65 lines
2.3 KiB
Mathematica
65 lines
2.3 KiB
Mathematica
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simulinkproject('./');
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% Stewart architecture definition
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% We first define some general Stewart architecture.
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stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart);
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stewart = computeJacobian(stewart);
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% Comparison for "pure" translations
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% Let's first compare the perfect and approximate solution of the inverse for pure $x$ translations.
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% We compute the approximate and exact required strut stroke to have the wanted mobile platform $x$ displacement.
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% The estimate required strut stroke for both the approximate and exact solutions are shown in Figure [[fig:inverse_kinematics_approx_validity_x_translation]].
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% The relative strut length displacement is shown in Figure [[fig:inverse_kinematics_approx_validity_x_translation_relative]].
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Xrs = logspace(-6, -1, 100); % Wanted X translation of the mobile platform [m]
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Ls_approx = zeros(6, length(Xrs));
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Ls_exact = zeros(6, length(Xrs));
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for i = 1:length(Xrs)
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Xr = Xrs(i);
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L_approx(:, i) = stewart.J*[Xr; 0; 0; 0; 0; 0;];
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[~, L_exact(:, i)] = inverseKinematics(stewart, 'AP', [Xr; 0; 0]);
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end
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figure;
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hold on;
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for i = 1:6
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set(gca,'ColorOrderIndex',i);
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plot(Xrs, abs(L_approx(i, :)));
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set(gca,'ColorOrderIndex',i);
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plot(Xrs, abs(L_exact(i, :)), '--');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Wanted $x$ displacement [m]');
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ylabel('Estimated required stroke');
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% #+NAME: fig:inverse_kinematics_approx_validity_x_translation
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% #+CAPTION: Comparison of the Approximate solution and True solution for the Inverse kinematic problem ([[./figs/inverse_kinematics_approx_validity_x_translation.png][png]], [[./figs/inverse_kinematics_approx_validity_x_translation.pdf][pdf]])
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% [[file:figs/inverse_kinematics_approx_validity_x_translation.png]]
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figure;
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hold on;
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for i = 1:6
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plot(Xrs, abs(L_approx(i, :) - L_exact(i, :))./abs(L_approx(i, :) + L_exact(i, :)), 'k-');
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Wanted $x$ displacement [m]');
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ylabel('Relative Stroke Error');
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