一种五自由度机械臂的运动学分析与逆运动学求解

Kinematics Analysis and Inverse Kinematics Solution of a 5-DOF Manipulator

对于通用六自由度机械臂,通常基于笛卡尔空间建立数学模型,可求解其末端执行器的位姿。利用同样的方法可以建立五自由度机械臂的模型,建立正运动学方程,得到其末端执行器的位姿。该位姿基于笛卡尔空间进行描述,具有六个独立变量,对应笛卡尔空间中的六个自由度。由于五自由度机械臂自由度不足,通过该位姿进行轨迹规划时,会出现逆运动学解不存在的情况。针对这一问题,提出了用几何法求解五自由度机械臂运动学逆解的方法。通过该方法,将逆运动学求解分为两个步骤:首先通过几何关系求出第五关节的位置坐标,再通过几何法求解前四个关节的角度。使用MATLAB Robotics Toolbox进行仿真与实验,证明了该方法的可行性。

For a universal six-degree-of-freedom manipulator, a mathematic model is usually established based on the Cartesian space to solve the pose of its end-effector. The same method can be used to establish the model of the five-degree-of-freedom manipulator, and the positive kinematics equation is established to obtain the position of the end-effector. The position is described based on the Cartesian space, with six independent variables, corresponding to six degrees of freedom in the Cartesian space. Due to the lack of degree of freedom of the five-degree-of-freedom manipulator, the inverse kinematics solution does not exist when the trajectory is planned by the pose. Aiming at the problem, a method of solving the inverse kinematics of five-degree-of- freedom manipulator is proposed by geometric method. Through this method, the inverse kinematics solution is divided into two steps. First, the position coordinates of the fifth joint are obtained, and the angle of the first four joints is solved by geometric method. The simulation experiment is carried out using MATLAB Robotics Toolbox, which proves the feasibility of the method.