Update all the initialization of hexapod and simscape of hexapod
This commit is contained in:
@@ -1,208 +1,171 @@
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function [stewart] = initializeHexapod(opts_param)
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%% Default values for opts
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opts = struct(...
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'height', 90, ... % Height of the platform [mm]
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'jacobian', 150, ... % Jacobian offset [mm]
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'density', 8000, ... % Density of hexapod [mm]
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'name', 'stewart' ... % Name of the file
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);
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%% Populate opts with input parameters
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if exist('opts_param','var')
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for opt = fieldnames(opts_param)'
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opts.(opt{1}) = opts_param.(opt{1});
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end
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end
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opts = struct(...
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'height', 90, ... % Height of the platform [mm]
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'density', 8000, ... % Density of the material used for the hexapod [kg/m3]
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'k_ax', 1e8, ... % Stiffness of each actuator [N/m]
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'c_ax', 100, ... % Damping of each actuator [N/(m/s)]
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'stroke', 50e-6, ... % Maximum stroke of each actuator [m]
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'name', 'stewart' ... % Name of the file
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);
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%% Stewart Object
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stewart = struct();
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stewart.h = opts.height; % Total height of the platform [mm]
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stewart.jacobian = opts.jacobian; % distance from the center of the top platform
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% where the jacobian is computed [mm]
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%% Bottom Plate
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BP = struct();
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BP.rad.int = 0; % Internal Radius [mm]
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BP.rad.ext = 150; % External Radius [mm]
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BP.thickness = 10; % Thickness [mm]
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BP.leg.rad = 100; % Radius where the legs articulations are positionned [mm]
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BP.leg.ang = 5; % Angle Offset [deg]
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BP.density = opts.density; % Density of the material [kg/m3]
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BP.color = [0.7 0.7 0.7]; % Color [rgb]
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BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness];
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%% Top Plate
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TP = struct();
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TP.rad.int = 0; % Internal Radius [mm]
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TP.rad.ext = 100; % Internal Radius [mm]
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TP.thickness = 10; % Thickness [mm]
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TP.leg.rad = 90; % Radius where the legs articulations are positionned [mm]
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TP.leg.ang = 5; % Angle Offset [deg]
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TP.density = opts.density; % Density of the material [kg/m3]
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TP.color = [0.7 0.7 0.7]; % Color [rgb]
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TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness];
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%% Leg
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Leg = struct();
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Leg.stroke = 80e-6; % Maximum Stroke of each leg [m]
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if strcmp(opts.actuator, 'piezo')
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Leg.k.ax = 1e7; % Stiffness of each leg [N/m]
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Leg.c.ax = 500; % [N/(m/s)]
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elseif strcmp(opts.actuator, 'lorentz')
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Leg.k.ax = 1e4; % Stiffness of each leg [N/m]
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Leg.c.ax = 200; % [N/(m/s)]
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elseif isnumeric(opts.actuator)
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Leg.k.ax = opts.actuator; % Stiffness of each leg [N/m]
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Leg.c.ax = 100; % [N/(m/s)]
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else
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error('opts.actuator should be piezo or lorentz or numeric value');
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end
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Leg.rad.bottom = 12; % Radius of the cylinder of the bottom part [mm]
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Leg.rad.top = 10; % Radius of the cylinder of the top part [mm]
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Leg.density = opts.density; % Density of the material [kg/m3]
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Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb]
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Leg.color.top = [0.5 0.5 0.5]; % Color [rgb]
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Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm]
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Leg.sphere.top = Leg.rad.top; % Size of the sphere at the end of the leg [mm]
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%% Sphere
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SP = struct();
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SP.height.bottom = 15; % [mm]
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SP.height.top = 15; % [mm]
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SP.density.bottom = opts.density; % [kg/m^3]
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SP.density.top = opts.density; % [kg/m^3]
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SP.color.bottom = [0.7 0.7 0.7]; % [rgb]
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SP.color.top = [0.7 0.7 0.7]; % [rgb]
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SP.k.ax = 0; % [N*m/deg]
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SP.c.ax = 0; % [N*m/deg]
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SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm]
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SP.thickness.top = SP.height.top-Leg.sphere.top; % [mm]
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SP.rad.bottom = Leg.sphere.bottom; % [mm]
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SP.rad.top = Leg.sphere.top; % [mm]
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%%
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Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom];
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Leg.support.top = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top];
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%%
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stewart.BP = BP;
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stewart.TP = TP;
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stewart.Leg = Leg;
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stewart.SP = SP;
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%%
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stewart = initializeParameters(stewart);
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%%
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save('./mat/stewart.mat', 'stewart')
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%% ==============================================================
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% Additional Functions
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% ===============================================================
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%% Initialize Parameters
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function [stewart] = initializeParameters(stewart)
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%% Connection points on base and top plate w.r.t. World frame at the center of the base plate
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stewart.pos_base = zeros(6, 3);
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stewart.pos_top = zeros(6, 3);
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alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases)
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alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top
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% Height [m] TODO
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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;
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radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base
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radius_t = stewart.TP.leg.rad*0.001; % top radius in meters
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for i = 1:3
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% base points
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angle_m_b = (2*pi/3)* (i-1) - alpha_b;
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angle_p_b = (2*pi/3)* (i-1) + alpha_b;
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stewart.pos_base(2*i-1,:) = [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0];
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stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0];
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% top points
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% Top points are 60 degrees offset
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angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6;
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angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6;
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stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height];
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stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height];
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end
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% permute pos_top points so that legs are end points of base and top points
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stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
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stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)];
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%% leg vectors
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legs = stewart.pos_top - stewart.pos_base;
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leg_length = zeros(6, 1);
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leg_vectors = zeros(6, 3);
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for i = 1:6
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leg_length(i) = norm(legs(i,:));
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leg_vectors(i,:) = legs(i,:) / leg_length(i);
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end
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stewart.Leg.lenght = 1000*leg_length(1)/1.5;
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stewart.Leg.shape.bot = [0 0; ...
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stewart.Leg.rad.bottom 0; ...
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stewart.Leg.rad.bottom stewart.Leg.lenght; ...
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stewart.Leg.rad.top stewart.Leg.lenght; ...
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stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
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0 0.2*stewart.Leg.lenght];
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%% Calculate revolute and cylindrical axes
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rev1 = zeros(6, 3);
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rev2 = zeros(6, 3);
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cyl1 = zeros(6, 3);
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for i = 1:6
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rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
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rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
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rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:));
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rev2(i,:) = rev2(i,:) / norm(rev2(i,:));
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cyl1(i,:) = leg_vectors(i,:);
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end
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%% Coordinate systems
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stewart.lower_leg = struct('rotation', eye(3));
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stewart.upper_leg = struct('rotation', eye(3));
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for i = 1:6
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stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
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stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
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end
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%% Position Matrix
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% TODO
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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)];
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%% Compute Jacobian Matrix
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% TODO
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% aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
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bb = stewart.pos_top_tranform - (stewart.TP.thickness + stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
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bb = bb - stewart.jacobian*1e-3*[zeros(6, 2),ones(6, 1)];
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stewart.J = getJacobianMatrix(leg_vectors', bb');
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stewart.K = stewart.Leg.k.ax*stewart.J'*stewart.J;
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end
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%% Compute the Jacobian Matrix
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function J = getJacobianMatrix(RM, M_pos_base)
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% RM - [3x6] unit vector of each leg in the fixed frame
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% M_pos_base - [3x6] vector of the leg connection at the top platform location in the fixed frame
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J = zeros(6);
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J(:, 1:3) = RM';
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J(:, 4:6) = cross(M_pos_base, RM)';
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if exist('opts_param','var')
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for opt = fieldnames(opts_param)'
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opts.(opt{1}) = opts_param.(opt{1});
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end
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end
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stewart = struct();
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stewart.H = opts.height; % [mm]
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BP = struct();
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BP.Rint = 0; % Internal Radius [mm]
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BP.Rext = 150; % External Radius [mm]
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BP.H = 10; % Thickness of the Bottom Plate [mm]
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BP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
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BP.alpha = 10; % Angle Offset [deg]
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BP.density = opts.density; % Density of the material [kg/m3]
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BP.color = [0.7 0.7 0.7]; % Color [RGB]
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BP.shape = [BP.Rint BP.H; BP.Rint 0; BP.Rext 0; BP.Rext BP.H]; % [mm]
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stewart.BP = BP;
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TP = struct();
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TP.Rint = 0; % [mm]
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TP.Rext = 100; % [mm]
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TP.H = 10; % [mm]
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TP.Rleg = 100; % Radius where the legs articulations are positionned [mm]
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TP.alpha = 20; % Angle [deg]
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TP.dalpha = 0; % Angle Offset from 0 position [deg]
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TP.density = opts.density; % Density of the material [kg/m3]
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TP.color = [0.7 0.7 0.7]; % Color [RGB]
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TP.shape = [TP.Rint TP.H; TP.Rint 0; TP.Rext 0; TP.Rext TP.H];
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stewart.TP = TP;
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Leg = struct();
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Leg.stroke = opts.stroke; % [m]
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Leg.k_ax = opts.k_ax; % Stiffness of each leg [N/m]
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Leg.c_ax = opts.c_ax; % Damping of each leg [N/(m/s)]
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Leg.Rtop = 10; % Radius of the cylinder of the top part of the leg[mm]
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Leg.Rbot = 12; % Radius of the cylinder of the bottom part of the leg [mm]
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Leg.density = opts.density; % Density of the material used for the legs [kg/m3]
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Leg.color = [0.5 0.5 0.5]; % Color of the top part of the leg [RGB]
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Leg.R = 1.3*Leg.Rbot; % Size of the sphere at the extremity of the leg [mm]
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stewart.Leg = Leg;
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SP = struct();
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SP.k = 0; % [N*m/deg]
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SP.c = 0; % [N*m/deg]
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SP.H = 15; % [mm]
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SP.R = Leg.R; % [mm]
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SP.section = [0 SP.H-SP.R;
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0 0;
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SP.R 0;
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SP.R SP.H];
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SP.density = opts.density; % [kg/m^3]
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SP.color = [0.7 0.7 0.7]; % [RGB]
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stewart.SP = SP;
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stewart = initializeParameters(stewart);
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save('./mat/stewart.mat', 'stewart')
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function [stewart] = initializeParameters(stewart)
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stewart.Aa = zeros(6, 3); % [mm]
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stewart.Ab = zeros(6, 3); % [mm]
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stewart.Bb = zeros(6, 3); % [mm]
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for i = 1:3
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stewart.Aa(2*i-1,:) = [stewart.BP.Rleg*cos( pi/180*(120*(i-1) - stewart.BP.alpha) ), ...
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stewart.BP.Rleg*sin( pi/180*(120*(i-1) - stewart.BP.alpha) ), ...
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stewart.BP.H+stewart.SP.H];
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stewart.Aa(2*i,:) = [stewart.BP.Rleg*cos( pi/180*(120*(i-1) + stewart.BP.alpha) ), ...
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stewart.BP.Rleg*sin( pi/180*(120*(i-1) + stewart.BP.alpha) ), ...
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stewart.BP.H+stewart.SP.H];
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stewart.Ab(2*i-1,:) = [stewart.TP.Rleg*cos( pi/180*(120*(i-1) + stewart.TP.dalpha - stewart.TP.alpha) ), ...
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stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha - stewart.TP.alpha) ), ...
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stewart.H - stewart.TP.H - stewart.SP.H];
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stewart.Ab(2*i,:) = [stewart.TP.Rleg*cos( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
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stewart.TP.Rleg*sin( pi/180*(120*(i-1) + stewart.TP.dalpha + stewart.TP.alpha) ), ...
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stewart.H - stewart.TP.H - stewart.SP.H];
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end
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stewart.Bb = stewart.Ab - stewart.H*[0,0,1];
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leg_length = zeros(6, 1); % [mm]
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leg_vectors = zeros(6, 3);
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legs = stewart.Ab - stewart.Aa;
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for i = 1:6
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leg_length(i) = norm(legs(i,:));
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leg_vectors(i,:) = legs(i,:) / leg_length(i);
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end
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stewart.Leg.lenght = leg_length(1)/1.5;
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stewart.Leg.shape.bot = ...
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[0 0; ...
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stewart.Leg.Rbot 0; ...
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stewart.Leg.Rbot stewart.Leg.lenght; ...
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stewart.Leg.Rtop stewart.Leg.lenght; ...
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stewart.Leg.Rtop 0.2*stewart.Leg.lenght; ...
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0 0.2*stewart.Leg.lenght];
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stewart.Rm = struct('R', eye(3));
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for i = 1:6
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sx = cross(leg_vectors(i,:), [1 0 0]);
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sx = sx/norm(sx);
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sy = -cross(sx, leg_vectors(i,:));
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sy = sy/norm(sy);
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sz = leg_vectors(i,:);
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sz = sz/norm(sz);
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stewart.Rm(i).R = [sx', sy', sz'];
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end
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J = zeros(6);
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for i = 1:6
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J(i, 1:3) = leg_vectors(i, :);
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J(i, 4:6) = cross(0.001*stewart.Bb(i, :), leg_vectors(i, :));
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end
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stewart.J = J;
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stewart.K = stewart.Leg.k_ax*stewart.J'*stewart.J;
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end
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end
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