凿岩机械臂逆运动学解流形分析及优化

Analysis and Optimization of Inverse Kinematics Solution Manifolds forRock-Drilling Manipulator

针对一款位姿强耦合的七自由度凿岩机械臂,提出一种基于旋量理论和微分流形理论的逆运动学求解算法。利用Paden-Kahan子问题和几何法得到该冗余机械臂的全部逆解。由于冗余关节的存在,通过末端执行器所需位姿进行求解可以得到无穷组关节逆解,其呈现出光滑流形结构,根据自运动流形的特点,将其分别映射到位置关节空间和姿态关节空间。随后根据实际作业需要,建立多目标优化泛函,对机械臂的解空间进行优化,得到优化解流形。最后针对优化解流形的一组关节逆解进行五次多项式轨迹规划。结果表明:选取的最优解使凿岩机械臂在整个定位过程中运动稳定,位姿误差较小,从而验证了逆运动学解法和优化流形的正确性。

An inverse kinematic solution algorithm based on screw theory and differential manifold theory was proposed for a seven-degree-of-freedom rock-drilling manipulator with strong coupling of position and posture.The Paden-Kahan subproblem and the geometric method were utilized to obtain all the inverse solutions of this redundant manipulator.Due to the existence of redundant joints,an infinite set of joint inverse solutions could be obtained by solving through the desired position and posture of the end-effector,which presented a smooth manifold structure,and it was mapped to the position joints space and the posture joints space,respectively,according to the characteristics of the self-motion manifold.Subsequently,according to the actual operational needs,a multi-objective optimization general function was established to optimize the solution space of the manipulator,and the optimized solution manifold was obtained.Finally,the fifth degree polynomial trajectory planning was carried out for a set of joint inverse solutions of the optimized solution manifold.The results show that the selected optimal solution makes the rock-drilling manipulator move stably during the whole positioning process and the position error is small,thus verifying the correctness of the inverse kinematics solution method and the optimized manifold.