From 057ac440aac3cd694e5628cc6af3bcb9d581a94e Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Wed, 20 Mar 2019 09:32:24 +0100 Subject: [PATCH] Add index.org file with matlab functions included --- .gitignore | 2 + index.org | 362 +++++++++++++++++++++++++++++++++++++++ mat/G.mat | Bin 0 -> 16341 bytes mat/G_iff.mat | Bin 0 -> 90985 bytes mat/G_jacobian.mat | Bin 0 -> 132424 bytes mat/K_iff.mat | Bin 0 -> 1030 bytes mat/K_iff_sisotool.mat | Bin 0 -> 2216 bytes mat/config.mat | Bin 0 -> 7928 bytes mat/controllers.mat | Bin 0 -> 21840 bytes mat/sample.mat | Bin 0 -> 286 bytes mat/stewart.mat | Bin 0 -> 1589 bytes src/getStiffnessMatrix.m | 4 +- src/identifyPlant.m | 2 +- src/initializeHexapod.m | 18 +- src/initializeSample.m | 4 +- 15 files changed, 378 insertions(+), 14 deletions(-) create mode 100644 .gitignore create mode 100644 index.org create mode 100644 mat/G.mat create mode 100644 mat/G_iff.mat create mode 100644 mat/G_jacobian.mat create mode 100644 mat/K_iff.mat create mode 100644 mat/K_iff_sisotool.mat create mode 100644 mat/config.mat create mode 100644 mat/controllers.mat create mode 100644 mat/sample.mat create mode 100644 mat/stewart.mat diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..ddb0206 --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +Figures/ +slprj/ \ No newline at end of file diff --git a/index.org b/index.org new file mode 100644 index 0000000..0b2787a --- /dev/null +++ b/index.org @@ -0,0 +1,362 @@ +#+TITLE: Stewart Platform with Simscape + +* Functions + :PROPERTIES: + :HEADER-ARGS:matlab+: :exports code + :HEADER-ARGS:matlab+: :comments no + :HEADER-ARGS:matlab+: :mkdir yes + :HEADER-ARGS:matlab+: :eval no + :END: +** getMaxPositions + :PROPERTIES: + :HEADER-ARGS:matlab+: :tangle src/getMaxPositions.m + :END: +#+begin_src matlab + function [X, Y, Z] = getMaxPositions(stewart) + Leg = stewart.Leg; + J = stewart.J; + theta = linspace(0, 2*pi, 100); + phi = linspace(-pi/2 , pi/2, 100); + dmax = zeros(length(theta), length(phi)); + + for i = 1:length(theta) + for j = 1:length(phi) + L = J*[cos(phi(j))*cos(theta(i)) cos(phi(j))*sin(theta(i)) sin(phi(j)) 0 0 0]'; + dmax(i, j) = Leg.stroke/max(abs(L)); + end + end + + X = dmax.*cos(repmat(phi,length(theta),1)).*cos(repmat(theta,length(phi),1))'; + Y = dmax.*cos(repmat(phi,length(theta),1)).*sin(repmat(theta,length(phi),1))'; + Z = dmax.*sin(repmat(phi,length(theta),1)); + end +#+end_src + +** getMaxPureDisplacement + :PROPERTIES: + :HEADER-ARGS:matlab+: :tangle src/getMaxPureDisplacement.m + :END: +#+begin_src matlab + function [max_disp] = getMaxPureDisplacement(Leg, J) + max_disp = zeros(6, 1); + max_disp(1) = Leg.stroke/max(abs(J*[1 0 0 0 0 0]')); + max_disp(2) = Leg.stroke/max(abs(J*[0 1 0 0 0 0]')); + max_disp(3) = Leg.stroke/max(abs(J*[0 0 1 0 0 0]')); + max_disp(4) = Leg.stroke/max(abs(J*[0 0 0 1 0 0]')); + max_disp(5) = Leg.stroke/max(abs(J*[0 0 0 0 1 0]')); + max_disp(6) = Leg.stroke/max(abs(J*[0 0 0 0 0 1]')); + end +#+end_src + +** getStiffnessMatrix + :PROPERTIES: + :HEADER-ARGS:matlab+: :tangle src/getStiffnessMatrix.m + :END: +#+begin_src matlab + function [K] = getStiffnessMatrix(k, J) + % k - leg stiffness + % J - Jacobian matrix + K = k*(J'*J); + end +#+end_src + +** identifyPlant + :PROPERTIES: + :HEADER-ARGS:matlab+: :tangle src/identifyPlant.m + :END: +#+begin_src matlab + function [sys] = identifyPlant(opts_param) + %% Default values for opts + opts = struct(); + + %% 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_identification'; + + %% Input/Output definition + io(1) = linio([mdl, '/F'], 1, 'input'); % Cartesian forces + io(2) = linio([mdl, '/Fl'], 1, 'input'); % Leg forces + io(3) = linio([mdl, '/Fd'], 1, 'input'); % Direct forces + io(4) = linio([mdl, '/Dw'], 1, 'input'); % Base motion + + io(5) = linio([mdl, '/Dm'], 1, 'output'); % Relative Motion + io(6) = linio([mdl, '/Dlm'], 1, 'output'); % Displacement of each leg + io(7) = linio([mdl, '/Flm'], 1, 'output'); % Force sensor in each leg + io(8) = linio([mdl, '/Xm'], 1, 'output'); % Absolute motion of platform + + %% Run the linearization + G = linearize(mdl, io, 0); + + %% Input/Output names + G.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz', ... + 'F1', 'F2', 'F3', 'F4', 'F5', 'F6', ... + 'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz', ... + 'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'}; + G.OutputName = {'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm', ... + 'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m', ... + 'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m', ... + 'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}; + + %% Cut into sub transfer functions + sys.G_cart = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'})); + sys.G_forc = minreal(G({'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})); + sys.G_legs = G({'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}); + sys.G_tran = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'})); + sys.G_comp = minreal(G({'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'})); + sys.G_iner = minreal(G({'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'}, {'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'})); + sys.G_all = minreal(G); + end +#+end_src + +** initializeHexapod + :PROPERTIES: + :HEADER-ARGS:matlab+: :tangle src/initializeHexapod.m + :END: +#+begin_src matlab + function [stewart] = initializeHexapod(opts_param) + %% Default values for opts + opts = struct(... + 'height', 90, ... % Height of the platform [mm] + 'jacobian', 150, ... % Jacobian offset [mm] + 'density', 8000, ... % Density of hexapod [mm] + 'name', 'stewart' ... % Name of the file + ); + + %% Populate opts with input parameters + if exist('opts_param','var') + for opt = fieldnames(opts_param)' + opts.(opt{1}) = opts_param.(opt{1}); + end + end + + %% Stewart Object + stewart = struct(); + stewart.h = opts.height; % Total height of the platform [mm] + stewart.jacobian = opts.jacobian; % distance from the center of the top platform + % where the jacobian is computed [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 = opts.density; % Density of the material [kg/m3] + 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 = opts.density; % Density of the material [kg/m3] + 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] + if strcmp(opts.actuator, 'piezo') + Leg.k.ax = 1e7; % Stiffness of each leg [N/m] + Leg.c.ax = 500; % [N/(m/s)] + elseif strcmp(opts.actuator, 'lorentz') + Leg.k.ax = 1e4; % Stiffness of each leg [N/m] + Leg.c.ax = 200; % [N/(m/s)] + elseif isnumeric(opts.actuator) + Leg.k.ax = opts.actuator; % Stiffness of each leg [N/m] + Leg.c.ax = 100; % [N/(m/s)] + else + error('opts.actuator should be piezo or lorentz or numeric value'); + end + 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 = opts.density; % Density of the material [kg/m3] + 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] + + %% Sphere + SP = struct(); + + SP.height.bottom = 15; % [mm] + SP.height.top = 15; % [mm] + SP.density.bottom = opts.density; % [kg/m^3] + SP.density.top = opts.density; % [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.c.ax = 0; % [N*m/deg] + + 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] + + + %% + 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') + + %% ============================================================== + % Additional Functions + % =============================================================== + + %% Initialize Parameters + function [stewart] = initializeParameters(stewart) + %% Connection points on base and top plate w.r.t. World frame at the center of the base plate + stewart.pos_base = zeros(6, 3); + stewart.pos_top = zeros(6, 3); + + alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases) + alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top + + % Height [m] TODO + height = (stewart.h-stewart.BP.thickness-stewart.TP.thickness-stewart.Leg.sphere.bottom-stewart.Leg.sphere.top-stewart.SP.thickness.bottom-stewart.SP.thickness.top)*0.001; + + radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base + radius_t = stewart.TP.leg.rad*0.001; % top radius in meters + + for i = 1:3 + % base points + angle_m_b = (2*pi/3)* (i-1) - alpha_b; + angle_p_b = (2*pi/3)* (i-1) + alpha_b; + stewart.pos_base(2*i-1,:) = [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0]; + stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0]; + + % top points + % Top points are 60 degrees offset + angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6; + angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6; + stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height]; + stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height]; + end + + % permute pos_top points so that legs are end points of base and top points + stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom + stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)]; + + %% leg vectors + legs = stewart.pos_top - stewart.pos_base; + leg_length = zeros(6, 1); + leg_vectors = zeros(6, 3); + for i = 1:6 + leg_length(i) = norm(legs(i,:)); + leg_vectors(i,:) = legs(i,:) / leg_length(i); + end + + stewart.Leg.lenght = 1000*leg_length(1)/1.5; + stewart.Leg.shape.bot = [0 0; ... + stewart.Leg.rad.bottom 0; ... + stewart.Leg.rad.bottom stewart.Leg.lenght; ... + stewart.Leg.rad.top stewart.Leg.lenght; ... + stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ... + 0 0.2*stewart.Leg.lenght]; + + %% Calculate revolute and cylindrical axes + rev1 = zeros(6, 3); + rev2 = zeros(6, 3); + cyl1 = zeros(6, 3); + for i = 1:6 + rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]); + rev1(i,:) = rev1(i,:) / norm(rev1(i,:)); + + rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:)); + rev2(i,:) = rev2(i,:) / norm(rev2(i,:)); + + cyl1(i,:) = leg_vectors(i,:); + end + + + %% Coordinate systems + stewart.lower_leg = struct('rotation', eye(3)); + stewart.upper_leg = struct('rotation', eye(3)); + + for i = 1:6 + stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; + stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; + end + + %% Position Matrix + % TODO + stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.thickness+stewart.Leg.sphere.top+stewart.SP.thickness.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)]; + + %% Compute Jacobian Matrix + % TODO + % aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; + bb = stewart.pos_top_tranform - (stewart.TP.thickness + stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; + bb = bb - stewart.jacobian*1e-3*[zeros(6, 2),ones(6, 1)]; + stewart.J = getJacobianMatrix(leg_vectors', bb'); + + stewart.K = stewart.Leg.k.ax*stewart.J'*stewart.J; + end + + %% Compute the Jacobian Matrix + function J = getJacobianMatrix(RM, M_pos_base) + % RM - [3x6] unit vector of each leg in the fixed frame + % M_pos_base - [3x6] vector of the leg connection at the top platform location in the fixed frame + J = zeros(6); + + J(:, 1:3) = RM'; + J(:, 4:6) = cross(M_pos_base, RM)'; + end + end +#+end_src + +** initializeSample + :PROPERTIES: + :HEADER-ARGS:matlab+: :tangle src/initializeSample.m + :END: +#+begin_src matlab + function [] = initializeSample(opts_param) + %% Default values for opts + sample = struct( ... + 'radius', 100, ... % radius of 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for opts opts = struct(... 'height', 90, ... % Height of the platform [mm] 'jacobian', 150, ... % Jacobian offset [mm] 'density', 8000, ... % Density of hexapod [mm] 'name', 'stewart' ... % Name of the file - ); + ); %% Populate opts with input parameters if exist('opts_param','var') @@ -54,10 +54,10 @@ function [stewart] = initializeHexapod(opts_param) elseif strcmp(opts.actuator, 'lorentz') Leg.k.ax = 1e4; % Stiffness of each leg [N/m] Leg.c.ax = 200; % [N/(m/s)] - elseif isnumeric(opts.actuator) + elseif isnumeric(opts.actuator) Leg.k.ax = opts.actuator; % Stiffness of each leg [N/m] Leg.c.ax = 100; % [N/(m/s)] - else + else error('opts.actuator should be piezo or lorentz or numeric value'); end Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm] @@ -109,7 +109,7 @@ function [stewart] = initializeHexapod(opts_param) %% Initialize Parameters function [stewart] = initializeParameters(stewart) - %% Connection points on base and top plate w.r.t. World frame at the center of the base plate + %% Connection points on base and top plate w.r.t. World frame at the center of the base plate stewart.pos_base = zeros(6, 3); stewart.pos_top = zeros(6, 3); @@ -188,18 +188,18 @@ function [stewart] = initializeHexapod(opts_param) %% Compute Jacobian Matrix % TODO -% aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; + % aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; bb = stewart.pos_top_tranform - (stewart.TP.thickness + stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; bb = bb - stewart.jacobian*1e-3*[zeros(6, 2),ones(6, 1)]; stewart.J = getJacobianMatrix(leg_vectors', bb'); - + stewart.K = stewart.Leg.k.ax*stewart.J'*stewart.J; end %% Compute the Jacobian Matrix function J = getJacobianMatrix(RM, M_pos_base) - % RM - [3x6] unit vector of each leg in the fixed frame - % M_pos_base - [3x6] vector of the leg connection at the top platform location in the fixed frame + % RM - [3x6] unit vector of each leg in the fixed frame + % M_pos_base - [3x6] vector of the leg connection at the top platform location in the fixed frame J = zeros(6); J(:, 1:3) = RM'; diff --git a/src/initializeSample.m b/src/initializeSample.m index 4bae940..d3100d0 100644 --- a/src/initializeSample.m +++ b/src/initializeSample.m @@ -1,5 +1,5 @@ function [] = initializeSample(opts_param) - %% Default values for opts +%% Default values for opts sample = struct( ... 'radius', 100, ... % radius of the cylinder [mm] 'height', 300, ... % height of the cylinder [mm] @@ -7,7 +7,7 @@ function [] = initializeSample(opts_param) 'measheight', 150, ... % measurement point z-offset [mm] 'offset', [0, 0, 0], ... % offset position of the sample [mm] 'color', [0.9 0.1 0.1] ... - ); + ); %% Populate opts with input parameters if exist('opts_param','var')