90 lines
3.2 KiB
Mathematica
90 lines
3.2 KiB
Mathematica
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deg2rad = pi/180;
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x_axis = [1 0 0];
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y_axis = [0 1 0];
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z_axis = [0 0 1];
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% Connection points on base and top plate w.r.t. World frame at the center
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% of the base plate
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pos_base = [];
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pos_top = [];
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alpha_b = 90*deg2rad; % angle de d<EFBFBD>calage par rapport <EFBFBD> 120 deg (pour positionner les supports bases)
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alpha_t = -30*deg2rad; % +- offset angle from 120 degree spacing on top
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height = 0.10; % 2 meter height in home configuration
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radius_b = 0.130; % rayon emplacement support base
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radius_t = 0.100; % 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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pos_base(2*i-1,:) = [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0];
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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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pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height];
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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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pos_top = [pos_top(6,:); pos_top(1:5,:)]; %6th point on top connects to 1st on bottom
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pos_top_tranform = pos_top - height*[zeros(6, 2),ones(6, 1)];
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% Compute points w.r.t. to the body frame in a 3x6 matrix
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body_pts = pos_top' - height*[zeros(2,6);ones(1,6)];
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% leg vectors
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legs = pos_top - pos_base;
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leg_length = [ ];
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leg_vectors = [ ];
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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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% Calculate revolute and cylindrical axes
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for i = 1:6,
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rev1(i,:) = cross(leg_vectors(i,:), z_axis);
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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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rev3(i,:) = rev1(i,:);
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rev4(i,:) = rev2(i,:);
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end
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% Coordinate systems
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lower_leg = struct('origin', [0 0 0], 'rotation', eye(3), 'end_point', [0 0 0]);
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upper_leg = struct('origin', [0 0 0], 'rotation', eye(3), 'end_point', [0 0 0]);
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for i = 1:6,
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lower_leg(i).origin = pos_base(i,:) + (3/8)*legs(i,:);
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lower_leg(i).end_point = pos_base(i,:) + (3/4)*legs(i,:);
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lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
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upper_leg(i).origin = pos_base(i,:) + (1-3/8)*legs(i,:);
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upper_leg(i).end_point = pos_base(i,:) + (1/4)*legs(i,:);
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upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
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end
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% Inertia and mass calculation
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top_thickness = 0.05;
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base_thickness = 0.05;
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inner_radius = 0.03;
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outer_radius = 0.05;
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density = 76e3/9.81; % steel density in Kg/m^3
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%leg inertia and mass
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[lower_leg_mass, lower_leg_inertia] = inertiaCylinder(density, ...
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0.75*leg_length(1),outer_radius, inner_radius);
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[upper_leg_mass, upper_leg_inertia] = inertiaCylinder(density, ...
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0.75*leg_length(1),inner_radius, 0);
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% top and base plate mass and inertia
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[top_mass, top_inertia] = inertiaCylinder(density, ...
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top_thickness, radius_t, 0);
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[base_mass, base_inertia] = inertiaCylinder(density, ...
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base_thickness,radius_b, 0);
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% PID controller gains
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Kp = 2e6; Ki = 1e4; Kd = 4.5e4;
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