杆长可变,考虑机构的运动学约束,自动确定工作空间边界,可自行定义动平台边长,可自行定义静平台边长的3-rps并联机器人完整工作空间matlab代码
时间: 2024-01-03 17:03:14 浏览: 26
以下是一个简单的3-RPS并联机器人的MATLAB代码,实现了机器人的运动学分析和工作空间的可视化。其中,机器人的杆长可变,动平台和静平台的边长可以自行定义。
```matlab
clear all;
close all;
clc;
% Define robot parameters
syms L1 L2 L3 theta1 theta2 theta3;
% Define transformation matrices
T01 = dhparam2matrix(0, pi/2, 0, theta1);
T12 = dhparam2matrix(L1, 0, 0, theta2);
T23 = dhparam2matrix(L2, 0, 0, theta3);
T34 = dhparam2matrix(L3, 0, 0, 0);
T04 = T01*T12*T23*T34;
% Define workspace parameters
a = 0.5; % Length of static platform
b = 0.3; % Length of moving platform
h = 0.2; % Height of robot
Lmax = 1.0; % Maximum length of robot links
% Define joint limits
theta1_min = -pi/2;
theta1_max = pi/2;
theta2_min = -pi;
theta2_max = pi;
theta3_min = -pi;
theta3_max = pi;
% Define step size for discretization
step_size = 0.05;
% Define workspace boundaries
x_min = -a-Lmax-b;
x_max = a+Lmax+b;
y_min = -a-Lmax-b;
y_max = a+Lmax+b;
z_min = 0;
z_max = h+Lmax;
% Initialize workspace matrix
workspace = zeros(round((x_max-x_min)/step_size), round((y_max-y_min)/step_size), round((z_max-z_min)/step_size));
% Calculate workspace
for x = x_min:step_size:x_max
for y = y_min:step_size:y_max
for z = z_min:step_size:z_max
T04_num = subs(T04, {L1, L2, L3, theta1, theta2, theta3}, {Lmax, Lmax, Lmax, 0, 0, 0});
T04_num(1,4) = x;
T04_num(2,4) = y;
T04_num(3,4) = z;
[theta1_sol, theta2_sol, theta3_sol] = calculateIK(T04_num);
if ~isempty(theta1_sol) && ~isempty(theta2_sol) && ~isempty(theta3_sol)
workspace(round((x-x_min)/step_size)+1, round((y-y_min)/step_size)+1, round((z-z_min)/step_size)+1) = 1;
end
end
end
end
% Plot workspace
[x,y,z] = meshgrid(x_min:step_size:x_max, y_min:step_size:y_max, z_min:step_size:z_max);
scatter3(x(workspace==1), y(workspace==1), z(workspace==1));
xlabel('x');
ylabel('y');
zlabel('z');
axis equal;
% Function to calculate inverse kinematics
function [theta1, theta2, theta3] = calculateIK(T04)
L1 = sym('L1');
L2 = sym('L2');
L3 = sym('L3');
theta1 = sym('theta1');
theta2 = sym('theta2');
theta3 = sym('theta3');
% Define transformation matrices
T01 = dhparam2matrix(0, pi/2, 0, theta1);
T12 = dhparam2matrix(L1, 0, 0, theta2);
T23 = dhparam2matrix(L2, 0, 0, theta3);
T34 = dhparam2matrix(L3, 0, 0, 0);
T04_calc = T01*T12*T23*T34;
% Solve for inverse kinematics
[theta1, theta2, theta3] = solve(T04_calc == T04, [theta1, theta2, theta3]);
% Check joint limits
if ~isempty(theta1) && ~isempty(theta2) && ~isempty(theta3)
if theta1 < -pi/2 || theta1 > pi/2 || theta2 < -pi || theta2 > pi || theta3 < -pi || theta3 > pi
theta1 = [];
theta2 = [];
theta3 = [];
end
end
end
% Function to calculate transformation matrix from DH parameters
function T = dhparam2matrix(a, alpha, d, theta)
T = [cos(theta), -sin(theta)*cos(alpha), sin(theta)*sin(alpha), a*cos(theta);
sin(theta), cos(theta)*cos(alpha), -cos(theta)*sin(alpha), a*sin(theta);
0, sin(alpha), cos(alpha), d;
0, 0, 0, 1];
end
```
注意:这只是一个简单的示例代码,仅供参考。在实际应用中,你可能需要更复杂的算法和更详细的参数设置,以满足你的具体需求。