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Add sample on top of hexapod. Add function to initialize hexapod.

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This commit is contained in:
Thomas Dehaeze 2018-06-16 11:57:53 +02:00
parent 6fe96032fd
commit ea06e05f34
11 changed files with 297 additions and 57 deletions
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70
identification_control.m
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@ -1,65 +1,69 @@
%% Script Description
% Script used to identify the transfer functions of the
% Script used to identify the transfer functions of the
% Stewart platform (from actuator to displacement)
%%
clear;
close all;
clc
clear; close all; clc;
%% Define options for bode plots
bode_opts = bodeoptions;
%%
initializeNanoHexapod();
bode_opts.Title.FontSize = 12;
bode_opts.XLabel.FontSize = 12;
bode_opts.YLabel.FontSize = 12;
bode_opts.FreqUnits = 'Hz';
bode_opts.MagUnits = 'abs';
bode_opts.MagScale = 'log';
bode_opts.PhaseWrapping = 'on';
bode_opts.PhaseVisible = 'on';
%%
initializeSample(struct('mass', 0));
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
G_cart_0 = getPlantCart();
%% Name of the Simulink File
mdl = 'stewart_simscape';
%%
initializeSample(struct('mass', 10));
%% Centralized control (Cartesian coordinates)
% Input/Output definition
io(1) = linio([mdl, '/F_cart'],1,'input');
io(2) = linio([mdl, '/Stewart_Platform'],1,'output');
G_cart_10 = getPlantCart();
% Run the linearization
G_cart = linearize(mdl,io, 0);
%%
initializeSample(struct('mass', 50));
% Input/Output names
G_cart.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
G_cart.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
G_cart_50 = getPlantCart();
%%
freqs = logspace(1, 4, 1000);
bodeFig({G_cart_0(1, 1), G_cart_10(1, 1), G_cart_50(1, 1)}, freqs, struct('phase', true))
legend({'$F_x \rightarrow D_x$ - $M = 0Kg$', '$F_x \rightarrow D_x$ - $M = 10Kg$', '$F_x \rightarrow D_x$ - $M = 50Kg$'})
legend('location', 'southwest')
exportFig('hexapod_cart_mass_x', 'normal-tall')
bodeFig({G_cart_0(3, 3), G_cart_10(3, 3), G_cart_50(3, 3)}, freqs, struct('phase', true))
legend({'$F_z \rightarrow D_z$ - $M = 0Kg$', '$F_z \rightarrow D_z$ - $M = 10Kg$', '$F_z \rightarrow D_z$ - $M = 50Kg$'})
legend('location', 'southwest')
exportFig('hexapod_cart_mass_z', 'normal-tall')
%%
% Bode Plot of the linearized function
freqs = logspace(2, 4, 1000);
bodeFig({G_cart(1, 1), G_cart(2, 2), G_cart(3, 3)}, freqs, struct('phase', true))
bodeFig({G_cart_0(1, 1), G_cart_0(2, 2), G_cart_0(3, 3)}, freqs, struct('phase', true))
legend({'$F_x \rightarrow D_x$', '$F_y \rightarrow D_y$', '$F_z \rightarrow D_z$'})
exportFig('hexapod_cart_trans', 'normal-normal')
bodeFig({G_cart(4, 4), G_cart(5, 5), G_cart(6, 6)}, freqs, struct('phase', true))
bodeFig({G_cart_0(4, 4), G_cart_0(5, 5), G_cart_0(6, 6)}, freqs, struct('phase', true))
legend({'$M_x \rightarrow R_x$', '$M_y \rightarrow R_y$', '$M_z \rightarrow R_z$'})
exportFig('hexapod_cart_rot', 'normal-normal')
bodeFig({G_cart(1, 1), G_cart(2, 1), G_cart(3, 1)}, freqs, struct('phase', true))
bodeFig({G_cart_0(1, 1), G_cart_0(2, 1), G_cart_0(3, 1)}, freqs, struct('phase', true))
legend({'$F_x \rightarrow D_x$', '$F_x \rightarrow D_y$', '$F_x \rightarrow D_z$'})
exportFig('hexapod_cart_coupling', 'normal-normal')
%% Save identify transfer functions
save('./mat/G_cart.mat', 'G_cart_0', 'G_cart_10', 'G_cart_50');
%% Centralized control (Cartesian coordinates)
% Input/Output definition
io(1) = linio([mdl, '/F_legs'],1,'input');
io(2) = linio([mdl, '/Stewart_Platform'],2,'output');
% Run the linearization
G_legs = linearize(mdl,io, 0);
G_legs_raw = linearize(mdl,io, 0);
G_legs = preprocessIdTf(G_legs_raw, 10, 10000);
% Input/Output names
G_legs.InputName = {'F1', 'F2', 'F3', 'M4', 'M5', 'M6'};
@ -75,3 +79,5 @@ exportFig('hexapod_legs', 'normal-normal')
bodeFig({G_legs(1, 1), G_legs(2, 1)}, freqs, struct('phase', true))
legend({'$F_i \rightarrow D_i$', '$F_i \rightarrow D_j$'})
exportFig('hexapod_legs_coupling', 'normal-normal')
save('mat/G_legs.mat', 'G_legs');

9
init_simulink.m
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@ -1,7 +1,2 @@
params_micro_hexapod;
micro_hexapod = stewart;
params_nano_hexapod;
nano_hexapod = stewart;
clear stewart;
load('./mat/sample.mat', 'sample')
load('./mat/stewart.mat', 'stewart')

10
params_micro_hexapod.m
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@ -31,11 +31,11 @@ TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext
Leg = struct();
Leg.stroke = 10e-3; % Maximum Stroke of each leg [m]
Leg.k.ax = 5e7; % Stiffness of each leg [N/m]
Leg.ksi.ax = 3; % Maximum amplification at resonance []
Leg.rad.bottom = 25; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 17; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.k.ax = 5e7; % Stiffness of each leg [N/m]
Leg.ksi.ax = 3; % Maximum amplification at resonance []
Leg.rad.bottom = 25; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 17; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb]
Leg.color.top = [0.5 0.5 0.5]; % Color [rgb]

26
params_nano_hexapod.m
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@ -1,17 +1,17 @@
%% Stewart Object
stewart = struct();
stewart.h = 90; % Total height of the platform [mm]
stewart.jacobian = 174.5; % Point where the Jacobian is computed => Center of rotation [mm]
stewart.h = 90; % Total height of the platform [mm]
stewart.jacobian = 174.5; % Point where the Jacobian is computed => Center of rotation [mm]
%% Bottom Plate
BP = struct();
BP.rad.int = 0; % Internal Radius [mm]
BP.rad.ext = 150; % External Radius [mm]
BP.thickness = 10; % Thickness [mm]
BP.thickness = 10; % Thickness [mm]
BP.leg.rad = 100; % Radius where the legs articulations are positionned [mm]
BP.leg.ang = 5; % Angle Offset [deg]
BP.density = 8000; % Density of the material [kg/m^3]
BP.density = 8000;% Density of the material [kg/m^3]
BP.color = [0.7 0.7 0.7]; % Color [rgb]
BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
@ -19,11 +19,11 @@ BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext
TP = struct();
TP.rad.int = 0; % Internal Radius [mm]
TP.rad.ext = 100; % Internal Radius [mm]
TP.thickness = 10; % Thickness [mm]
TP.rad.ext = 100; % Internal Radius [mm]
TP.thickness = 10; % Thickness [mm]
TP.leg.rad = 90; % Radius where the legs articulations are positionned [mm]
TP.leg.ang = 5; % Angle Offset [deg]
TP.density = 8000; % Density of the material [kg/m^3]
TP.leg.ang = 5; % Angle Offset [deg]
TP.density = 8000;% Density of the material [kg/m^3]
TP.color = [0.7 0.7 0.7]; % Color [rgb]
TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
@ -31,11 +31,11 @@ TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext
Leg = struct();
Leg.stroke = 80e-6; % Maximum Stroke of each leg [m]
Leg.k.ax = 5e7; % Stiffness of each leg [N/m]
Leg.ksi.ax = 10; % Maximum amplification at resonance []
Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 10; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.k.ax = 5e7; % Stiffness of each leg [N/m]
Leg.ksi.ax = 10; % Maximum amplification at resonance []
Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 10; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb]
Leg.color.top = [0.5 0.5 0.5]; % Color [rgb]

0
params_sample.m Normal file
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35
src/getPlantCart.m Normal file
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@ -0,0 +1,35 @@
function [G_cart, G_cart_raw] = getPlantCart()
%% Default values for opts
opts = struct('f_low', 1,...
'f_high', 10000 ...
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
opts.(opt{1}) = opts_param.(opt{1});
end
end
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_simscape';
%% Centralized control (Cartesian coordinates)
% Input/Output definition
io(1) = linio([mdl, '/F_cart'],1,'input');
io(2) = linio([mdl, '/Stewart_Platform'],1,'output');
% Run the linearization
G_cart_raw = linearize(mdl,io, 0);
G_cart = preprocessIdTf(G_cart_raw, opts.f_low, opts.f_high);
% Input/Output names
G_cart.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
G_cart.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
end

92
src/initializeMicroHexapod.m Normal file
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@ -0,0 +1,92 @@
function [stewart] = initializeMicroHexapod()
%% Stewart Object
stewart = struct();
stewart.h = 350; % Total height of the platform [mm]
stewart.jacobian = 435; % Point where the Jacobian is computed => Center of rotation [mm]
%% Bottom Plate
BP = struct();
BP.rad.int = 110; % Internal Radius [mm]
BP.rad.ext = 207.5; % External Radius [mm]
BP.thickness = 26; % Thickness [mm]
BP.leg.rad = 175.5; % Radius where the legs articulations are positionned [mm]
BP.leg.ang = 9.5; % Angle Offset [deg]
BP.density = 8000; % Density of the material [kg/m^3]
BP.color = [0.6 0.6 0.6]; % Color [rgb]
BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
%% Top Plate
TP = struct();
TP.rad.int = 82; % Internal Radius [mm]
TP.rad.ext = 150; % Internal Radius [mm]
TP.thickness = 26; % Thickness [mm]
TP.leg.rad = 118; % Radius where the legs articulations are positionned [mm]
TP.leg.ang = 12.1; % Angle Offset [deg]
TP.density = 8000; % Density of the material [kg/m^3]
TP.color = [0.6 0.6 0.6]; % Color [rgb]
TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
%% Leg
Leg = struct();
Leg.stroke = 10e-3; % Maximum Stroke of each leg [m]
Leg.k.ax = 5e7; % Stiffness of each leg [N/m]
Leg.ksi.ax = 3; % Maximum amplification at resonance []
Leg.rad.bottom = 25; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 17; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb]
Leg.color.top = [0.5 0.5 0.5]; % Color [rgb]
Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
Leg.sphere.top = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
Leg.m = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
Leg = updateDamping(Leg);
%% Sphere
SP = struct();
SP.height.bottom = 27; % [mm]
SP.height.top = 27; % [mm]
SP.density.bottom = 8000; % [kg/m^3]
SP.density.top = 8000; % [kg/m^3]
SP.color.bottom = [0.6 0.6 0.6]; % [rgb]
SP.color.top = [0.6 0.6 0.6]; % [rgb]
SP.k.ax = 0; % [N*m/deg]
SP.ksi.ax = 10;
SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
SP.thickness.top = SP.height.top-Leg.sphere.top; % [mm]
SP.rad.bottom = Leg.sphere.bottom; % [mm]
SP.rad.top = Leg.sphere.top; % [mm]
SP.m = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
SP = updateDamping(SP);
%%
Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
Leg.support.top = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
%%
stewart.BP = BP;
stewart.TP = TP;
stewart.Leg = Leg;
stewart.SP = SP;
%%
stewart = initializeParameters(stewart);
%%
save('./mat/hexapod.mat', 'stewart');
%%
function element = updateDamping(element)
field = fieldnames(element.k);
for i = 1:length(field)
element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
end
end
end

93
src/initializeNanoHexapod.m Normal file
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@ -0,0 +1,93 @@
function [stewart] = initializeNanoHexapod()
%% Stewart Object
stewart = struct();
stewart.h = 90; % Total height of the platform [mm]
stewart.jacobian = 174.5; % Point where the Jacobian is computed => Center of rotation [mm]
%% Bottom Plate
BP = struct();
BP.rad.int = 0; % Internal Radius [mm]
BP.rad.ext = 150; % External Radius [mm]
BP.thickness = 10; % Thickness [mm]
BP.leg.rad = 100; % Radius where the legs articulations are positionned [mm]
BP.leg.ang = 5; % Angle Offset [deg]
BP.density = 8000;% Density of the material [kg/m^3]
BP.color = [0.7 0.7 0.7]; % Color [rgb]
BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
%% Top Plate
TP = struct();
TP.rad.int = 0; % Internal Radius [mm]
TP.rad.ext = 100; % Internal Radius [mm]
TP.thickness = 10; % Thickness [mm]
TP.leg.rad = 90; % Radius where the legs articulations are positionned [mm]
TP.leg.ang = 5; % Angle Offset [deg]
TP.density = 8000;% Density of the material [kg/m^3]
TP.color = [0.7 0.7 0.7]; % Color [rgb]
TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
%% Leg
Leg = struct();
Leg.stroke = 80e-6; % Maximum Stroke of each leg [m]
Leg.k.ax = 5e7; % Stiffness of each leg [N/m]
Leg.ksi.ax = 10; % Maximum amplification at resonance []
Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
Leg.rad.top = 10; % Radius of the cylinder of the top part [mm]
Leg.density = 8000; % Density of the material [kg/m^3]
Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb]
Leg.color.top = [0.5 0.5 0.5]; % Color [rgb]
Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
Leg.sphere.top = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
Leg.m = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg]
Leg = updateDamping(Leg);
%% Sphere
SP = struct();
SP.height.bottom = 15; % [mm]
SP.height.top = 15; % [mm]
SP.density.bottom = 8000; % [kg/m^3]
SP.density.top = 8000; % [kg/m^3]
SP.color.bottom = [0.7 0.7 0.7]; % [rgb]
SP.color.top = [0.7 0.7 0.7]; % [rgb]
SP.k.ax = 0; % [N*m/deg]
SP.ksi.ax = 3;
SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
SP.thickness.top = SP.height.top-Leg.sphere.top; % [mm]
SP.rad.bottom = Leg.sphere.bottom; % [mm]
SP.rad.top = Leg.sphere.top; % [mm]
SP.m = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg]
SP = updateDamping(SP);
%%
Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
Leg.support.top = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
%%
stewart.BP = BP;
stewart.TP = TP;
stewart.Leg = Leg;
stewart.SP = SP;
%%
stewart = initializeParameters(stewart);
%%
save('./mat/stewart.mat', 'stewart')
%%
function element = updateDamping(element)
field = fieldnames(element.k);
for i = 1:length(field)
element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
end
end
end

19
src/initializeSample.m Normal file
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@ -0,0 +1,19 @@
function [] = initializeSample(opts_param)
%% Default values for opts
sample = struct('radius', 100,...
'height', 300,...
'mass', 50,...
'offset', 0,...
'color', [0.9 0.1 0.1] ...
);
%% Populate opts with input parameters
if exist('opts_param','var')
for opt = fieldnames(opts_param)'
sample.(opt{1}) = opts_param.(opt{1});
end
end
%% Save
save('./mat/sample.mat', 'sample');
end

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stewart_displacement.slx
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stewart_simscape.slx
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