Compare commits
23 Commits
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18
figs/inkscape/convert_svg.sh
Executable file
18
figs/inkscape/convert_svg.sh
Executable file
@@ -0,0 +1,18 @@
|
|||||||
|
#!/bin/bash
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||||||
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||||||
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# Directory containing SVG files
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||||||
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INPUT_DIR="."
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||||||
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||||||
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# Loop through all SVG files in the directory
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||||||
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for svg_file in "$INPUT_DIR"/*.svg; do
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||||||
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# Check if there are SVG files in the directory
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||||||
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if [ -f "$svg_file" ]; then
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||||||
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# Output PDF file name
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||||||
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pdf_file="../${svg_file%.svg}.pdf"
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||||||
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png_file="../${svg_file%.svg}"
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||||||
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||||||
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# Convert SVG to PDF using Inkscape
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||||||
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inkscape "$svg_file" --export-filename="$pdf_file" && \
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||||||
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pdftocairo -png -singlefile -cropbox "$pdf_file" "$png_file"
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||||||
|
fi
|
||||||
|
done
|
||||||
1047
figs/inkscape/nhexa_actuator_model.svg
Normal file
1047
figs/inkscape/nhexa_actuator_model.svg
Normal file
File diff suppressed because it is too large
Load Diff
|
After Width: | Height: | Size: 83 KiB |
9516
figs/inkscape/nhexa_parallel_architecture_shen.svg
Normal file
9516
figs/inkscape/nhexa_parallel_architecture_shen.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 702 KiB |
1312
figs/inkscape/nhexa_serial_architecture_kenton.svg
Normal file
1312
figs/inkscape/nhexa_serial_architecture_kenton.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 304 KiB |
179
figs/inkscape/nhexa_stages_nazaretski.svg
Normal file
179
figs/inkscape/nhexa_stages_nazaretski.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 876 KiB |
1422
figs/inkscape/nhexa_stages_sapoti.svg
Normal file
1422
figs/inkscape/nhexa_stages_sapoti.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 703 KiB |
202
figs/inkscape/nhexa_stages_schroer.svg
Normal file
202
figs/inkscape/nhexa_stages_schroer.svg
Normal file
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 647 KiB |
469
figs/inkscape/nhexa_stages_villar.svg
Normal file
469
figs/inkscape/nhexa_stages_villar.svg
Normal file
@@ -0,0 +1,469 @@
|
|||||||
|
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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|
<!-- Created with Inkscape (http://www.inkscape.org/) -->
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|
|
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|
<svg
|
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|
version="1.1"
|
||||||
|
id="svg1"
|
||||||
|
width="405.81152"
|
||||||
|
height="284.11676"
|
||||||
|
viewBox="0 0 405.81153 284.11676"
|
||||||
|
sodipodi:docname="nhexa_stages_villar.svg"
|
||||||
|
inkscape:version="1.4 (e7c3feb100, 2024-10-09)"
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|
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
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|
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
|
||||||
|
xmlns="http://www.w3.org/2000/svg"
|
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|
xmlns:svg="http://www.w3.org/2000/svg">
|
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|
<defs
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id="defs1">
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style="overflow:visible"
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inkscape:isstock="true"
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preserveAspectRatio="xMidYMid">
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inkscape:isstock="true"
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inkscape:collect="always"
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pagecolor="#ffffff"
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bordercolor="#666666"
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borderopacity="1.0"
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inkscape:showpageshadow="2"
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inkscape:window-height="1440"
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inkscape:window-y="0"
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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
|
||||||
|
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||||
|
|
||||||
|
%% Data directory
|
||||||
|
data_dir = './mat/';
|
||||||
|
|
||||||
|
% Simulink Model name
|
||||||
|
mdl = 'nano_hexapod_model';
|
||||||
|
|
||||||
|
%% Colors for the figures
|
||||||
|
colors = colororder;
|
||||||
|
|
||||||
|
%% Frequency Vector [Hz]
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
%% Estimate the errors associated with approximate forward kinematics using the Jacobian matrix
|
||||||
|
stewart = initializeSimplifiedNanoHexapod('H', 100e-3);
|
||||||
|
|
||||||
|
Xrs = logspace(-6, -1, 10); % Wanted X translation of the mobile platform [m]
|
||||||
|
phis = linspace(-pi, pi, 100); % Tested azimutal angles [rad]
|
||||||
|
thetas = linspace(0, pi, 100); % Tested polar angles [rad]
|
||||||
|
|
||||||
|
% Compute the strut exact length for each X-position
|
||||||
|
Xrs_errors = zeros(1, length(Xrs)); % Maximum distance error [m]
|
||||||
|
Rrs_errors = zeros(1, length(Xrs)); % Maximum angular error [rad]
|
||||||
|
for i = 1:length(Xrs)
|
||||||
|
Xrs_error_min = 0;
|
||||||
|
Rrs_error_min = 0;
|
||||||
|
for theta = thetas
|
||||||
|
for phi = phis
|
||||||
|
ix = [sin(theta)*cos(phi); sin(theta)*sin(phi);cos(theta)]; % Unit vector for the displacement direction
|
||||||
|
[~, L_exact] = inverseKinematics(stewart, 'AP', Xrs(i)*ix); % Compute exact strut length for the wanted position
|
||||||
|
Xrs_approx = inv(stewart.geometry.J)*L_exact; % Approximate the position using the Jacobian
|
||||||
|
Xrs_error = norm(Xrs(i)*ix - Xrs_approx(1:3), 2); % Compute the position estimation error
|
||||||
|
Rrs_error = norm(Xrs_approx(4:6), 2); % Compute the angular estimation error
|
||||||
|
if Xrs_error > Xrs_error_min
|
||||||
|
Xrs_error_min = Xrs_error;
|
||||||
|
end
|
||||||
|
if Rrs_error > Rrs_error_min
|
||||||
|
Rrs_error_min = Rrs_error;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
Xrs_errors(i) = Xrs_error_min;
|
||||||
|
Rrs_errors(i) = Rrs_error_min;
|
||||||
|
end
|
||||||
|
|
||||||
|
%% Errors associated with the use of the Jacobian matrix to solve the forward kinematic problem
|
||||||
|
figure;
|
||||||
|
yyaxis left
|
||||||
|
hold on;
|
||||||
|
plot(1e6*Xrs, 1e9*Xrs_errors, 'DisplayName', '$\epsilon_D$');
|
||||||
|
plot(1e6*Xrs, 1e6*Xrs, '--', 'DisplayName', '$0.1\%$ error');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
xlim([1, 1e4]); ylim([1, 1e4]);
|
||||||
|
xlabel('Motion Stroke');
|
||||||
|
ylabel('Kinematic Errors');
|
||||||
|
xticks([1, 10, 100, 1000, 10000]);
|
||||||
|
yticks([1, 10, 100, 1000, 10000]);
|
||||||
|
xticklabels({'$1\mu m$', '$10\mu m$', '$100\mu m$', '$1mm$', '$10mm$'});
|
||||||
|
yticklabels({'$1nm$', '$10nm$', '$100nm$', '$1\mu m$', '$10\mu m$'});
|
||||||
|
|
||||||
|
yyaxis right
|
||||||
|
plot(1e6*Xrs, 1e9*Rrs_errors, 'DisplayName', '$\epsilon_R$');
|
||||||
|
set(gca, 'YScale', 'log');
|
||||||
|
ylim([1, 1e4]);
|
||||||
|
yticks([1, 10, 100, 1000, 10000]);
|
||||||
|
yticklabels({'$1$nrad', '$10$nrad', '$100$nrad', '$1\mu$rad', '$10\mu$rad'});
|
||||||
224
matlab/nhexa_2_model.m
Normal file
224
matlab/nhexa_2_model.m
Normal file
@@ -0,0 +1,224 @@
|
|||||||
|
%% 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
|
||||||
|
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||||
|
|
||||||
|
%% Data directory
|
||||||
|
data_dir = './mat/';
|
||||||
|
|
||||||
|
% Simulink Model name
|
||||||
|
mdl = 'nano_hexapod_model';
|
||||||
|
|
||||||
|
%% Colors for the figures
|
||||||
|
colors = colororder;
|
||||||
|
|
||||||
|
%% Frequency Vector [Hz]
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
%% Plant using Analytical Equations
|
||||||
|
% Stewart platform definition
|
||||||
|
k = 1e6; % Actuator stiffness [N/m]
|
||||||
|
c = 1e1; % Actuator damping [N/(m/s)]
|
||||||
|
|
||||||
|
stewart = initializeSimplifiedNanoHexapod(...
|
||||||
|
'Mpm', 1e-3, ...
|
||||||
|
'actuator_type', '1dof', ...
|
||||||
|
'actuator_k', k, ...
|
||||||
|
'actuator_kp', 0, ...
|
||||||
|
'actuator_c', c ...
|
||||||
|
);
|
||||||
|
|
||||||
|
% Payload: Cylinder
|
||||||
|
h = 300e-3; % Height of the cylinder [m]
|
||||||
|
r = 110e-3; % Radius of the cylinder [m]
|
||||||
|
m = 10; % Mass of the payload [kg]
|
||||||
|
initializeSample('type', 'cylindrical', 'm', m, 'H', h, 'R', r);
|
||||||
|
|
||||||
|
% Mass Matrix
|
||||||
|
M = zeros(6,6);
|
||||||
|
M(1,1) = m;
|
||||||
|
M(2,2) = m;
|
||||||
|
M(3,3) = m;
|
||||||
|
M(4,4) = 1/12*m*(3*r^2 + h^2);
|
||||||
|
M(5,5) = 1/12*m*(3*r^2 + h^2);
|
||||||
|
M(6,6) = 1/2*m*r^2;
|
||||||
|
|
||||||
|
% Stiffness and Damping matrices
|
||||||
|
K = k*eye(6);
|
||||||
|
C = c*eye(6);
|
||||||
|
|
||||||
|
% Compute plant in the frame of the struts
|
||||||
|
G_analytical = inv(ss(inv(stewart.geometry.J')*M*inv(stewart.geometry.J)*s^2 + C*s + K));
|
||||||
|
|
||||||
|
% Compare with Simscape model
|
||||||
|
initializeLoggingConfiguration('log', 'none');
|
||||||
|
initializeController('type', 'open-loop');
|
||||||
|
|
||||||
|
% Input/Output definition
|
||||||
|
clear io; io_i = 1;
|
||||||
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||||
|
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'dL'); io_i = io_i + 1; % Encoders [m]
|
||||||
|
|
||||||
|
G_simscape = linearize(mdl, io);
|
||||||
|
G_simscape.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
G_simscape.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6'};
|
||||||
|
|
||||||
|
%% Comparison of the analytical transfer functions and the multi-body model
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_simscape(i,1), freqs, 'Hz'))), 'color', [colors(i,:), 0.5], 'linewidth', 2.5, ...
|
||||||
|
'DisplayName', sprintf('$l_%i/f_1$ - Multi-Body', i))
|
||||||
|
end
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_analytical(i,1), freqs, 'Hz'))), '--', 'color', [colors(i,:)], ...
|
||||||
|
'DisplayName', sprintf('$l_%i/f_1$ - Analytical', i))
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 1e-4]);
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 6, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_simscape(i,1), freqs, 'Hz'))), 'color', [colors(i,:),0.5], 'linewidth', 2.5);
|
||||||
|
end
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_analytical(i,1), freqs, 'Hz'))), '--', 'color', colors(i,:));
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
|
|
||||||
|
%% Multi-Body model of the Nano-Hexapod
|
||||||
|
% Initialize 1DoF
|
||||||
|
initializeSimplifiedNanoHexapod('flex_type_F', '2dof', 'flex_type_M', '3dof', 'actuator_type', '1dof');
|
||||||
|
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
|
||||||
|
initializeLoggingConfiguration('log', 'none');
|
||||||
|
initializeController('type', 'open-loop');
|
||||||
|
|
||||||
|
% Input/Output definition
|
||||||
|
clear io; io_i = 1;
|
||||||
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||||
|
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'dL'); io_i = io_i + 1; % Encoders [m]
|
||||||
|
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors [N]
|
||||||
|
|
||||||
|
% With no payload
|
||||||
|
G = linearize(mdl, io);
|
||||||
|
G.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
G.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6', ...
|
||||||
|
'fn1', 'fn2', 'fn3', 'fn4', 'fn5', 'fn6'};
|
||||||
|
|
||||||
|
%% Multi-Body model of the Nano-Hexapod without parallel stiffness
|
||||||
|
% Initialize 1DoF
|
||||||
|
initializeSimplifiedNanoHexapod('flex_type_F', '2dof', 'flex_type_M', '3dof', 'actuator_type', '1dof', 'actuator_kp', 0);
|
||||||
|
|
||||||
|
% With no payload
|
||||||
|
G_no_kp = linearize(mdl, io);
|
||||||
|
G_no_kp.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
G_no_kp.OutputName = {'dL1', 'dL2', 'dL3', 'dL4', 'dL5', 'dL6', ...
|
||||||
|
'fn1', 'fn2', 'fn3', 'fn4', 'fn5', 'fn6'};
|
||||||
|
|
||||||
|
%% Transfer function from actuator force inputs to displacement of each strut
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'DisplayName', '$l_i/f_i$')
|
||||||
|
for i = 2:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(1,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$l_i/f_j$')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 1e-4]);
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G(i,i), freqs, 'Hz'))), 'color', [colors(1,:),0.5]);
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
|
|
||||||
|
%% Transfer function from actuator force inputs to force sensor in each strut
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(6+i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(7,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'DisplayName', '$f_{ni}/f_i$')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_no_kp(7,1), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||||
|
'DisplayName', '$f_{ni}/f_i$ (no $k_p$)')
|
||||||
|
for i = 2:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(6+i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_no_kp(6+i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G(7,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$f_{ni}/f_j$')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-4, 1e2]);
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G(6+i,i), freqs, 'Hz'))), 'color', colors(1,:));
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_no_kp(6+i,i), freqs, 'Hz'))), 'color', colors(2,:));
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
397
matlab/nhexa_3_control.m
Normal file
397
matlab/nhexa_3_control.m
Normal file
@@ -0,0 +1,397 @@
|
|||||||
|
%% 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
|
||||||
|
addpath('./subsystems/'); % Path for Subsystems Simulink files
|
||||||
|
|
||||||
|
%% Data directory
|
||||||
|
data_dir = './mat/';
|
||||||
|
|
||||||
|
% Simulink Model name
|
||||||
|
mdl = 'nano_hexapod_model';
|
||||||
|
|
||||||
|
%% Colors for the figures
|
||||||
|
colors = colororder;
|
||||||
|
|
||||||
|
%% Frequency Vector [Hz]
|
||||||
|
freqs = logspace(0, 3, 1000);
|
||||||
|
|
||||||
|
%% Identify plant from actuator forces to external metrology
|
||||||
|
stewart = initializeSimplifiedNanoHexapod();
|
||||||
|
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
|
||||||
|
initializeLoggingConfiguration('log', 'none');
|
||||||
|
initializeController('type', 'open-loop');
|
||||||
|
|
||||||
|
% Input/Output definition
|
||||||
|
clear io; io_i = 1;
|
||||||
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||||
|
io(io_i) = linio([mdl, '/plant'], 1, 'openoutput'); io_i = io_i + 1; % External Metrology [m, rad]
|
||||||
|
|
||||||
|
% With no payload
|
||||||
|
G = linearize(mdl, io);
|
||||||
|
G.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
|
||||||
|
|
||||||
|
%% Plant in the Cartesian Frame
|
||||||
|
G_cart = G*inv(stewart.geometry.J');
|
||||||
|
G_cart.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
|
||||||
|
|
||||||
|
%% Plant in the frame of the struts
|
||||||
|
G_struts = stewart.geometry.J*G;
|
||||||
|
G_struts.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
|
||||||
|
|
||||||
|
%% Bode plot of the plant projected in the frame of the struts
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
|
||||||
|
for i = 2:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(1,2), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j$')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 1e-4]);
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:),0.5]);
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
|
|
||||||
|
%% Bode plot of the plant projected in the Cartesian frame
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(i,j), freqs, 'Hz'))), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'DisplayName', '$\epsilon_{D_x}/\mathcal{F}_x$ [m/N]')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(2,2), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||||
|
'DisplayName', '$\epsilon_{D_y}/\mathcal{F}_y$ [m/N]')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(3,3), freqs, 'Hz'))), 'color', colors(3,:), ...
|
||||||
|
'DisplayName', '$\epsilon_{D_z}/\mathcal{F}_z$ [m/N]')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(4,4), freqs, 'Hz'))), 'color', colors(4,:), ...
|
||||||
|
'DisplayName', '$\epsilon_{R_x}/\mathcal{M}_x$ [rad/Nm]')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(5,5), freqs, 'Hz'))), 'color', colors(5,:), ...
|
||||||
|
'DisplayName', '$\epsilon_{R_y}/\mathcal{M}_y$ [rad/Nm]')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(6,6), freqs, 'Hz'))), 'color', colors(6,:), ...
|
||||||
|
'DisplayName', '$\epsilon_{R_z}/\mathcal{M}_z$ [rad/Nm]')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_cart(1,5), freqs, 'Hz'))), 'color', [0, 0, 0, 0.5], ...
|
||||||
|
'DisplayName', 'Coupling')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 4e-3]);
|
||||||
|
leg = legend('location', 'southwest', 'FontSize', 7, 'NumColumns', 3);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cart(i,i), freqs, 'Hz'))), 'color', colors(i,:));
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
|
|
||||||
|
%% Identify the IFF Plant
|
||||||
|
stewart = initializeSimplifiedNanoHexapod('actuator_kp', 0); % Ignoring parallel stiffness for now
|
||||||
|
initializeSample('type', 'cylindrical', 'm', 10, 'H', 300e-3);
|
||||||
|
initializeLoggingConfiguration('log', 'none');
|
||||||
|
initializeController('type', 'open-loop');
|
||||||
|
|
||||||
|
% Input/Output definition
|
||||||
|
clear io; io_i = 1;
|
||||||
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||||
|
io(io_i) = linio([mdl, '/plant'], 2, 'openoutput', [], 'fn'); io_i = io_i + 1; % Force Sensors [N]
|
||||||
|
|
||||||
|
% With no payload
|
||||||
|
G_iff = linearize(mdl, io);
|
||||||
|
G_iff.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
G_iff.OutputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||||
|
|
||||||
|
%% IFF Controller Design
|
||||||
|
Kiff = -500/s * ... % Gain
|
||||||
|
eye(6); % Diagonal 6x6 controller (i.e. decentralized)
|
||||||
|
|
||||||
|
Kiff.InputName = {'fm1', 'fm2', 'fm3', 'fm4', 'fm5', 'fm6'};
|
||||||
|
Kiff.OutputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
|
||||||
|
%% Root Locus plot of the Decentralized IFF Control
|
||||||
|
gains = logspace(-2, 1, 200);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
tiledlayout(1, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||||
|
nexttile();
|
||||||
|
hold on;
|
||||||
|
plot(real(pole(G_iff)), imag(pole(G_iff)), 'x', 'color', colors(1,:), ...
|
||||||
|
'DisplayName', '$g = 0$');
|
||||||
|
plot(real(tzero(G_iff)), imag(tzero(G_iff)), 'o', 'color', colors(1,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
|
||||||
|
for g = gains
|
||||||
|
clpoles = pole(feedback(G_iff, g*Kiff, +1));
|
||||||
|
plot(real(clpoles), imag(clpoles), '.', 'color', colors(1,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
|
||||||
|
% Optimal gain
|
||||||
|
clpoles = pole(feedback(G_iff, Kiff, +1));
|
||||||
|
plot(real(clpoles), imag(clpoles), 'kx', ...
|
||||||
|
'DisplayName', '$g_{opt}$');
|
||||||
|
hold off;
|
||||||
|
axis equal;
|
||||||
|
xlim([-600, 50]); ylim([-50, 600]);
|
||||||
|
xticks([-600:100:0]);
|
||||||
|
yticks([0:100:600]);
|
||||||
|
set(gca, 'XTickLabel',[]); set(gca, 'YTickLabel',[]);
|
||||||
|
xlabel('Real part'); ylabel('Imaginary part');
|
||||||
|
|
||||||
|
%% Loop gain for the Decentralized IFF
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
plot(freqs, abs(squeeze(freqresp(-G_iff(1,1)*Kiff(1,1), freqs, 'Hz'))));
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-2, 1e2]);
|
||||||
|
% leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
% leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(-G_iff(1,1)*Kiff(1,1), freqs, 'Hz'))));
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
ylim([-180, 180])
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([1, 1e3]);
|
||||||
|
|
||||||
|
%% Identify the IFF Plant
|
||||||
|
initializeController('type', 'iff');
|
||||||
|
|
||||||
|
% Input/Output definition
|
||||||
|
clear io; io_i = 1;
|
||||||
|
io(io_i) = linio([mdl, '/Controller'], 1, 'input'); io_i = io_i + 1; % Actuator Inputs [N]
|
||||||
|
io(io_i) = linio([mdl, '/plant'], 1, 'openoutput'); io_i = io_i + 1; % External Metrology [m,rad]
|
||||||
|
|
||||||
|
% With no payload
|
||||||
|
G_hac = linearize(mdl, io);
|
||||||
|
G_hac.InputName = {'f1', 'f2', 'f3', 'f4', 'f5', 'f6'};
|
||||||
|
G_hac.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
|
||||||
|
|
||||||
|
%% Plant in the frame of the struts
|
||||||
|
G_hac_struts = stewart.geometry.J*G_hac;
|
||||||
|
G_hac_struts.OutputName = {'D1', 'D2', 'D3', 'D4', 'D5', 'D6'};
|
||||||
|
|
||||||
|
%% Bode plot of the plant projected in the frame of the struts
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(i,j), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
|
||||||
|
for i = 2:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(1,2), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j$')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 1e-4]);
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', colors(1,:));
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
|
|
||||||
|
%% Bode plot of the plant projected in the frame of the struts
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_hac_struts(i,j), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(1,1), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i$')
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,1), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_i^\prime$')
|
||||||
|
for i = 2:6
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_hac_struts(i,i), freqs, 'Hz'))), 'color', colors(2,:), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,2), freqs, 'Hz'))), 'color', [0,0,0,0.1], ...
|
||||||
|
'DisplayName', '$-\epsilon_{\mathcal{L}i}/f_j^\prime$')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 1e-4]);
|
||||||
|
leg = legend('location', 'northwest', 'FontSize', 8, 'NumColumns', 1);
|
||||||
|
leg.ItemTokenSize(1) = 15;
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_struts(i,i), freqs, 'Hz'))), 'color', [colors(1,:), 0.2]);
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_struts(i,i), freqs, 'Hz'))), 'color', colors(2,:));
|
||||||
|
end
|
||||||
|
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]);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([freqs(1), freqs(end)]);
|
||||||
|
|
||||||
|
%% High Authority Controller - Mid Stiffness Nano-Hexapod
|
||||||
|
% Wanted crossover
|
||||||
|
wc = 2*pi*20; % [rad/s]
|
||||||
|
|
||||||
|
% Integrator
|
||||||
|
H_int = wc/s;
|
||||||
|
|
||||||
|
% Lead to increase phase margin
|
||||||
|
a = 2; % Amount of phase lead / width of the phase lead / high frequency gain
|
||||||
|
H_lead = 1/sqrt(a)*(1 + s/(wc/sqrt(a)))/(1 + s/(wc*sqrt(a)));
|
||||||
|
|
||||||
|
% Low Pass filter to increase robustness
|
||||||
|
H_lpf = 1/(1 + s/2/pi/200);
|
||||||
|
|
||||||
|
% Gain to have unitary crossover at 5Hz
|
||||||
|
H_gain = 1./abs(evalfr(G_hac_struts(1, 1), 1j*wc));
|
||||||
|
|
||||||
|
% Decentralized HAC
|
||||||
|
Khac = H_gain * ... % Gain
|
||||||
|
H_int * ... % Integrator
|
||||||
|
H_lpf * ... % Low Pass filter
|
||||||
|
eye(6); % 6x6 Diagonal
|
||||||
|
|
||||||
|
%% Plot of the eigenvalues of L in the complex plane
|
||||||
|
Ldet = zeros(6, length(freqs));
|
||||||
|
Lmimo = squeeze(freqresp(G_hac_struts*Khac, freqs, 'Hz'));
|
||||||
|
for i_f = 2:length(freqs)
|
||||||
|
Ldet(:, i_f) = eig(squeeze(Lmimo(:,:,i_f)));
|
||||||
|
end
|
||||||
|
mod_margin = min(min(abs(Ldet + ones(size(Ldet)))));
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i = 1:6
|
||||||
|
plot(real(squeeze(Ldet(i,:))), imag(squeeze(Ldet(i,:))), ...
|
||||||
|
'.', 'color', colors(1, :), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(real(squeeze(Ldet(i,:))), -imag(squeeze(Ldet(i,:))), ...
|
||||||
|
'.', 'color', colors(1, :), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(-1, 0, 'kx', 'HandleVisibility', 'off');
|
||||||
|
patch(-1 + mod_margin*cos([0:0.1:2*pi+0.1]), mod_margin*sin([0:0.1:2*pi+0.1]), colors(5,:), 'linestyle', '--', 'EdgeColor','black', 'FaceAlpha', 0.5, 'HandleVisibility', 'off');
|
||||||
|
text(-1,0.1, 'Robustness', 'FontSize', 8, 'horizontalalignment', 'center')
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Real Part'); ylabel('Imaginary Part');
|
||||||
|
axis square
|
||||||
|
xlim([-1.8, 0.2]); ylim([-1, 1]);
|
||||||
|
|
||||||
|
%% Loop gain for the Decentralized HAC_IFF
|
||||||
|
i_fb = find(abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), freqs, 'Hz')))<1, 1);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'compact', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
patch([freqs(1:i_fb), freqs(i_fb), freqs(1)], [abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), [freqs(1:i_fb)], 'Hz'))); 1; 1], colors(5,:), 'EdgeColor','none', 'FaceAlpha', 0.5)
|
||||||
|
plot(freqs, abs(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), freqs, 'Hz'))));
|
||||||
|
text(1.2,2.5,{'Disturbance', 'rejection'}, 'FontSize', 8)
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-2, 1e2]);
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
plot(freqs, 180/pi*angle(squeeze(freqresp(G_hac_struts(1,1)*Khac(1,1), freqs, 'Hz'))));
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
ylim([-180, 180])
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([1, 1e3]);
|
||||||
37
matlab/src/computeJacobian.m
Normal file
37
matlab/src/computeJacobian.m
Normal file
@@ -0,0 +1,37 @@
|
|||||||
|
function [stewart] = computeJacobian(stewart)
|
||||||
|
% computeJacobian -
|
||||||
|
%
|
||||||
|
% Syntax: [stewart] = computeJacobian(stewart)
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% - stewart - With at least the following fields:
|
||||||
|
% - geometry.As [3x6] - The 6 unit vectors for each strut expressed in {A}
|
||||||
|
% - geometry.Ab [3x6] - The 6 position of the joints bi expressed in {A}
|
||||||
|
% - actuators.K [6x1] - Total stiffness of the actuators
|
||||||
|
%
|
||||||
|
% Outputs:
|
||||||
|
% - stewart - With the 3 added field:
|
||||||
|
% - geometry.J [6x6] - The Jacobian Matrix
|
||||||
|
% - geometry.K [6x6] - The Stiffness Matrix
|
||||||
|
% - geometry.C [6x6] - The Compliance Matrix
|
||||||
|
|
||||||
|
assert(isfield(stewart.geometry, 'As'), 'stewart.geometry should have attribute As')
|
||||||
|
As = stewart.geometry.As;
|
||||||
|
|
||||||
|
assert(isfield(stewart.geometry, 'Ab'), 'stewart.geometry should have attribute Ab')
|
||||||
|
Ab = stewart.geometry.Ab;
|
||||||
|
|
||||||
|
assert(isfield(stewart.actuators, 'k'), 'stewart.actuators should have attribute k')
|
||||||
|
Ki = stewart.actuators.k;
|
||||||
|
|
||||||
|
J = [As' , cross(Ab, As)'];
|
||||||
|
|
||||||
|
K = J'*diag(Ki)*J;
|
||||||
|
|
||||||
|
C = inv(K);
|
||||||
|
|
||||||
|
stewart.geometry.J = J;
|
||||||
|
stewart.geometry.K = K;
|
||||||
|
stewart.geometry.C = C;
|
||||||
|
|
||||||
|
end
|
||||||
80
matlab/src/computeJointsPose.m
Normal file
80
matlab/src/computeJointsPose.m
Normal file
@@ -0,0 +1,80 @@
|
|||||||
|
function [stewart] = computeJointsPose(stewart)
|
||||||
|
% computeJointsPose -
|
||||||
|
%
|
||||||
|
% Syntax: [stewart] = computeJointsPose(stewart)
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% - stewart - A structure with the following fields
|
||||||
|
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
|
||||||
|
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
|
||||||
|
% - platform_F.FO_A [3x1] - Position of {A} with respect to {F}
|
||||||
|
% - platform_M.MO_B [3x1] - Position of {B} with respect to {M}
|
||||||
|
% - geometry.FO_M [3x1] - Position of {M} with respect to {F}
|
||||||
|
%
|
||||||
|
% Outputs:
|
||||||
|
% - stewart - A structure with the following added fields
|
||||||
|
% - geometry.Aa [3x6] - The i'th column is the position of ai with respect to {A}
|
||||||
|
% - geometry.Ab [3x6] - The i'th column is the position of bi with respect to {A}
|
||||||
|
% - geometry.Ba [3x6] - The i'th column is the position of ai with respect to {B}
|
||||||
|
% - geometry.Bb [3x6] - The i'th column is the position of bi with respect to {B}
|
||||||
|
% - geometry.l [6x1] - The i'th element is the initial length of strut i
|
||||||
|
% - geometry.As [3x6] - The i'th column is the unit vector of strut i expressed in {A}
|
||||||
|
% - geometry.Bs [3x6] - The i'th column is the unit vector of strut i expressed in {B}
|
||||||
|
% - struts_F.l [6x1] - Length of the Fixed part of the i'th strut
|
||||||
|
% - struts_M.l [6x1] - Length of the Mobile part of the i'th strut
|
||||||
|
% - platform_F.FRa [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the bottom of the i'th strut from {F}
|
||||||
|
% - platform_M.MRb [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the top of the i'th strut from {M}
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_F, 'Fa'), 'stewart.platform_F should have attribute Fa')
|
||||||
|
Fa = stewart.platform_F.Fa;
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_M, 'Mb'), 'stewart.platform_M should have attribute Mb')
|
||||||
|
Mb = stewart.platform_M.Mb;
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
|
||||||
|
FO_A = stewart.platform_F.FO_A;
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
|
||||||
|
MO_B = stewart.platform_M.MO_B;
|
||||||
|
|
||||||
|
assert(isfield(stewart.geometry, 'FO_M'), 'stewart.geometry should have attribute FO_M')
|
||||||
|
FO_M = stewart.geometry.FO_M;
|
||||||
|
|
||||||
|
Aa = Fa - repmat(FO_A, [1, 6]);
|
||||||
|
Bb = Mb - repmat(MO_B, [1, 6]);
|
||||||
|
|
||||||
|
Ab = Bb - repmat(-MO_B-FO_M+FO_A, [1, 6]);
|
||||||
|
Ba = Aa - repmat( MO_B+FO_M-FO_A, [1, 6]);
|
||||||
|
|
||||||
|
As = (Ab - Aa)./vecnorm(Ab - Aa); % As_i is the i'th vector of As
|
||||||
|
|
||||||
|
l = vecnorm(Ab - Aa)';
|
||||||
|
|
||||||
|
Bs = (Bb - Ba)./vecnorm(Bb - Ba);
|
||||||
|
|
||||||
|
FRa = zeros(3,3,6);
|
||||||
|
MRb = zeros(3,3,6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
FRa(:,:,i) = [cross([0;1;0], As(:,i)) , cross(As(:,i), cross([0;1;0], As(:,i))) , As(:,i)];
|
||||||
|
FRa(:,:,i) = FRa(:,:,i)./vecnorm(FRa(:,:,i));
|
||||||
|
|
||||||
|
MRb(:,:,i) = [cross([0;1;0], Bs(:,i)) , cross(Bs(:,i), cross([0;1;0], Bs(:,i))) , Bs(:,i)];
|
||||||
|
MRb(:,:,i) = MRb(:,:,i)./vecnorm(MRb(:,:,i));
|
||||||
|
end
|
||||||
|
|
||||||
|
stewart.geometry.Aa = Aa;
|
||||||
|
stewart.geometry.Ab = Ab;
|
||||||
|
stewart.geometry.Ba = Ba;
|
||||||
|
stewart.geometry.Bb = Bb;
|
||||||
|
stewart.geometry.As = As;
|
||||||
|
stewart.geometry.Bs = Bs;
|
||||||
|
stewart.geometry.l = l;
|
||||||
|
|
||||||
|
stewart.struts_F.l = l/2;
|
||||||
|
stewart.struts_M.l = l/2;
|
||||||
|
|
||||||
|
stewart.platform_F.FRa = FRa;
|
||||||
|
stewart.platform_M.MRb = MRb;
|
||||||
|
|
||||||
|
end
|
||||||
80
matlab/src/describeStewartPlatform.m
Normal file
80
matlab/src/describeStewartPlatform.m
Normal file
@@ -0,0 +1,80 @@
|
|||||||
|
function [] = describeStewartPlatform(stewart)
|
||||||
|
% describeStewartPlatform - Display some text describing the current defined Stewart Platform
|
||||||
|
%
|
||||||
|
% Syntax: [] = describeStewartPlatform(args)
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% - stewart
|
||||||
|
%
|
||||||
|
% Outputs:
|
||||||
|
|
||||||
|
arguments
|
||||||
|
stewart
|
||||||
|
end
|
||||||
|
|
||||||
|
fprintf('GEOMETRY:\n')
|
||||||
|
fprintf('- The height between the fixed based and the top platform is %.3g [mm].\n', 1e3*stewart.geometry.H)
|
||||||
|
|
||||||
|
if stewart.platform_M.MO_B(3) > 0
|
||||||
|
fprintf('- Frame {A} is located %.3g [mm] above the top platform.\n', 1e3*stewart.platform_M.MO_B(3))
|
||||||
|
else
|
||||||
|
fprintf('- Frame {A} is located %.3g [mm] below the top platform.\n', - 1e3*stewart.platform_M.MO_B(3))
|
||||||
|
end
|
||||||
|
|
||||||
|
fprintf('- The initial length of the struts are:\n')
|
||||||
|
fprintf('\t %.3g, %.3g, %.3g, %.3g, %.3g, %.3g [mm]\n', 1e3*stewart.geometry.l)
|
||||||
|
fprintf('\n')
|
||||||
|
|
||||||
|
fprintf('ACTUATORS:\n')
|
||||||
|
if stewart.actuators.type == 1
|
||||||
|
fprintf('- The actuators are modelled as 1DoF.\n')
|
||||||
|
fprintf('- The Stiffness and Damping of each actuators is:\n')
|
||||||
|
fprintf('\t k = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.k(1), stewart.actuators.c(1))
|
||||||
|
if stewart.actuators.kp > 0
|
||||||
|
fprintf('\t Added parallel stiffness: kp = %.0e [N/m] \t c = %.0e [N/(m/s)]\n', stewart.actuators.kp(1))
|
||||||
|
end
|
||||||
|
elseif stewart.actuators.type == 2
|
||||||
|
fprintf('- The actuators are modelled as 2DoF (APA).\n')
|
||||||
|
fprintf('- The vertical stiffness and damping contribution of the piezoelectric stack is:\n')
|
||||||
|
fprintf('\t ka = %.0e [N/m] \t ca = %.0e [N/(m/s)]\n', stewart.actuators.ka(1), stewart.actuators.ca(1))
|
||||||
|
fprintf('- Vertical stiffness when the piezoelectric stack is removed is:\n')
|
||||||
|
fprintf('\t kr = %.0e [N/m] \t cr = %.0e [N/(m/s)]\n', stewart.actuators.kr(1), stewart.actuators.cr(1))
|
||||||
|
elseif stewart.actuators.type == 3
|
||||||
|
fprintf('- The actuators are modelled with a flexible element (FEM).\n')
|
||||||
|
end
|
||||||
|
fprintf('\n')
|
||||||
|
|
||||||
|
fprintf('JOINTS:\n')
|
||||||
|
|
||||||
|
switch stewart.joints_F.type
|
||||||
|
case 1
|
||||||
|
fprintf('- The joints on the fixed based are universal joints (2DoF)\n')
|
||||||
|
case 2
|
||||||
|
fprintf('- The joints on the fixed based are spherical joints (3DoF)\n')
|
||||||
|
end
|
||||||
|
|
||||||
|
switch stewart.joints_M.type
|
||||||
|
case 1
|
||||||
|
fprintf('- The joints on the mobile based are universal joints (2DoF)\n')
|
||||||
|
case 2
|
||||||
|
fprintf('- The joints on the mobile based are spherical joints (3DoF)\n')
|
||||||
|
end
|
||||||
|
|
||||||
|
fprintf('- The position of the joints on the fixed based with respect to {F} are (in [mm]):\n')
|
||||||
|
fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_F.Fa)
|
||||||
|
|
||||||
|
fprintf('- The position of the joints on the mobile based with respect to {M} are (in [mm]):\n')
|
||||||
|
fprintf('\t % .3g \t % .3g \t % .3g\n', 1e3*stewart.platform_M.Mb)
|
||||||
|
fprintf('\n')
|
||||||
|
|
||||||
|
fprintf('KINEMATICS:\n')
|
||||||
|
|
||||||
|
if isfield(stewart.kinematics, 'K')
|
||||||
|
fprintf('- The Stiffness matrix K is (in [N/m]):\n')
|
||||||
|
fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.K)
|
||||||
|
end
|
||||||
|
|
||||||
|
if isfield(stewart.kinematics, 'C')
|
||||||
|
fprintf('- The Damping matrix C is (in [m/N]):\n')
|
||||||
|
fprintf('\t % .0e \t % .0e \t % .0e \t % .0e \t % .0e \t % .0e\n', stewart.kinematics.C)
|
||||||
|
end
|
||||||
240
matlab/src/displayArchitecture.m
Normal file
240
matlab/src/displayArchitecture.m
Normal file
@@ -0,0 +1,240 @@
|
|||||||
|
function [] = displayArchitecture(stewart, args)
|
||||||
|
% displayArchitecture - 3D plot of the Stewart platform architecture
|
||||||
|
%
|
||||||
|
% Syntax: [] = displayArchitecture(args)
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% - stewart
|
||||||
|
% - args - Structure with 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}
|
||||||
|
% - ARB [3x3] - The rotation matrix that gives the wanted orientation of {B} with respect to {A}
|
||||||
|
% - F_color [color] - Color used for the Fixed elements
|
||||||
|
% - M_color [color] - Color used for the Mobile elements
|
||||||
|
% - L_color [color] - Color used for the Legs elements
|
||||||
|
% - frames [true/false] - Display the Frames
|
||||||
|
% - legs [true/false] - Display the Legs
|
||||||
|
% - joints [true/false] - Display the Joints
|
||||||
|
% - labels [true/false] - Display the Labels
|
||||||
|
% - platforms [true/false] - Display the Platforms
|
||||||
|
% - views ['all', 'xy', 'yz', 'xz', 'default'] -
|
||||||
|
%
|
||||||
|
% Outputs:
|
||||||
|
|
||||||
|
arguments
|
||||||
|
stewart
|
||||||
|
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
|
||||||
|
args.ARB (3,3) double {mustBeNumeric} = eye(3)
|
||||||
|
args.F_color = [0 0.4470 0.7410]
|
||||||
|
args.M_color = [0.8500 0.3250 0.0980]
|
||||||
|
args.L_color = [0 0 0]
|
||||||
|
args.frames logical {mustBeNumericOrLogical} = true
|
||||||
|
args.legs logical {mustBeNumericOrLogical} = true
|
||||||
|
args.joints logical {mustBeNumericOrLogical} = true
|
||||||
|
args.labels logical {mustBeNumericOrLogical} = true
|
||||||
|
args.platforms logical {mustBeNumericOrLogical} = true
|
||||||
|
args.views char {mustBeMember(args.views,{'all', 'xy', 'xz', 'yz', 'default'})} = 'default'
|
||||||
|
end
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_F, 'FO_A'), 'stewart.platform_F should have attribute FO_A')
|
||||||
|
FO_A = stewart.platform_F.FO_A;
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_M, 'MO_B'), 'stewart.platform_M should have attribute MO_B')
|
||||||
|
MO_B = stewart.platform_M.MO_B;
|
||||||
|
|
||||||
|
assert(isfield(stewart.geometry, 'H'), 'stewart.geometry should have attribute H')
|
||||||
|
H = stewart.geometry.H;
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_F, 'Fa'), 'stewart.platform_F should have attribute Fa')
|
||||||
|
Fa = stewart.platform_F.Fa;
|
||||||
|
|
||||||
|
assert(isfield(stewart.platform_M, 'Mb'), 'stewart.platform_M should have attribute Mb')
|
||||||
|
Mb = stewart.platform_M.Mb;
|
||||||
|
|
||||||
|
if ~strcmp(args.views, 'all')
|
||||||
|
figure;
|
||||||
|
else
|
||||||
|
f = figure('visible', 'off');
|
||||||
|
end
|
||||||
|
|
||||||
|
hold on;
|
||||||
|
|
||||||
|
FTa = [eye(3), FO_A; ...
|
||||||
|
zeros(1,3), 1];
|
||||||
|
ATb = [args.ARB, args.AP; ...
|
||||||
|
zeros(1,3), 1];
|
||||||
|
BTm = [eye(3), -MO_B; ...
|
||||||
|
zeros(1,3), 1];
|
||||||
|
|
||||||
|
FTm = FTa*ATb*BTm;
|
||||||
|
|
||||||
|
d_unit_vector = H/4;
|
||||||
|
|
||||||
|
d_label = H/20;
|
||||||
|
|
||||||
|
Ff = [0, 0, 0];
|
||||||
|
if args.frames
|
||||||
|
quiver3(Ff(1)*ones(1,3), Ff(2)*ones(1,3), Ff(3)*ones(1,3), ...
|
||||||
|
[d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
|
||||||
|
|
||||||
|
if args.labels
|
||||||
|
text(Ff(1) + d_label, ...
|
||||||
|
Ff(2) + d_label, ...
|
||||||
|
Ff(3) + d_label, '$\{F\}$', 'Color', args.F_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if args.frames
|
||||||
|
quiver3(FO_A(1)*ones(1,3), FO_A(2)*ones(1,3), FO_A(3)*ones(1,3), ...
|
||||||
|
[d_unit_vector 0 0], [0 d_unit_vector 0], [0 0 d_unit_vector], '-', 'Color', args.F_color)
|
||||||
|
|
||||||
|
if args.labels
|
||||||
|
text(FO_A(1) + d_label, ...
|
||||||
|
FO_A(2) + d_label, ...
|
||||||
|
FO_A(3) + d_label, '$\{A\}$', 'Color', args.F_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if args.platforms && stewart.platform_F.type == 1
|
||||||
|
theta = [0:0.01:2*pi+0.01]; % Angles [rad]
|
||||||
|
v = null([0; 0; 1]'); % Two vectors that are perpendicular to the circle normal
|
||||||
|
center = [0; 0; 0]; % Center of the circle
|
||||||
|
radius = stewart.platform_F.R; % Radius of the circle [m]
|
||||||
|
|
||||||
|
points = center*ones(1, length(theta)) + radius*(v(:,1)*cos(theta) + v(:,2)*sin(theta));
|
||||||
|
|
||||||
|
plot3(points(1,:), ...
|
||||||
|
points(2,:), ...
|
||||||
|
points(3,:), '-', 'Color', args.F_color);
|
||||||
|
end
|
||||||
|
|
||||||
|
if args.joints
|
||||||
|
scatter3(Fa(1,:), ...
|
||||||
|
Fa(2,:), ...
|
||||||
|
Fa(3,:), 'MarkerEdgeColor', args.F_color);
|
||||||
|
if args.labels
|
||||||
|
for i = 1:size(Fa,2)
|
||||||
|
text(Fa(1,i) + d_label, ...
|
||||||
|
Fa(2,i), ...
|
||||||
|
Fa(3,i), sprintf('$a_{%i}$', i), 'Color', args.F_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
Fm = FTm*[0; 0; 0; 1]; % Get the position of frame {M} w.r.t. {F}
|
||||||
|
|
||||||
|
if args.frames
|
||||||
|
FM_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
|
||||||
|
quiver3(Fm(1)*ones(1,3), Fm(2)*ones(1,3), Fm(3)*ones(1,3), ...
|
||||||
|
FM_uv(1,1:3), FM_uv(2,1:3), FM_uv(3,1:3), '-', 'Color', args.M_color)
|
||||||
|
|
||||||
|
if args.labels
|
||||||
|
text(Fm(1) + d_label, ...
|
||||||
|
Fm(2) + d_label, ...
|
||||||
|
Fm(3) + d_label, '$\{M\}$', 'Color', args.M_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
FB = FO_A + args.AP;
|
||||||
|
|
||||||
|
if args.frames
|
||||||
|
FB_uv = FTm*[d_unit_vector*eye(3); zeros(1,3)]; % Rotated Unit vectors
|
||||||
|
quiver3(FB(1)*ones(1,3), FB(2)*ones(1,3), FB(3)*ones(1,3), ...
|
||||||
|
FB_uv(1,1:3), FB_uv(2,1:3), FB_uv(3,1:3), '-', 'Color', args.M_color)
|
||||||
|
|
||||||
|
if args.labels
|
||||||
|
text(FB(1) - d_label, ...
|
||||||
|
FB(2) + d_label, ...
|
||||||
|
FB(3) + d_label, '$\{B\}$', 'Color', args.M_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if args.platforms && stewart.platform_M.type == 1
|
||||||
|
theta = [0:0.01:2*pi+0.01]; % Angles [rad]
|
||||||
|
v = null((FTm(1:3,1:3)*[0;0;1])'); % Two vectors that are perpendicular to the circle normal
|
||||||
|
center = Fm(1:3); % Center of the circle
|
||||||
|
radius = stewart.platform_M.R; % Radius of the circle [m]
|
||||||
|
|
||||||
|
points = center*ones(1, length(theta)) + radius*(v(:,1)*cos(theta) + v(:,2)*sin(theta));
|
||||||
|
|
||||||
|
plot3(points(1,:), ...
|
||||||
|
points(2,:), ...
|
||||||
|
points(3,:), '-', 'Color', args.M_color);
|
||||||
|
end
|
||||||
|
|
||||||
|
if args.joints
|
||||||
|
Fb = FTm*[Mb;ones(1,6)];
|
||||||
|
|
||||||
|
scatter3(Fb(1,:), ...
|
||||||
|
Fb(2,:), ...
|
||||||
|
Fb(3,:), 'MarkerEdgeColor', args.M_color);
|
||||||
|
|
||||||
|
if args.labels
|
||||||
|
for i = 1:size(Fb,2)
|
||||||
|
text(Fb(1,i) + d_label, ...
|
||||||
|
Fb(2,i), ...
|
||||||
|
Fb(3,i), sprintf('$b_{%i}$', i), 'Color', args.M_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if args.legs
|
||||||
|
for i = 1:6
|
||||||
|
plot3([Fa(1,i), Fb(1,i)], ...
|
||||||
|
[Fa(2,i), Fb(2,i)], ...
|
||||||
|
[Fa(3,i), Fb(3,i)], '-', 'Color', args.L_color);
|
||||||
|
|
||||||
|
if args.labels
|
||||||
|
text((Fa(1,i)+Fb(1,i))/2 + d_label, ...
|
||||||
|
(Fa(2,i)+Fb(2,i))/2, ...
|
||||||
|
(Fa(3,i)+Fb(3,i))/2, sprintf('$%i$', i), 'Color', args.L_color);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
switch args.views
|
||||||
|
case 'default'
|
||||||
|
view([1 -0.6 0.4]);
|
||||||
|
case 'xy'
|
||||||
|
view([0 0 1]);
|
||||||
|
case 'xz'
|
||||||
|
view([0 -1 0]);
|
||||||
|
case 'yz'
|
||||||
|
view([1 0 0]);
|
||||||
|
end
|
||||||
|
axis equal;
|
||||||
|
axis off;
|
||||||
|
|
||||||
|
if strcmp(args.views, 'all')
|
||||||
|
hAx = findobj('type', 'axes');
|
||||||
|
|
||||||
|
figure;
|
||||||
|
s1 = subplot(2,2,1);
|
||||||
|
copyobj(get(hAx(1), 'Children'), s1);
|
||||||
|
view([0 0 1]);
|
||||||
|
axis equal;
|
||||||
|
axis off;
|
||||||
|
title('Top')
|
||||||
|
|
||||||
|
s2 = subplot(2,2,2);
|
||||||
|
copyobj(get(hAx(1), 'Children'), s2);
|
||||||
|
view([1 -0.6 0.4]);
|
||||||
|
axis equal;
|
||||||
|
axis off;
|
||||||
|
|
||||||
|
s3 = subplot(2,2,3);
|
||||||
|
copyobj(get(hAx(1), 'Children'), s3);
|
||||||
|
view([1 0 0]);
|
||||||
|
axis equal;
|
||||||
|
axis off;
|
||||||
|
title('Front')
|
||||||
|
|
||||||
|
s4 = subplot(2,2,4);
|
||||||
|
copyobj(get(hAx(1), 'Children'), s4);
|
||||||
|
view([0 -1 0]);
|
||||||
|
axis equal;
|
||||||
|
axis off;
|
||||||
|
title('Side')
|
||||||
|
|
||||||
|
close(f);
|
||||||
|
end
|
||||||
41
matlab/src/generateGeneralConfiguration.m
Normal file
41
matlab/src/generateGeneralConfiguration.m
Normal file
@@ -0,0 +1,41 @@
|
|||||||
|
function [stewart] = generateGeneralConfiguration(stewart, args)
|
||||||
|
% generateGeneralConfiguration - Generate a Very General Configuration
|
||||||
|
%
|
||||||
|
% Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% - args - Can have the following fields:
|
||||||
|
% - 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]
|
||||||
|
% - FTh [6x1] - Angles of the fixed joints in the X-Y plane with respect to the X axis [rad]
|
||||||
|
% - MH [1x1] - Height of the position of the mobile joints with respect to the frame {M} [m]
|
||||||
|
% - FR [1x1] - Radius of the position of the mobile joints in the X-Y [m]
|
||||||
|
% - MTh [6x1] - Angles of the mobile joints in the X-Y plane with respect to the X axis [rad]
|
||||||
|
%
|
||||||
|
% Outputs:
|
||||||
|
% - stewart - updated Stewart structure with the added fields:
|
||||||
|
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
|
||||||
|
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
|
||||||
|
|
||||||
|
arguments
|
||||||
|
stewart
|
||||||
|
args.FH (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
|
||||||
|
args.FR (1,1) double {mustBeNumeric, mustBePositive} = 115e-3;
|
||||||
|
args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180);
|
||||||
|
args.MH (1,1) double {mustBeNumeric, mustBeNonnegative} = 15e-3
|
||||||
|
args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e-3;
|
||||||
|
args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180);
|
||||||
|
end
|
||||||
|
|
||||||
|
Fa = zeros(3,6);
|
||||||
|
Mb = zeros(3,6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
Fa(:,i) = [args.FR*cos(args.FTh(i)); args.FR*sin(args.FTh(i)); args.FH];
|
||||||
|
Mb(:,i) = [args.MR*cos(args.MTh(i)); args.MR*sin(args.MTh(i)); -args.MH];
|
||||||
|
end
|
||||||
|
|
||||||
|
stewart.platform_F.Fa = Fa;
|
||||||
|
stewart.platform_M.Mb = Mb;
|
||||||
|
|
||||||
|
end
|
||||||
24
matlab/src/initializeController.m
Normal file
24
matlab/src/initializeController.m
Normal file
@@ -0,0 +1,24 @@
|
|||||||
|
function [] = initializeController(args)
|
||||||
|
|
||||||
|
arguments
|
||||||
|
args.type char {mustBeMember(args.type,{'open-loop', 'iff'})} = 'open-loop'
|
||||||
|
end
|
||||||
|
|
||||||
|
controller = struct();
|
||||||
|
|
||||||
|
switch args.type
|
||||||
|
case 'open-loop'
|
||||||
|
controller.type = 1;
|
||||||
|
controller.name = 'Open-Loop';
|
||||||
|
case 'iff'
|
||||||
|
controller.type = 2;
|
||||||
|
controller.name = 'Decentralized Integral Force Feedback';
|
||||||
|
end
|
||||||
|
|
||||||
|
if exist('./mat', 'dir')
|
||||||
|
save('mat/nano_hexapod_model_controller.mat', 'controller');
|
||||||
|
elseif exist('./matlab', 'dir')
|
||||||
|
save('matlab/mat/nano_hexapod_model_controller.mat', 'controller');
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
61
matlab/src/initializeCylindricalPlatforms.m
Normal file
61
matlab/src/initializeCylindricalPlatforms.m
Normal file
@@ -0,0 +1,61 @@
|
|||||||
|
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:
|
||||||
|
% - platform_F [struct] - structure with the following fields:
|
||||||
|
% - type = 1
|
||||||
|
% - M [1x1] - Fixed Platform Mass [kg]
|
||||||
|
% - I [3x3] - Fixed Platform Inertia matrix [kg*m^2]
|
||||||
|
% - H [1x1] - Fixed Platform Height [m]
|
||||||
|
% - R [1x1] - Fixed Platform Radius [m]
|
||||||
|
% - platform_M [struct] - structure with the following fields:
|
||||||
|
% - M [1x1] - Mobile Platform Mass [kg]
|
||||||
|
% - I [3x3] - Mobile Platform Inertia matrix [kg*m^2]
|
||||||
|
% - H [1x1] - Mobile Platform Height [m]
|
||||||
|
% - R [1x1] - Mobile Platform Radius [m]
|
||||||
|
|
||||||
|
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
|
||||||
|
|
||||||
|
I_F = diag([1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
|
||||||
|
1/12*args.Fpm * (3*args.Fpr^2 + args.Fph^2), ...
|
||||||
|
1/2 *args.Fpm * args.Fpr^2]);
|
||||||
|
|
||||||
|
I_M = diag([1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
|
||||||
|
1/12*args.Mpm * (3*args.Mpr^2 + args.Mph^2), ...
|
||||||
|
1/2 *args.Mpm * args.Mpr^2]);
|
||||||
|
|
||||||
|
stewart.platform_F.type = 1;
|
||||||
|
|
||||||
|
stewart.platform_F.I = I_F;
|
||||||
|
stewart.platform_F.M = args.Fpm;
|
||||||
|
stewart.platform_F.R = args.Fpr;
|
||||||
|
stewart.platform_F.H = args.Fph;
|
||||||
|
|
||||||
|
stewart.platform_M.type = 1;
|
||||||
|
|
||||||
|
stewart.platform_M.I = I_M;
|
||||||
|
stewart.platform_M.M = args.Mpm;
|
||||||
|
stewart.platform_M.R = args.Mpr;
|
||||||
|
stewart.platform_M.H = args.Mph;
|
||||||
|
|
||||||
|
end
|
||||||
50
matlab/src/initializeCylindricalStruts.m
Normal file
50
matlab/src/initializeCylindricalStruts.m
Normal file
@@ -0,0 +1,50 @@
|
|||||||
|
function [stewart] = initializeCylindricalStruts(stewart, args)
|
||||||
|
% initializeCylindricalStruts - Define the mass and moment of inertia of cylindrical struts
|
||||||
|
%
|
||||||
|
% Syntax: [stewart] = initializeCylindricalStruts(args)
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% - args - Structure with the following fields:
|
||||||
|
% - Fsm [1x1] - Mass of the Fixed part of the struts [kg]
|
||||||
|
% - Fsh [1x1] - Height of cylinder for the Fixed part of the struts [m]
|
||||||
|
% - Fsr [1x1] - Radius of cylinder for the Fixed part of the struts [m]
|
||||||
|
% - Msm [1x1] - Mass of the Mobile part of the struts [kg]
|
||||||
|
% - Msh [1x1] - Height of cylinder for the Mobile part of the struts [m]
|
||||||
|
% - Msr [1x1] - Radius of cylinder for the Mobile part of the struts [m]
|
||||||
|
%
|
||||||
|
% Outputs:
|
||||||
|
% - stewart - updated Stewart structure with the added fields:
|
||||||
|
% - struts_F [struct] - structure with the following fields:
|
||||||
|
% - M [6x1] - Mass of the Fixed part of the struts [kg]
|
||||||
|
% - I [3x3x6] - Moment of Inertia for the Fixed part of the struts [kg*m^2]
|
||||||
|
% - H [6x1] - Height of cylinder for the Fixed part of the struts [m]
|
||||||
|
% - R [6x1] - Radius of cylinder for the Fixed part of the struts [m]
|
||||||
|
% - struts_M [struct] - structure with the following fields:
|
||||||
|
% - M [6x1] - Mass of the Mobile part of the struts [kg]
|
||||||
|
% - I [3x3x6] - Moment of Inertia for the Mobile part of the struts [kg*m^2]
|
||||||
|
% - H [6x1] - Height of cylinder for the Mobile part of the struts [m]
|
||||||
|
% - R [6x1] - Radius of cylinder for the Mobile part of the struts [m]
|
||||||
|
|
||||||
|
arguments
|
||||||
|
stewart
|
||||||
|
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
||||||
|
args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
|
||||||
|
args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
|
||||||
|
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
|
||||||
|
args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
|
||||||
|
args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
|
||||||
|
end
|
||||||
|
|
||||||
|
stewart.struts_M.type = 1;
|
||||||
|
|
||||||
|
stewart.struts_M.M = args.Msm;
|
||||||
|
stewart.struts_M.R = args.Msr;
|
||||||
|
stewart.struts_M.H = args.Msh;
|
||||||
|
|
||||||
|
stewart.struts_F.type = 1;
|
||||||
|
|
||||||
|
stewart.struts_F.M = args.Fsm;
|
||||||
|
stewart.struts_F.R = args.Fsr;
|
||||||
|
stewart.struts_F.H = args.Fsh;
|
||||||
|
|
||||||
|
end
|
||||||
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Reference in New Issue
Block a user