube is at the center of the Stewart platform.
@ -304,14 +304,14 @@ We observe that $k_{\theta_x} = k_{\theta_y}$ and $k_{\theta_z}$ increase linear
In that case, the legs will the further separated. Size of the cube is then limited by allowed space. In that case, the legs will the further separated. Size of the cube is then limited by allowed space.
#+end_important #+end_important
* initializeCubicConfiguration * TODO initializeCubicConfiguration
:PROPERTIES: :PROPERTIES:
:HEADER-ARGS:matlab+: :exports code :HEADER-ARGS:matlab+: :exports code
:HEADER-ARGS:matlab+: :comments no :HEADER-ARGS:matlab+: :comments no
:HEADER-ARGS:matlab+: :eval no :HEADER-ARGS:matlab+: :eval no
:HEADER-ARGS:matlab+: :tangle src/initializeCubicConfiguration.m :HEADER-ARGS:matlab+: :tangle src/initializeCubicConfiguration.m
:END: :END:
<<sec:initializeCubicConfiguration>> <<sec:initializeCubicConfiguration>>
** Function description ** Function description
#+begin_src matlab #+begin_src matlab
@ -449,7 +449,7 @@ And the location of the joints on the mobile platform with respect to $\{B\}$.
end end
#+end_src #+end_src
* Tests * TODO Tests
** First attempt to parametrisation ** First attempt to parametrisation
#+name: fig:stewart_bottom_plate #+name: fig:stewart_bottom_plate
#+caption: Schematic of the bottom plates with all the parameters #+caption: Schematic of the bottom plates with all the parameters

36
dynamics-study.org
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@ -41,11 +41,14 @@
** test ** test
#+begin_src matlab #+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); stewart = initializeFramesPositions();
stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
#+end_src #+end_src
Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$: Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
@ -126,11 +129,14 @@ Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}
** Compare external forces and forces applied by the actuators ** Compare external forces and forces applied by the actuators
Initialization of the Stewart platform. Initialization of the Stewart platform.
#+begin_src matlab #+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); stewart = initializeFramesPositions();
stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
#+end_src #+end_src
Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$: Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
@ -188,11 +194,14 @@ Seems quite similar.
** Comparison of the static transfer function and the Compliance matrix ** Comparison of the static transfer function and the Compliance matrix
Initialization of the Stewart platform. Initialization of the Stewart platform.
#+begin_src matlab #+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); stewart = initializeFramesPositions();
stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
#+end_src #+end_src
Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$: Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}$:
@ -248,11 +257,14 @@ The low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{
** Transfer function from forces applied in the legs to the displacement of the legs ** Transfer function from forces applied in the legs to the displacement of the legs
Initialization of the Stewart platform. Initialization of the Stewart platform.
#+begin_src matlab #+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3); stewart = initializeFramesPositions();
stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3); stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
#+end_src #+end_src
Estimation of the transfer function from $\bm{\tau}$ to $\bm{L}$: Estimation of the transfer function from $\bm{\tau}$ to $\bm{L}$:

153
simscape-model.org
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@ -106,8 +106,11 @@ By following this procedure, we obtain a Matlab structure =stewart= that contain
stewart = generateGeneralConfiguration(stewart); stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart); stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1)); stewart = initializeStrutDynamics(stewart, 'Ki', 1e6*ones(6,1), 'Ci', 1e2*ones(6,1));
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart); stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart); stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart, 'AP', [0;0;0.01], 'ARB', eye(3));
[Li, dLi] = inverseKinematics(stewart, 'AP', [0;0;0.00001], 'ARB', eye(3)); [Li, dLi] = inverseKinematics(stewart, 'AP', [0;0;0.00001], 'ARB', eye(3));
[P, R] = forwardKinematicsApprox(stewart, 'dL', dLi); [P, R] = forwardKinematicsApprox(stewart, 'dL', dLi);
#+end_src #+end_src
@ -268,8 +271,6 @@ This Matlab function is accessible [[file:src/generateGeneralConfiguration.m][he
% Syntax: [stewart] = generateGeneralConfiguration(stewart, args) % Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
% %
% Inputs: % Inputs:
% - stewart - A structure with the following fields
% - H [1x1] - Total height of the platform [m]
% - args - Can have the following fields: % - args - Can have the following fields:
% - FH [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m] % - FH [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m]
% - FR [1x1] - Radius of the position of the fixed joints in the X-Y [m] % - FR [1x1] - Radius of the position of the fixed joints in the X-Y [m]
@ -477,6 +478,81 @@ This Matlab function is accessible [[file:src/computeJacobian.m][here]].
#+end_src #+end_src
* Initialize the Geometry of the Mechanical Elements * Initialize the Geometry of the Mechanical Elements
** =initializeCylindricalPlatforms=: Initialize the geometry of the Fixed and Mobile Platforms
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeCylindricalPlatforms.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:initializeCylindricalPlatforms>>
This Matlab function is accessible [[file:src/initializeCylindricalPlatforms.m][here]].
*** Function description
#+begin_src matlab
function [stewart] = initializeCylindricalPlatforms(stewart, args)
% initializeCylindricalPlatforms - Initialize the geometry of the Fixed and Mobile Platforms
%
% Syntax: [stewart] = initializeCylindricalPlatforms(args)
%
% Inputs:
% - args - Structure with the following fields:
% - Fpm [1x1] - Fixed Platform Mass [kg]
% - Fph [1x1] - Fixed Platform Height [m]
% - Fpr [1x1] - Fixed Platform Radius [m]
% - Mpm [1x1] - Mobile Platform Mass [kg]
% - Mph [1x1] - Mobile Platform Height [m]
% - Mpr [1x1] - Mobile Platform Radius [m]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - platforms [struct] - structure with the following fields:
% - Fpm [1x1] - Fixed Platform Mass [kg]
% - Msi [3x3] - Mobile Platform Inertia matrix [kg*m^2]
% - Fph [1x1] - Fixed Platform Height [m]
% - Fpr [1x1] - Fixed Platform Radius [m]
% - Mpm [1x1] - Mobile Platform Mass [kg]
% - Fsi [3x3] - Fixed Platform Inertia matrix [kg*m^2]
% - Mph [1x1] - Mobile Platform Height [m]
% - Mpr [1x1] - Mobile Platform Radius [m]
#+end_src
*** Optional Parameters
#+begin_src matlab
arguments
stewart
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 125e-3
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
end
#+end_src
*** Create the =platforms= struct
#+begin_src matlab
platforms = struct();
platforms.Fpm = args.Fpm;
platforms.Fph = args.Fph;
platforms.Fpr = args.Fpr;
platforms.Fpi = diag([1/12 * platforms.Fpm * (3*platforms.Fpr^2 + platforms.Fph^2), ...
1/12 * platforms.Fpm * (3*platforms.Fpr^2 + platforms.Fph^2), ...
1/2 * platforms.Fpm * platforms.Fpr^2]);
platforms.Mpm = args.Mpm;
platforms.Mph = args.Mph;
platforms.Mpr = args.Mpr;
platforms.Mpi = diag([1/12 * platforms.Mpm * (3*platforms.Mpr^2 + platforms.Mph^2), ...
1/12 * platforms.Mpm * (3*platforms.Mpr^2 + platforms.Mph^2), ...
1/2 * platforms.Mpm * platforms.Mpr^2]);
#+end_src
*** Save the =platforms= struct
#+begin_src matlab
stewart.platforms = platforms;
#+end_src
** =initializeCylindricalStruts=: Define the mass and moment of inertia of cylindrical struts ** =initializeCylindricalStruts=: Define the mass and moment of inertia of cylindrical struts
:PROPERTIES: :PROPERTIES:
:header-args:matlab+: :tangle src/initializeCylindricalStruts.m :header-args:matlab+: :tangle src/initializeCylindricalStruts.m
@ -556,79 +632,50 @@ This Matlab function is accessible [[file:src/initializeCylindricalStruts.m][her
stewart.struts = struts; stewart.struts = struts;
#+end_src #+end_src
** =initializeCylindricalPlatforms=: Initialize the geometry of the Fixed and Mobile Platforms * =initializeStewartPose=: Determine the initial stroke in each leg to have the wanted pose
:PROPERTIES: :PROPERTIES:
:header-args:matlab+: :tangle src/initializeCylindricalPlatforms.m :header-args:matlab+: :tangle src/initializeStewartPose.m
:header-args:matlab+: :comments none :mkdirp yes :eval no :header-args:matlab+: :comments none :mkdirp yes :eval no
:END: :END:
<<sec:initializeCylindricalPlatforms>> <<sec:initializeStewartPose>>
This Matlab function is accessible [[file:src/initializeCylindricalPlatforms.m][here]]. This Matlab function is accessible [[file:src/initializeStewartPose.m][here]].
*** Function description ** Function description
#+begin_src matlab #+begin_src matlab
function [stewart] = initializeCylindricalPlatforms(stewart, args) function [stewart] = initializeStewartPose(stewart, args)
% initializeCylindricalPlatforms - Initialize the geometry of the Fixed and Mobile Platforms % initializeStewartPose - Determine the initial stroke in each leg to have the wanted pose
% It uses the inverse kinematic
% %
% Syntax: [stewart] = initializeCylindricalPlatforms(args) % Syntax: [stewart] = initializeStewartPose(stewart, args)
% %
% Inputs: % Inputs:
% - args - Structure with the following fields: % - stewart - A structure with the following fields
% - Fpm [1x1] - Fixed Platform Mass [kg] % - Aa [3x6] - The positions ai expressed in {A}
% - Fph [1x1] - Fixed Platform Height [m] % - Bb [3x6] - The positions bi expressed in {B}
% - Fpr [1x1] - Fixed Platform Radius [m] % - args - Can have the following fields:
% - Mpm [1x1] - Mobile Platform Mass [kg] % - AP [3x1] - The wanted position of {B} with respect to {A}
% - Mph [1x1] - Mobile Platform Height [m] % - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
% - Mpr [1x1] - Mobile Platform Radius [m]
% %
% Outputs: % Outputs:
% - stewart - updated Stewart structure with the added fields: % - stewart - updated Stewart structure with the added fields:
% - platforms [struct] - structure with the following fields: % - dLi[6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
% - Fpm [1x1] - Fixed Platform Mass [kg]
% - Msi [3x3] - Mobile Platform Inertia matrix [kg*m^2]
% - Fph [1x1] - Fixed Platform Height [m]
% - Fpr [1x1] - Fixed Platform Radius [m]
% - Mpm [1x1] - Mobile Platform Mass [kg]
% - Fsi [3x3] - Fixed Platform Inertia matrix [kg*m^2]
% - Mph [1x1] - Mobile Platform Height [m]
% - Mpr [1x1] - Mobile Platform Radius [m]
#+end_src #+end_src
*** Optional Parameters ** Optional Parameters
#+begin_src matlab #+begin_src matlab
arguments arguments
stewart stewart
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1 args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3 args.ARB (3,3) double {mustBeNumeric} = eye(3)
args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 125e-3
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
end end
#+end_src #+end_src
*** Create the =platforms= struct ** Use the Inverse Kinematic function
#+begin_src matlab #+begin_src matlab
platforms = struct(); [Li, dLi] = inverseKinematics(stewart, 'AP', args.AP, 'ARB', args.ARB);
platforms.Fpm = args.Fpm; stewart.dLi = dLi;
platforms.Fph = args.Fph;
platforms.Fpr = args.Fpr;
platforms.Fpi = diag([1/12 * platforms.Fpm * (3*platforms.Fpr^2 + platforms.Fph^2), ...
1/12 * platforms.Fpm * (3*platforms.Fpr^2 + platforms.Fph^2), ...
1/2 * platforms.Fpm * platforms.Fpr^2]);
platforms.Mpm = args.Mpm;
platforms.Mph = args.Mph;
platforms.Mpr = args.Mpr;
platforms.Mpi = diag([1/12 * platforms.Mpm * (3*platforms.Mpr^2 + platforms.Mph^2), ...
1/12 * platforms.Mpm * (3*platforms.Mpr^2 + platforms.Mph^2), ...
1/2 * platforms.Mpm * platforms.Mpr^2]);
#+end_src
*** Save the =platforms= struct
#+begin_src matlab
stewart.platforms = platforms;
#+end_src #+end_src
* Utility Functions * Utility Functions

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simscape_subsystems/stewart_strut.slx
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simulink/stewart_platform_dynamics.slx
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src/initializeStewartPose.m Normal file
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@ -0,0 +1,27 @@
function [stewart] = initializeStewartPose(stewart, args)
% initializeStewartPose - Determine the initial stroke in each leg to have the wanted pose
% It uses the inverse kinematic
%
% Syntax: [stewart] = initializeStewartPose(stewart, args)
%
% Inputs:
% - stewart - A structure with the following fields
% - Aa [3x6] - The positions ai expressed in {A}
% - Bb [3x6] - The positions bi expressed in {B}
% - args - Can have the following fields:
% - AP [3x1] - The wanted position of {B} with respect to {A}
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - dLi[6x1] - The 6 needed displacement of the struts from the initial position in [m] to have the wanted pose of {B} w.r.t. {A}
arguments
stewart
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
end
[Li, dLi] = inverseKinematics(stewart, 'AP', args.AP, 'ARB', args.ARB);
stewart.dLi = dLi;

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<a accesskey="h" href="./index.html"> UP </a>
|
<a accesskey="H" href="./index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Stiffness of the Stewart Platform</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org4cfa1de">1. Functions</a>
<ul>
<li><a href="#orgf252177">1.1. getStiffnessMatrix</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org4cfa1de" class="outline-2">
<h2 id="org4cfa1de"><span class="section-number-2">1</span> Functions</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-orgf252177" class="outline-3">
<h3 id="orgf252177"><span class="section-number-3">1.1</span> getStiffnessMatrix</h3>
<div class="outline-text-3" id="text-1-1">
<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">getStiffnessMatrix</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">k</span>, <span class="org-variable-name">J</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-comment">% k - leg stiffness</span>
<span class="org-comment">% J - Jacobian matrix</span>
K = k<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>J'<span class="org-type">*</span>J<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-08-26 lun. 11:56</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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#+TITLE: Stiffness of the Stewart Platform
:DRAWER:
#+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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#+HTML_HEAD: <script src="./js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script src="./js/readtheorg.js"></script>
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :tangle matlab/stiffness_study.m
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :noweb yes
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:matlab+ :output-dir figs
:END:
* Functions
:PROPERTIES:
:HEADER-ARGS:matlab+: :exports code
:HEADER-ARGS:matlab+: :comments no
:HEADER-ARGS:matlab+: :mkdir yes
:HEADER-ARGS:matlab+: :eval no
:END:
** getStiffnessMatrix
:PROPERTIES:
:HEADER-ARGS:matlab+: :tangle src/getStiffnessMatrix.m
:END:
#+begin_src matlab
function [K] = getStiffnessMatrix(k, J)
% k - leg stiffness
% J - Jacobian matrix
K = k*(J'*J);
end
#+end_src