一种改进的串联机械臂逆运动学问题数值解法  

An improved numerical method for inverse kinematics of serial manipulator

作　　者：马建伟[1] 闫惠腾 沈亚彬 张红园 吕琦 高松[1] MA Jianwei;YAN Huiteng;SHEN Yabin;ZHANG Hongyuan;LYU Qi;GAO Song(Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education,Dalian University of Technology,Dalian 116000,China)

机构地区：[1]大连理工大学精密与特种加工教育部重点实验室,辽宁大连116000

出　　处：《重庆理工大学学报（自然科学）》2022年第7期119-125,共7页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(51975098);辽宁省“兴辽英才”计划项目(XLYC1907006,XLYCYSZX1901,XLYC1801008)。

摘　　要：逆运动学问题是机械臂运动控制的基础,数值法因其较好的通用性而被广泛使用。然而,常规基于Levenberg-Marquardt(LM)迭代法的机械臂逆运动学数值解法存在收敛速度慢、易出现不收敛的问题,影响算法鲁棒性。为解决上述问题,提高算法收敛速度和收敛能力,在常规数值解法基础上提出了一种改进的机械臂逆运动学问题数值解法。创新将LM迭代法中每一迭代步的参数因子由当前迭代步对应的微分运动向量二范数确定,并额外设置步长因子以提高每一迭代步的迭代步长。基于6自由度串联机械臂的验证结果表明,相比于Matlab Robotics Toolbox中ikine函数的数值解法,提出方法的收敛能力提高了约1.8倍,收敛速度提高了7.9倍,有效弥补了常规的数值解法鲁棒性不足的缺点。Inverse kinematics is the foundation of manipulator motion control. Numerical method is widely used to cope with the inverse kinematics because of its good robustness. However, the conventional numerical method based on Levenberg-Marquardt(LM) iterative method has problems of slow convergence and non-convergence, which affects the robustness of algorithm. In order to improve the convergence speed and the convergence ability of the algorithm, an improved numerical method for the inverse kinematics of manipulator is proposed based on the conventional numerical method. The parameter factor of each iteration step in the LM iteration method is innovatively determined by the second norm of the differential motion vector corresponding to the current iteration step. In addition, another factor is set to increase the step length of each iteration step. Finally, the experimental results on a 6-DOF serial manipulator show that the convergence speed and the convergence ability of the proposed method are increased by 7.9 times and 1.8 times respectively compared with the numerical method of function ikine in Matlab Robotics Toolbox, which effectively makes up for the shortcomings of the conventional numerical method in robustness.

关 键 词：串联机械臂 逆运动学 Levenberg-Marquardt迭代法 微分运动向量 收敛能力 

分 类 号：TP24[自动化与计算机技术—检测技术与自动化装置]