89 lines
3.2 KiB
Matlab
89 lines
3.2 KiB
Matlab
% get robot description
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run('plnr_idntfcn.m');
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% Symbolic generilized coordiates, their first and second deriatives
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q_sym = sym('q%d',[2,1],'real');
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qd_sym = sym('qd%d',[2,1],'real');
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q2d_sym = sym('q2d%d',[2,1],'real');
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% Getting energy functions, to derive dynamics
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T_pk = sym(zeros(4,4,2)); % transformation between links
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w_kk(:,1) = sym(zeros(3,1)); % angular velocity k in frame k
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v_kk(:,1) = sym(zeros(3,1)); % linear velocity of the origin of frame k in frame k
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g_kk(:,1) = sym([0,0,9.81])'; % vector of graviatational accelerations in frame k
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p_kk(:,1) = sym(zeros(3,1)); % origin of frame k in frame k
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for i = 1:2
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jnt_axs_k = str2num(plnr.robot.joint{i}.axis.Attributes.xyz)';
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% Transformation from parent link frame p to current joint frame
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rpy_k = sym(str2num(plnr.robot.joint{i}.origin.Attributes.rpy));
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R_pj = RPY(rpy_k);
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% R_pj(abs(R_pj)<sqrt(eps)) = sym(0); % to avoid numerical errors
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R_pj(abs(R_pj)<1e-5) = sym(0); % to avoid numerical errors
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p_pj = str2num(plnr.robot.joint{i}.origin.Attributes.xyz)';
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T_pj = sym([R_pj, p_pj; zeros(1,3), 1]); % to avoid numerical errors
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% Tranformation from joint frame of the joint that rotaties body k to
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% link frame. The transformation is pure rotation
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R_jk = Rot(q_sym(i),sym(jnt_axs_k));
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p_jk = sym(zeros(3,1));
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T_jk = [R_jk, p_jk; sym(zeros(1,3)),sym(1)];
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% Transformation from parent link frame p to current link frame k
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T_pk(:,:,i) = T_pj*T_jk;
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z_kk(:,i) = sym(jnt_axs_k);
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w_kk(:,i+1) = T_pk(1:3,1:3,i)'*w_kk(:,i) + sym(jnt_axs_k)*qd_sym(i);
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v_kk(:,i+1) = T_pk(1:3,1:3,i)'*(v_kk(:,i) + cross(w_kk(:,i),sym(p_pj)));
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g_kk(:,i+1) = T_pk(1:3,1:3,i)'*g_kk(:,i);
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p_kk(:,i+1) = T_pk(1:3,1:3,i)'*(p_kk(:,i) + sym(p_pj));
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K_reg(i,:) = [sym(0.5)*w2wtlda(w_kk(:,i+1)),...
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v_kk(:,i+1)'*vec2skewSymMat(w_kk(:,i+1)),...
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sym(0.5)*v_kk(:,i+1)'*v_kk(:,i+1)];
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P_reg(i,:) = [sym(zeros(1,6)), g_kk(:,i+1)',...
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g_kk(:,i+1)'*p_kk(:,i+1)];
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end
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% Compose lagrangian
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Lagr = [K_reg(1,:) - P_reg(1,:), K_reg(2,:) - P_reg(2,:)];
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% Use Lagrange equations to derive regressor matrix
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dLagr_dq = jacobian(Lagr,q_sym)';
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dLagr_dqd = jacobian(Lagr,qd_sym)';
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t1 = sym(zeros(2,20));
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for i = 1:2
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t1 = t1 + diff(dLagr_dqd,q_sym(i))*qd_sym(i)+...
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diff(dLagr_dqd,qd_sym(i))*q2d_sym(i);
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end
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Y = simplify(t1 - dLagr_dq);
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Y_fcn = matlabFunction(Y,'Vars',{q_sym, qd_sym, q2d_sym});
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% Testing if regressor computed correctly using matlab Robotics Robotics
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rbt = importrobot('planar_manip.urdf');
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rbt.DataFormat = 'column';
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rbt.Gravity = [0 0 -9.81];
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noIter = 100;
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err1 = zeros(noIter,1);
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for i = 1:noIter
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q = rand(2,1);
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qd = rand(2,1);
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q2d = rand(2,1);
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Ylgr = Y_fcn(q,qd,q2d);
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tau1 = inverseDynamics(rbt,q,qd,q2d);
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tau2 = Ylgr*plnr.pi(:);
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% verifying if regressor is computed correctly
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err1(i) = norm(tau1 - tau2);
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end
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plot(err1)
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if all(err1<1e-6)
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disp('Regressor matrix is computed correctly!')
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disp('Generating regressor matrix function...')
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matlabFunction(Y,'File','planar2DOF/full_regressor_plnr',...
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'Vars',{q_sym, qd_sym, q2d_sym});
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else
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disp('Regressor matrix is not computed correctly. Check derivation')
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end
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