六自由度机械臂逆运动学通用Matlab程序代码
时间: 2023-09-13 16:12:27 浏览: 54
以下是一个基本的六自由度机械臂逆运动学通用Matlab程序代码示例:
``` matlab
function [q1,q2,q3,q4,q5,q6] = inv_kinematics(T)
% T是位姿矩阵,6x6大小的矩阵,代表机械臂末端执行器的位姿
% 求解逆运动学
% 坐标系原点
O = T(1:3,4);
% 坐标系z轴
z = T(1:3,3);
% 坐标系y轴
y = -T(1:3,2);
% 转换成DH参数
[d1,a1,~,~] = dh_parameters();
d6 = 0.088;
a6 = 0.2;
% 求解逆运动学第一步:求解关节1的角度
q1 = atan2(O(2),O(1));
% 求解逆运动学第二步:求解关节3的角度
r = sqrt(O(1)^2 + O(2)^2);
s = O(3) - d1;
D = (r^2 + s^2 - a1^2 - a6^2 - d6^2)/(2*a1);
q3_1 = atan2(sqrt(1-D^2),D);
q3_2 = atan2(-sqrt(1-D^2),D);
q2_1 = atan2(s,r) - atan2(a6*sin(q3_1),a1+a6*cos(q3_1));
q2_2 = atan2(s,r) - atan2(a6*sin(q3_2),a1+a6*cos(q3_2));
q3 = [q3_1,q3_2];
q2 = [q2_1,q2_2];
% 求解逆运动学第三步:求解关节2、3、4的角度
for i = 1:length(q2)
T1 = get_trans_matrix(q1,q2(i),q3(i),0);
T6 = T1\T;
R36 = T6(1:3,1:3);
p36 = T6(1:3,4);
p13 = [a1*cos(q2(i)),a1*sin(q2(i)),d1];
p64 = [-a6*sin(q3(i)),0,a6*cos(q3(i))]';
p16 = p36 - R36*p64;
q5_1 = acos(R36(3,3));
q5_2 = -q5_1;
q4_1 = atan2(-R36(2,3)/sin(q5_1),-R36(1,3)/sin(q5_1));
q4_2 = atan2(R36(2,3)/sin(q5_2),R36(1,3)/sin(q5_2));
q6_1 = atan2(-R36(3,2)/sin(q5_1),R36(3,1)/sin(q5_1));
q6_2 = atan2(-R36(3,2)/sin(q5_2),R36(3,1)/sin(q5_2));
q4 = [q4_1,q4_2];
q5 = [q5_1,q5_2];
q6 = [q6_1,q6_2];
for j = 1:length(q4)
T2 = get_trans_matrix(q1,q2(i),q3(i),q4(j));
T4 = get_trans_matrix(0,0,0,q5(1));
T5 = get_trans_matrix(0,0,0,q6(1));
T3 = T2\T1;
T6_1 = T1*T2*T3*T4*T5;
T2 = get_trans_matrix(q1,q2(i),q3(i),q4(j));
T4 = get_trans_matrix(0,0,0,q5(2));
T5 = get_trans_matrix(0,0,0,q6(2));
T3 = T2\T1;
T6_2 = T1*T2*T3*T4*T5;
p6_1 = T6_1(1:3,4);
p6_2 = T6_2(1:3,4);
if norm(p6_1-p16) < norm(p6_2-p16)
q5 = q5_1;
q6 = q6_1;
else
q5 = q5_2;
q6 = q6_2;
end
end
end
end
function T = get_trans_matrix(q1,q2,q3,q4)
% 生成位姿矩阵
[d1,a1,~,~] = dh_parameters();
T_01 = get_dh_matrix(q1,d1,a1,-pi/2);
T_12 = get_dh_matrix(q2,0,0,pi/2);
T_23 = get_dh_matrix(q3,0,0,-pi/2);
T_34 = get_dh_matrix(q4,0,0,pi/2);
T = T_01*T_12*T_23*T_34;
end
function T = get_dh_matrix(q,d,a,alpha)
% 生成DH矩阵
T = [cos(q),-sin(q)*cos(alpha),sin(q)*sin(alpha),a*cos(q);
sin(q),cos(q)*cos(alpha),-cos(q)*sin(alpha),a*sin(q);
0,sin(alpha),cos(alpha),d;
0,0,0,1];
end
function [d,a,alpha,q] = dh_parameters()
% DH参数
d = [0.333,0,0.316,0,0.384,0.107];
a = [0.035,0.305,0.0,0.0,0.0,0.088];
alpha = [-pi/2,0,-pi/2,pi/2,-pi/2,0];
q = [0,0,0,0,0,0];
end
```
在这个代码中,我们使用DH参数来描述机械臂的几何结构。程序中的`get_dh_matrix`函数用于生成DH矩阵,`get_trans_matrix`函数用于生成位姿矩阵。`dh_parameters`函数给出了机械臂每个关节的DH参数。`inv_kinematics`函数是主函数,用于求解逆运动学。它接受一个6x6的位姿矩阵,并返回机械臂每个关节的角度。这个程序使用迭代法求解逆运动学,通过对机械臂的几何结构进行建模,将位姿转换为关节角度,以控制机械臂的运动。