89 lines
3.9 KiB
Mathematica
89 lines
3.9 KiB
Mathematica
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function generate_load_regressor(path_to_urdf)
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% ----------------------------------------------------------------------
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% The function generates regressor for the load, which is assumed to be
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% a rigid body
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% -----------------------------------------------------------------------
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% Parse urdf to get robot description
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ur10 = parse_urdf(path_to_urdf);
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% Create symbolic generilized coordiates, their first and second deriatives
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q_sym = sym('q%d',[6,1],'real');
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qd_sym = sym('qd%d',[6,1],'real');
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q2d_sym = sym('q2d%d',[6,1],'real');
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% ------------------------------------------------------------------------
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% Getting gradient of energy functions, to derive dynamics
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% ------------------------------------------------------------------------
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T_pk = sym(zeros(4,4,6)); % 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 = 1:6
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jnt_axs_k = str2num(ur10.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(ur10.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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p_pj = str2num(ur10.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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beta_K(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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beta_P(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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% --------------------------------------------------------------------
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% Gradient of the kinetic and potential energy of the load
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% --------------------------------------------------------------------
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% Transformation from link 6 frame to end-effector frame
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rpy_ee = sym(str2num(ur10.robot.joint{7}.origin.Attributes.rpy));
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R_6ee = RPY(rpy_ee);
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R_6ee(abs(R_6ee)<sqrt(eps)) = sym(0); % to avoid numerical errors
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p_6ee = str2num(ur10.robot.joint{7}.origin.Attributes.xyz)';
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T_6ee = sym([R_6ee, p_6ee; zeros(1,3), 1]); % to avoid numerical errors
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w_eeee = T_6ee(1:3,1:3)'*w_kk(:,7);
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v_eeee = T_6ee(1:3,1:3)'*(v_kk(:,7) + cross(w_kk(:,i+1),sym(p_6ee)));
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g_eeee = T_6ee(1:3,1:3)'*g_kk(:,7);
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p_eeee = T_6ee(1:3,1:3)'*(p_kk(:,7) + sym(p_6ee));
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beta_Kl = [sym(0.5)*w2wtlda(w_eeee), v_eeee'*vec2skewSymMat(w_eeee),...
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sym(0.5)*(v_eeee'*v_eeee)];
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beta_Pl = [sym(zeros(1,6)), g_eeee', g_eeee'*p_eeee];
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% ---------------------------------------------------------------------
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% Dynamic regressor of the load
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% ---------------------------------------------------------------------
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beta_Ll = beta_Kl - beta_Pl;
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dbetaLl_dq = jacobian(beta_Ll,q_sym)';
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dbetaLl_dqd = jacobian(beta_Ll,qd_sym)';
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tl = sym(zeros(6,10));
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for i = 1:6
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tl = tl + diff(dbetaLl_dqd,q_sym(i))*qd_sym(i)+...
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diff(dbetaLl_dqd,qd_sym(i))*q2d_sym(i);
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end
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Y_l = tl - dbetaLl_dq;
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% Generate a function from a symbolic expression
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matlabFunction(Y_l,'File','autogen/load_regressor_UR10E',...
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'Vars',{q_sym, qd_sym, q2d_sym});
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