Stewart平台逆运动学求解Simulink M函数代码

以下是Stewart平台逆运动学求解的Simulink M函数代码：

function [th1,th2,th3,th4,th5,th6] = Stewart_IK(x,y,z,phi,theta,psi,L,l)

% 六个支座坐标 P1 = [L/2,-l/2,0]; P2 = [-L/2,-l/2,0]; P3 = [-L/2,l/2,0]; P4 = [L/2,l/2,0]; P5 = [0,0,-l/2]; P6 = [0,0,l/2];

% 将欧拉角转换为旋转矩阵 R_phi = [1,0,0;0,cos(phi),-sin(phi);0,sin(phi),cos(phi)]; R_theta = [cos(theta),0,sin(theta);0,1,0;-sin(theta),0,cos(theta)]; R_psi = [cos(psi),-sin(psi),0;sin(psi),cos(psi),0;0,0,1]; R = R_phiR_thetaR_psi;

% 将平移向量和旋转矩阵组合成变换矩阵 T = [R,[x;y;z];0,0,0,1];

% 将六个支座坐标转换到工作空间坐标系中 P1_w = T*[P1';1]; P2_w = T*[P2';1]; P3_w = T*[P3';1]; P4_w = T*[P4';1]; P5_w = T*[P5';1]; P6_w = T*[P6';1];

% 计算六个支座到工作点的向量 V1 = [x-P1_w(1);y-P1_w(2);z-P1_w(3)]; V2 = [x-P2_w(1);y-P2_w(2);z-P2_w(3)]; V3 = [x-P3_w(1);y-P3_w(2);z-P3_w(3)]; V4 = [x-P4_w(1);y-P4_w(2);z-P4_w(3)]; V5 = [x-P5_w(1);y-P5_w(2);z-P5_w(3)]; V6 = [x-P6_w(1);y-P6_w(2);z-P6_w(3)];

% 计算六个支座到工作点的距离 d1 = norm(V1); d2 = norm(V2); d3 = norm(V3); d4 = norm(V4); d5 = norm(V5); d6 = norm(V6);

% 计算六个支座到工作点的方向向量 v1 = V1/d1; v2 = V2/d2; v3 = V3/d3; v4 = V4/d4; v5 = V5/d5; v6 = V6/d6;

% 计算初始位置下的六个支座到工作点的夹角 alpha1 = acos((P1_v'*v1)/(norm(P1_v)*norm(v1))); alpha2 = acos((P2_v'*v2)/(norm(P2_v)*norm(v2))); alpha3 = acos((P3_v'*v3)/(norm(P3_v)*norm(v3))); alpha4 = acos((P4_v'*v4)/(norm(P4_v)*norm(v4))); alpha5 = acos((P5_v'*v5)/(norm(P5_v)*norm(v5))); alpha6 = acos((P6_v'*v6)/(norm(P6_v)*norm(v6)));

% 计算六个支座的位移向量 dP1 = P1_v/norm(P1_v)d1cos(alpha1)-v1d1sin(alpha1); dP2 = P2_v/norm(P2_v)d2cos(alpha2)-v2d2sin(alpha2); dP3 = P3_v/norm(P3_v)d3cos(alpha3)-v3d3sin(alpha3); dP4 = P4_v/norm(P4_v)d4cos(alpha4)-v4d4sin(alpha4); dP5 = P5_v/norm(P5_v)d5cos(alpha5)-v5d5sin(alpha5); dP6 = P6_v/norm(P6_v)d6cos(alpha6)-v6d6sin(alpha6);

% 计算六个支座的位移向量在工作空间坐标系中的投影 dP1_w = T*[dP1';0]; dP2_w = T*[dP2';0]; dP3_w = T*[dP3';0]; dP4_w = T*[dP4';0]; dP5_w = T*[dP5';0]; dP6_w = T*[dP6';0];

% 计算六个支座的位移向量在工作空间坐标系中的模长 delta1 = norm(dP1_w); delta2 = norm(dP2_w); delta3 = norm(dP3_w); delta4 = norm(dP4_w); delta5 = norm(dP5_w); delta6 = norm(dP6_w);

% 计算六个支座的位移向量在工作空间坐标系中的方向向量 dv1 = dP1_w/delta1; dv2 = dP2_w/delta2; dv3 = dP3_w/delta3; dv4 = dP4_w/delta4; dv5 = dP5_w/delta5; dv6 = dP6_w/delta6;

% 计算六个支座的位移向量在工作空间坐标系中的夹角 beta1 = acos(dv1'*v1); beta2 = acos(dv2'*v2); beta3 = acos(dv3'*v3); beta4 = acos(dv4'*v4); beta5 = acos(dv5'*v5); beta6 = acos(dv6'*v6);

% 计算六个支座的位移向量在工作空间坐标系中的模长和方向向量的乘积 delta1_v1 = delta1v1; delta2_v2 = delta2v2; delta3_v3 = delta3v3; delta4_v4 = delta4v4; delta5_v5 = delta5v5; delta6_v6 = delta6v6;

% 计算六个支座的位移向量在工作空间坐标系中的旋转矩阵 R1 = expm([0,-dv1(3),dv1(2);dv1(3),0,-dv1(1);-dv1(2),dv1(1),0]*beta1); R2 = expm([0,-dv2(3),dv2(2);dv2(3),0,-dv2(1);-dv2(2),dv2(1),0]*beta2); R3 = expm([0,-dv3(3),dv3(2);dv3(3),0,-dv3(1);-dv3(2),dv3(1),0]*beta3); R4 = expm([0,-dv4(3),dv4(2);dv4(3),0,-dv4(1);-dv4(2),dv4(1),0]*beta4); R5 = expm([0,-dv5(3),dv5(2);dv5(3),0,-dv5(1);-dv5(2),dv5(1),0]*beta5); R6 = expm([0,-dv6(3),dv6(2);dv6(3),0,-dv6(1);-dv6(2),dv6(1),0]*beta6);

% 计算六个支座的位移向量在工作空间坐标系中的旋转矩阵和模长的乘积 delta1_R1 = delta1R1; delta2_R2 = delta2R2; delta3_R3 = delta3R3; delta4_R4 = delta4R4; delta5_R5 = delta5R5; delta6_R6 = delta6R6;

% 计算六个支座的位移向量在工作空间坐标系中的合力矢量 F_w = delta1_R1+delta2_R2+delta3_R3+delta4_R4+delta5_R5+delta6_R6;

% 计算六个支座的位移向量在工作空间坐标系中的合力矢量的模长 F_w_norm = norm(F_w);

% 计算六个支座的位移向量在工作空间坐标系中的合力矢量的方向向量 F_w_v = F_w/F_w_norm;

% 计算六个支座的位移向量在工作空间坐标系中的合力矢量和各支座到工作点的位移向量的夹角 gamma1 = acos(F_w_v'*dv1); gamma2 = acos(F_w_v'*dv2); gamma3 = acos(F_w_v'*dv3); gamma4 = acos(F_w_v'*dv4); gamma5 = acos(F_w_v'*dv5); gamma6 = acos(F_w_v'*dv6);

% 计算六个支座关节角度 th1 = alpha1+beta1+gamma1; th2 = alpha2+beta2+gamma2; th3 = alpha3+beta3+gamma3; th4 = alpha4+beta4+gamma4; th5 = alpha5+beta5+gamma5; th6 = alpha6+beta6+gamma6;

% 将角度转换为弧度 th1 = th1pi/180; th2 = th2pi/180; th3 = th3pi/180; th4 = th4pi/180; th5 = th5pi/180; th6 = th6pi/180;

end

其中，x、y、z、phi、theta、psi、L和l为输入参数，分别表示工作点在工作空间坐标系中的坐标和姿态，以及Stewart平台的尺寸参数。函数的输出为六个支座的关节角度。