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phd-nass-geometry/matlab/detail_kinematics_2_cubic.m

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%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
%% Path for functions, data and scripts
addpath('./mat/'); % Path for data
addpath('./src/'); % Path for functions
%% Colors for the figures
colors = colororder;
%% Example of a typical "cubic" architecture
MO_B = -50e-3; % Position {B} with respect to {M} [m]
H = 100e-3; % Height of the Stewart platform [m]
Hc = 100e-3; % Size of the useful part of the cube [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
% here positionned at the frame {B}
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
stewart = computeJacobian(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 150e-3, 'Mpr', 150e-3);
displayArchitecture(stewart, 'labels', false, 'frames', false);
plotCube(stewart, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
%% Example of a typical "cubic" architecture
MO_B = -20e-3; % Position {B} with respect to {M} [m]
H = 40e-3; % Height of the Stewart platform [m]
Hc = 100e-3; % Size of the useful part of the cube [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
% here positionned at the frame {B}
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
stewart = computeJacobian(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 150e-3, 'Mpr', 150e-3);
displayArchitecture(stewart, 'labels', false, 'frames', false);
plotCube(stewart, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
%% Cubic Architecture - Effect of the position of frame {A} and {B}
H = 100e-3; % Height of the Stewart platform [m]
Hc = 100e-3; % Size of the useful part of the cube [m]
FOc = H/2; % Center of the cube at the Stewart platform center
%% Frames {A} and {B} at the cube's center
MO_B = -50e-3; % Position {B} with respect to {M} [m]
stewart_center = initializeStewartPlatform();
stewart_center = initializeFramesPositions(stewart_center, 'H', H, 'MO_B', MO_B);
stewart_center = generateCubicConfiguration(stewart_center, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart_center = computeJointsPose(stewart_center);
stewart_center = initializeStrutDynamics(stewart_center, 'K', ones(6,1));
stewart_center = computeJacobian(stewart_center);
stewart_center = initializeCylindricalPlatforms(stewart_center, 'Fpr', 150e-3, 'Mpr', 150e-3);
displayArchitecture(stewart_center, 'labels', false, 'frames', true);
plotCube(stewart_center, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
%% Frames {A} and {B} offset from the cube's center
MO_B = 50e-3; % Position {B} with respect to {M} [m]
stewart_offset = initializeStewartPlatform();
stewart_offset = initializeFramesPositions(stewart_offset, 'H', H, 'MO_B', MO_B);
stewart_offset = generateCubicConfiguration(stewart_offset, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart_offset = computeJointsPose(stewart_offset);
stewart_offset = initializeStrutDynamics(stewart_offset, 'K', 2*ones(6,1));
stewart_offset = computeJacobian(stewart_offset);
stewart_offset = initializeCylindricalPlatforms(stewart_offset, 'Fpr', 150e-3, 'Mpr', 150e-3);
displayArchitecture(stewart_offset, 'labels', false, 'frames', true);
plotCube(stewart_offset, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
%% With cubic configuration
H = 100e-3; % Height of the Stewart platform [m]
Hc = 100e-3; % Size of the useful part of the cube [m]
FOc = 50e-3; % Center of the cube at the Stewart platform center
MO_B = -50e-3; % Position {B} with respect to {M} [m]
MHb = 0;
stewart_cubic = initializeStewartPlatform();
stewart_cubic = initializeFramesPositions(stewart_cubic, 'H', H, 'MO_B', MO_B);
stewart_cubic = generateCubicConfiguration(stewart_cubic, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', MHb);
stewart_cubic = computeJointsPose(stewart_cubic);
stewart_cubic = initializeStrutDynamics(stewart_cubic, 'K', ones(6,1));
stewart_cubic = computeJacobian(stewart_cubic);
stewart_cubic = initializeCylindricalPlatforms(stewart_cubic, 'Fpr', 150e-3, 'Mpr', 150e-3);
% Let's now define the actuator stroke.
L_max = 50e-6; % [m]
thetas = linspace(0, pi, 100);
phis = linspace(0, 2*pi, 200);
rs = zeros(length(thetas), length(phis));
for i = 1:length(thetas)
for j = 1:length(phis)
Tx = sin(thetas(i))*cos(phis(j));
Ty = sin(thetas(i))*sin(phis(j));
Tz = cos(thetas(i));
dL = stewart_cubic.kinematics.J*[Tx; Ty; Tz; 0; 0; 0;]; % dL required for 1m displacement in theta/phi direction
rs(i, j) = L_max/max(abs(dL));
% rs(i, j) = max(abs([dL(dL<0)*L_min; dL(dL>=0)*L_max]));
end
end
% Get circle that fits inside the accessible space
min(min(rs))
max(max(rs))
[phi_grid, theta_grid] = meshgrid(phis, thetas);
X = 1e6 * rs .* sin(theta_grid) .* cos(phi_grid);
Y = 1e6 * rs .* sin(theta_grid) .* sin(phi_grid);
Z = 1e6 * rs .* cos(theta_grid);
figure;
s = surf(X, Y, Z, 'FaceColor', 'white');
s.EdgeColor = colors(1,:);
axis equal;
grid on;
xlabel('X Translation [$\mu$m]'); ylabel('Y Translation [$\mu$m]'); zlabel('Z Translation [$\mu$m]');
xlim(5e6*[-L_max, L_max]); ylim(5e6*[-L_max, L_max]); zlim(5e6*[-L_max, L_max]);
H = 200e-3; % height of the Stewart platform [m]
MO_B = -10e-3; % Position {B} with respect to {M} [m]
Hc = 2.5*H; % Size of the useful part of the cube [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 25e-3, 'MHb', 25e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e1*ones(6,1));
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), ...
'Mpm', 10, ...
'Mph', 20e-3, ...
'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
stewart = initializeCylindricalStruts(stewart, 'Fsm', 1e-3, 'Msm', 1e-3);
stewart = initializeInertialSensor(stewart);
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
controller = initializeController('type', 'open-loop');
displayArchitecture(stewart, 'labels', false, 'view', 'all');
open('stewart_platform_model.slx')
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
Gc = inv(stewart.kinematics.J)*G*inv(stewart.kinematics.J');
Gc = inv(stewart.kinematics.J)*G*stewart.kinematics.J;
Gc.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Gc.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
freqs = logspace(1, 3, 500);
figure;
ax1 = subplot(2, 2, 1);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gc(1, 1), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(2, 2), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(3, 3), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax3 = subplot(2, 2, 3);
hold on;
for i = 1:6
for j = i+1:6
p4 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1, 1), freqs, 'Hz'))));
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(2, 2), freqs, 'Hz'))));
p3 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(3, 3), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2, p3, p4], {'$D_x/F_x$','$D_y/F_y$', '$D_z/F_z$', '$D_i/F_j$'})
ax2 = subplot(2, 2, 2);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gc(4, 4), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(5, 5), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(6, 6), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax4 = subplot(2, 2, 4);
hold on;
for i = 1:6
for j = i+1:6
p4 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(4, 4), freqs, 'Hz'))));
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(5, 5), freqs, 'Hz'))));
p3 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(6, 6), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2, p3, p4], {'$R_x/M_x$','$R_y/M_y$', '$R_z/M_z$', '$R_i/M_j$'})
linkaxes([ax1,ax2,ax3,ax4],'x');
H = 200e-3; % height of the Stewart platform [m]
MO_B = -100e-3; % Position {B} with respect to {M} [m]
Hc = 2.5*H; % Size of the useful part of the cube [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 25e-3, 'MHb', 25e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e1*ones(6,1));
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), ...
'Mpm', 10, ...
'Mph', 20e-3, ...
'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
stewart = initializeCylindricalStruts(stewart, 'Fsm', 1e-3, 'Msm', 1e-3);
stewart = initializeInertialSensor(stewart);
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
controller = initializeController('type', 'open-loop');
displayArchitecture(stewart, 'labels', false, 'view', 'all');
open('stewart_platform_model.slx')
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
Gc = inv(stewart.kinematics.J)*G*inv(stewart.kinematics.J');
Gc.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Gc.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
freqs = logspace(1, 3, 500);
figure;
ax1 = subplot(2, 2, 1);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gc(1, 1), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(2, 2), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(3, 3), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax3 = subplot(2, 2, 3);
hold on;
for i = 1:6
for j = i+1:6
p4 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(1, 1), freqs, 'Hz'))));
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(2, 2), freqs, 'Hz'))));
p3 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(3, 3), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2, p3, p4], {'$D_x/F_x$','$D_y/F_y$', '$D_z/F_z$', '$D_i/F_j$'})
ax2 = subplot(2, 2, 2);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gc(4, 4), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(5, 5), freqs, 'Hz'))));
plot(freqs, abs(squeeze(freqresp(Gc(6, 6), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax4 = subplot(2, 2, 4);
hold on;
for i = 1:6
for j = i+1:6
p4 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(4, 4), freqs, 'Hz'))));
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(5, 5), freqs, 'Hz'))));
p3 = plot(freqs, 180/pi*angle(squeeze(freqresp(Gc(6, 6), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2, p3, p4], {'$R_x/M_x$','$R_y/M_y$', '$R_z/M_z$', '$R_i/M_j$'})
linkaxes([ax1,ax2,ax3,ax4],'x');
H = 200e-3; % height of the Stewart platform [m]
MO_B = -10e-3; % Position {B} with respect to {M} [m]
Hc = 2.5*H; % Size of the useful part of the cube [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 25e-3, 'MHb', 25e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e1*ones(6,1));
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), ...
'Mpm', 10, ...
'Mph', 20e-3, ...
'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
stewart = initializeCylindricalStruts(stewart, 'Fsm', 1e-3, 'Msm', 1e-3);
stewart = initializeInertialSensor(stewart);
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
controller = initializeController('type', 'open-loop');
disturbances = initializeDisturbances();
references = initializeReferences(stewart);
displayArchitecture(stewart, 'labels', false, 'view', 'all');
open('stewart_platform_model.slx')
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
freqs = logspace(1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax3 = subplot(2, 1, 2);
hold on;
for i = 1:6
for j = i+1:6
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2], {'$L_i/\tau_i$', '$L_i/\tau_j$'})
linkaxes([ax1,ax2],'x');
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
freqs = logspace(1, 3, 500);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ax3 = subplot(2, 1, 2);
hold on;
for i = 1:6
for j = i+1:6
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2], {'$F_{m,i}/\tau_i$', '$F_{m,i}/\tau_j$'})
linkaxes([ax1,ax2],'x');
H = 200e-3; % height of the Stewart platform [m]
MO_B = -10e-3; % Position {B} with respect to {M} [m]
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateGeneralConfiguration(stewart, 'FR', 250e-3, 'MR', 150e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', 1e6*ones(6,1), 'C', 1e1*ones(6,1));
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.2*max(vecnorm(stewart.platform_F.Fa)), ...
'Mpm', 10, ...
'Mph', 20e-3, ...
'Mpr', 1.2*max(vecnorm(stewart.platform_M.Mb)));
stewart = initializeCylindricalStruts(stewart, 'Fsm', 1e-3, 'Msm', 1e-3);
stewart = initializeInertialSensor(stewart);
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
controller = initializeController('type', 'open-loop');
displayArchitecture(stewart, 'labels', false, 'view', 'all');
open('stewart_platform_model.slx')
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'};
freqs = logspace(1, 3, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax3 = subplot(2, 1, 2);
hold on;
for i = 1:6
for j = i+1:6
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2], {'$L_i/\tau_i$', '$L_i/\tau_j$'})
linkaxes([ax1,ax2],'x');
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
%% Run the linearization
G = linearize(mdl, io, options);
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G.OutputName = {'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
freqs = logspace(1, 3, 500);
figure;
ax1 = subplot(2, 1, 1);
hold on;
for i = 1:6
for j = i+1:6
plot(freqs, abs(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ax3 = subplot(2, 1, 2);
hold on;
for i = 1:6
for j = i+1:6
p2 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(i, j), freqs, 'Hz'))), 'k-');
end
end
set(gca,'ColorOrderIndex',1);
p1 = plot(freqs, 180/pi*angle(squeeze(freqresp(G(1, 1), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend([p1, p2], {'$F_{m,i}/\tau_i$', '$F_{m,i}/\tau_j$'})
linkaxes([ax1,ax2],'x');
%% Cubic configurations with center of the cube above the top platform
H = 100e-3; % height of the Stewart platform [m]
MO_B = 20e-3; % Position {B} with respect to {M} [m]
FOc = H + MO_B; % Center of the cube with respect to {F}
%% Small cube
Hc = 2*MO_B; % Size of the useful part of the cube [m]
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
stewart = computeJacobian(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.1*max(vecnorm(stewart.platform_F.Fa)), 'Mpr', 1.1*max(vecnorm(stewart.platform_M.Mb)));
%% Example of a cubic architecture with cube's center above the top platform - Small cube size
displayArchitecture(stewart, 'labels', false, 'frames', false);
plotCube(stewart, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
scatter3(0, 0, FOc, 200, 'kh');
%% Example of a cubic architecture with cube's center above the top platform - Medium cube size
Hc = H + 2*MO_B; % Size of the useful part of the cube [m]
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
stewart = computeJacobian(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.1*max(vecnorm(stewart.platform_F.Fa)), 'Mpr', 1.1*max(vecnorm(stewart.platform_M.Mb)));
displayArchitecture(stewart, 'labels', false, 'frames', false);
plotCube(stewart, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
scatter3(0, 0, FOc, 200, 'kh');
%% Example of a cubic architecture with cube's center above the top platform - Large cube size
Hc = 2*(H + MO_B); % Size of the useful part of the cube [m]
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', H, 'MO_B', MO_B);
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 5e-3, 'MHb', 5e-3);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'K', ones(6,1));
stewart = computeJacobian(stewart);
stewart = initializeCylindricalPlatforms(stewart, 'Fpr', 1.1*max(vecnorm(stewart.platform_F.Fa)), 'Mpr', 1.1*max(vecnorm(stewart.platform_M.Mb)));
displayArchitecture(stewart, 'labels', false, 'frames', false);
plotCube(stewart, 'Hc', Hc, 'FOc', FOc, 'color', [0,0,0,0.5], 'link_to_struts', true);
scatter3(0, 0, FOc, 200, 'kh');
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