matlab并联机构轨迹规划
时间: 2023-11-20 18:58:58 浏览: 65
根据引用所述,求解并联机构的轨迹规划需要先进行运动学逆解,即根据末端执行器的位置和姿态,求解出各个关节的角度。而在Matlab中,可以使用符号计算工具箱来求解运动学逆解。具体步骤如下:
1. 建立符号变量和符号函数
```matlab
syms L1 L2 L3 theta1 theta2 theta3 real
assume(L1 > 0)
assume(L2 > 0)
assume(L3 > 0)
```
2. 建立正运动学方程
```matlab
T01 = [cos(theta1) -sin(theta1) 0 0;
sin(theta1) cos(theta1) 0 0;
0 0 1 L1;
0 0 0 1];
T12 = [cos(theta2) -sin(theta2) 0 L2;
sin(theta2) cos(theta2) 0 0;
0 0 1 0;
0 0 0 1];
T23 = [cos(theta3) -sin(theta3) 0 L3;
sin(theta3) cos(theta3) 0 0;
0 0 1 0;
0 0 0 1];
T03 = T01 * T12 * T23;
```
3. 建立逆运动学方程
```matlab
x = T03(1,4);
y = T03(2,4);
z = T03(3,4);
phi = atan2(T03(2,1), T03(1,1));
theta = atan2(-T03(3,1), sqrt(T03(3,2)^2 + T03(3,3)^2));
psi = atan2(T03(3,2), T03(3,3));
eq1 = x^2 + y^2 + z^2 - L1^2 - L2^2 - L3^2 + 2*L2*L3*cos(theta2)*cos(theta3) + 2*L1*L2*cos(theta1)*cos(theta2) + 2*L1*L3*cos(theta1)*cos(theta3) == 0;
eq2 = L2*sin(theta2)*cos(theta3) + L3*sin(theta3)*cos(theta2) + (L1 + L2*cos(theta2) + L3*cos(theta3))*cos(theta1) - x == 0;
eq3 = L2*sin(theta2)*sin(theta3) + L3*sin(theta3)*sin(theta2) + (L1 + L2*cos(theta2) + L3*cos(theta3))*sin(theta1) - y == 0;
eq4 = psi - phi == 0;
eq5 = theta - pi/2 == 0;
[theta1_sol, theta2_sol, theta3_sol] = solve([eq1, eq2, eq3, eq4, eq5], [theta1, theta2, theta3]);
```
4. 根据求解出的逆运动学方程,生成轨迹规划
```matlab
% 生成关节角度随时间变化的函数
t = 0:0.1:10;
theta1_fun = matlabFunction(theta1_sol);
theta2_fun = matlabFunction(theta2_sol);
theta3_fun = matlabFunction(theta3_sol);
theta1_traj = theta1_fun(L1, L2, L3, 0, 0, 0, t);
theta2_traj = theta2_fun(L1, L2, L3, 0, 0, 0, t);
theta3_traj = theta3_fun(L1, L2, L3, 0, 0, 0, t);
% 生成末端执行器的位置和姿态随时间变化的函数
T03_fun = matlabFunction(T03);
T03_traj = zeros(4, 4, length(t));
for i = 1:length(t)
T03_traj(:,:,i) = T03_fun(L1, L2, L3, theta1_traj(i), theta2_traj(i), theta3_traj(i));
end
% 生成末端执行器的轨迹
x_traj = squeeze(T03_traj(1,4,:));
y_traj = squeeze(T03_traj(2,4,:));
z_traj = squeeze(T03_traj(3,4,:));
phi_traj = atan2(squeeze(T03_traj(2,1,:)), squeeze(T03_traj(1,1,:)));
theta_traj = atan2(-squeeze(T03_traj(3,1,:)), sqrt(squeeze(T03_traj(3,2,:)).^2 + squeeze(T03_traj(3,3,:)).^2));
psi_traj = atan2(squeeze(T03_traj(3,2,:)), squeeze(T03_traj(3,3,:)));
```
以上代码生成了关节角度随时间变化的函数和末端执行器的位置和姿态随时间变化的函数,可以根据这些函数生成末端执行器的轨迹。具体实现可以参考Matlab Robotics Toolbox中的示例代码。
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