MATLAB四自由度机械手模型，已知末端执行器的位姿矩阵，反求各关节角度值代码

假设机械手有4个自由度（4个关节），关节1-4的角度值分别为theta1、theta2、theta3、theta4，末端执行器的位姿矩阵为T，可以用MATLAB中的机器人工具箱来求解。

具体步骤如下：

1. 定义机器人模型

使用robotics.RigidBodyTree函数定义机器人模型，包括关节类型、DH参数、连杆长度等信息。

例如，假设机械手的4个关节类型都是旋转关节，DH参数分别为：

a1=0, alpha1=pi/2, d1=0, theta1=theta1

a2=0, alpha2=-pi/2, d2=0, theta2=theta2

a3=0, alpha3=pi/2, d3=0, theta3=theta3

a4=0, alpha4=0, d4=0, theta4=theta4

则可以定义机器人模型：

robot = robotics.RigidBodyTree;

body1 = robotics.RigidBody('body1');
jnt1 = robotics.Joint('jnt1', 'revolute');
setFixedTransform(jnt1, trvec2tform([0 0 0]));
jnt1.JointAxis = [0 0 1];
jnt1.HomePosition = 0;
body1.Joint = jnt1;

body2 = robotics.RigidBody('body2');
jnt2 = robotics.Joint('jnt2', 'revolute');
setFixedTransform(jnt2, trvec2tform([0 0 0]));
jnt2.JointAxis = [1 0 0];
jnt2.HomePosition = 0;
body2.Joint = jnt2;

body3 = robotics.RigidBody('body3');
jnt3 = robotics.Joint('jnt3', 'revolute');
setFixedTransform(jnt3, trvec2tform([0 0 0]));
jnt3.JointAxis = [0 0 1];
jnt3.HomePosition = 0;
body3.Joint = jnt3;

body4 = robotics.RigidBody('body4');
jnt4 = robotics.Joint('jnt4', 'revolute');
setFixedTransform(jnt4, trvec2tform([0 0 0]));
jnt4.JointAxis = [0 1 0];
jnt4.HomePosition = 0;
body4.Joint = jnt4;

addBody(robot, body1, 'base');
addBody(robot, body2, 'body1');
addBody(robot, body3, 'body2');
addBody(robot, body4, 'body3');

2. 计算正运动学

使用robotics.RigidBodyTree的getTransform函数计算正运动学，得到末端执行器的位姿矩阵T。

T = getTransform(robot, [theta1 theta2 theta3 theta4], 'body4', 'base');

3. 反解关节角度

使用robotics.RigidBodyTree的inverseKinematics函数进行反解，得到关节角度值。

ik = robotics.InverseKinematics('RigidBodyTree', robot);
weights = [0.25 0.25 0.25 0.25];
initialguess = [0 0 0 0];
[configSoln, ~] = ik('body4', T, weights, initialguess);
theta1 = configSoln(1);
theta2 = configSoln(2);
theta3 = configSoln(3);
theta4 = configSoln(4);

完整代码如下：

robot = robotics.RigidBodyTree;

body1 = robotics.RigidBody('body1');
jnt1 = robotics.Joint('jnt1', 'revolute');
setFixedTransform(jnt1, trvec2tform([0 0 0]));
jnt1.JointAxis = [0 0 1];
jnt1.HomePosition = 0;
body1.Joint = jnt1;

body2 = robotics.RigidBody('body2');
jnt2 = robotics.Joint('jnt2', 'revolute');
setFixedTransform(jnt2, trvec2tform([0 0 0]));
jnt2.JointAxis = [1 0 0];
jnt2.HomePosition = 0;
body2.Joint = jnt2;

body3 = robotics.RigidBody('body3');
jnt3 = robotics.Joint('jnt3', 'revolute');
setFixedTransform(jnt3, trvec2tform([0 0 0]));
jnt3.JointAxis = [0 0 1];
jnt3.HomePosition = 0;
body3.Joint = jnt3;

body4 = robotics.RigidBody('body4');
jnt4 = robotics.Joint('jnt4', 'revolute');
setFixedTransform(jnt4, trvec2tform([0 0 0]));
jnt4.JointAxis = [0 1 0];
jnt4.HomePosition = 0;
body4.Joint = jnt4;

addBody(robot, body1, 'base');
addBody(robot, body2, 'body1');
addBody(robot, body3, 'body2');
addBody(robot, body4, 'body3');

T = [1 0 0 0;
     0 1 0 0;
     0 0 1 0.1;
     0 0 0 1]; % 末端执行器的位姿矩阵

ik = robotics.InverseKinematics('RigidBodyTree', robot);
weights = [0.25 0.25 0.25 0.25];
initialguess = [0 0 0 0];
[configSoln, ~] = ik('body4', T, weights, initialguess);
theta1 = configSoln(1);
theta2 = configSoln(2);
theta3 = configSoln(3);
theta4 = configSoln(4);