针对重力补偿型冗余机械臂的逆解不唯一问题,提出了以改进型粒子群优化算法求解其最优逆解的方法,得到了机械臂在配重砝码位移最小时的逆解.首先通过正运动学分析了配重砝码位移与关节角和舵机补偿力矩之间的关系.在此基础之上,构建了以配重砝码位移最小为优化目标,以位置误差精度为约束条件的逆解方程,并使用改进型粒子群优化算法进行了求解.实验结果表明,该方法得到了机械臂在以配重砝码位移最小为优化目标下的最优逆解,解决了其逆解不唯一问题,对重力补偿型冗余机械臂的后续实验有良好的应用意义.
A method based on an improved particle swarm optimization algorithm was proposed to address the non-uniqueness problem of the inverse kinematics of a gravity compensation redundant manipulator and to obtain the optimal inverse kinematics solution for the manipulator with minimum displacement of the counterweight mass. First, the relationship between the displacement of the counterweight mass, joint angles, and servo compensation torque was analyzed using forward kinematics. Based on this, an inverse kinematics equation was constructed with the minimum displacement of the counterweight mass as the optimization objective and the position error accuracy as the constraint condition. An improved particle swarm optimization algorithm was used for the solution. The experimental results show that the optimal inverse kinematics solution for the manipulator with the minimum displacement of the counterweight mass as optimization objective was obtained, and that the non-uniqueness problem of the inverse kinematics was solved. This result is significant for follow-up experiments on the gravity-compensated redundant manipulator.
[1] 高涵, 张明路, 张小俊. 冗余机械臂空间轨迹规划综述[J]. 机械传动, 2016, 40(10): 176-180.
[2] 燕胜. 多功能机械臂遥操作维护系统的相关视觉技术研究[D]. 合肥: 中国科学技术大学, 2019.
[3] Hirose S. Float arm Ⅵ: wire-driven weight compensation mechanism with single pulleys [C]// Proceedings of the 23rd Annual Conference on Robotics Society of Japan. 2005: 333-336.
[4] Hirose S, Richard C. Development of a light weight torque limiting M-Drive actuator for hyper-redundant manipulator Float Arm [C]// Proceedings 1999 IEEE International Conference on Robotics and Automation. 1999: 2831-2836.
[5] Aoyagi S, Tashiro K, Minami M, et al. Development of redundant robot simulator for avoiding arbitrary obstacles based on semi-analytical method of solving inverse kinematics [C]// 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. 2007: 3497-3502.
[6] TØrdal S S, Hovland G, Tyapin I. Efficient implementation of inverse kinematics on a 6-DOF industrial robot using conformal geometric algebra [J]. Advances in Applied Clifiord Algebras, 2017, 27(3): 2067-2082.
[7] Ogawa T, Matsuura H, Kanada H. A solution of inverse kinematics of robot arm using network inversion [C]// International Conference on Computational Intelligence for Modelling, Control and Automation, 2005 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce. 2005: 858-862.
[8] Wang J. Obstacle avoidance for kinematically redundant manipulators based on recurrent neural networks [C]// First International Conference of Intelligent Robotics and Applications. 2008: 15-17.
[9] 马东阳, 库祥臣, 米显, 等. 基于改进粒子群算法的避障轨迹规划[J]. 制造技术与机床, 2022(7): 11-17.
[10] Ghosh A, Singh O, Ray A K. Inverse kinematic solution of a 7 DOF robotic manipulator using boundary restricted particle swarm optimization [J]. IFAC-PapersOnLine, 2022, 55(1): 101-105.
[11] Huang H C, Chen C P, Wang P R. Particle swarm optimization for solving the inverse kinematics of 7-DOF robotic manipulators [C]// IEEE International Conference on Systems. 2012: 3105-3110.
[12] 邝逸灵, 吴迪, 后国炜, 等. 一种用于冗余机械臂解析逆运动学的多目标优化方法[J]. 机械科学与技术, 2024, 43(6): 934-942.
[13] 孙立新, 耿庆琳, 唐家豪, 等. 存在关节限位的冗余机械臂逆运动学研究[J]. 现代制造工程, 2022(8): 46-52.
[14] 石建平. 基于群智能优化算法的冗余机械臂运动学逆解研究[D]. 南昌: 南昌大学, 2020.
[15] Sancaktar I, Burak T, Mustafa U. Inverse kinematics application on medical robot using adapted PSO method [J]. Engineering Science and Technology, an International Journal, 2018, 21(5): 1006-1010.
[16] 邱正师, 倪鹤鹏, 张承瑞, 等. 基于粒子群迭代的一种冗余机械手逆解算法[J]. 制造技术与机床, 2017(4): 85-92.
[17] 张铮, 朱齐丹, 吕晓龙, 等. 冗余机械臂运动学逆解的求解优化方法[J]. 吉林大学学报(工学版), 2023, 53(12): 3379-3387.
[18] 杨青, 周建兴, 葛亮. 机械臂逆运动学避障最优求解算法[J]. 科学技术与工程, 2022, 22(24): 10611-10618.
[19] 熊有伦. 机器人学: 建模、 控制与视觉[M]. 武汉: 华中科技大学出版社, 2020.
[20] Kennedy J, Eberhart R. Particle swarm optimization [C]// Proceedings of IEEE International Conference on Neural Networks. 1995: 1942-1948.
[21] 易云飞, 陈国鸿. 一种基于收缩因子的改进粒子群算法[J]. 软件导刊, 2009, 8(9): 59-60.
[22] 石建平, 刘鹏, 陈冬云. 基于改进粒子群优化算法的冗余机械臂逆运动学求解[J]. 机械传动, 2021, 45(2): 69-75.
