基于旋量理论的球形关节动力学建模与运动控制研究  

Research on dynamic modeling and motion control of sphericaljoint based on spinor theory

作　　者：鞠鲁峰 王磊 文彦[2,4] 李国丽[1,3] 许家紫 李申奥[1,3] JU Lufeng;WANG Lei;WEN Yan;LI Guoli;XU Jiazi;LI Shenao(School of Electrical Engineering and Automation,Anhui University,Hefei 230601,China;National Engineering Laboratory of Energy-Saving Motor&Control Technology,Anhui University,Hefei 230601,China;Anhui Key Laboratory of Power Quality,Ministry of Education,Anhui University,Hefei 230601,China;School of Internet,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学电气工程与自动化学院,安徽合肥230601 [2]安徽大学高节能电机及控制技术国家地方联合实验室,安徽合肥230601 [3]安徽大学工业节电与用电安全安徽省重点实验室,安徽合肥230601 [4]安徽大学互联网学院,安徽合肥230601

出　　处：《电机与控制学报》2025年第2期160-170,共11页Electric Machines and Control

基　　金：国家自然科学基金区域创新联合基金重点项目(U23A20647);安徽省自然科学基金青年项目(2308085QE182);安徽省高校自然科学研究重点项目(2022AH050094);安徽大学高节能电机及控制技术国家地方联合工程实验室开放课题(KFKT202106)。

摘　　要：为了实现多电机集成系统在一定空间内有效完成多自由度运动工作,提出一种新型三自由度球形关节及其动力学建模方法与运动控制策略,以解决其空间运动问题。首先,采用李群及旋量理论和指数积公式完成球形关节的运动学分析与建模;接着,结合旋量理论和凯恩方程,得到基于旋量理论的球形关节动力学凯恩方程;然后,为实现对三自由度球形关节的高精度运动控制,设计一种基于饱和函数趋近律的滑模控制算法。相较于常规的基于符号函数趋近律的滑模控制算法,该算法有效解决了传统滑模控制中存在的抖振较大的问题;最后,对球形关节动力学方程进行仿真,验证了其动力学方程的正确性,并对所提出的控制策略开展仿真分析和实验验证,其结果验证了所提控制策略的可行性和有效性。To achieve effective multi-degree-of-freedom motion in a limited space for a multi-motor integrated system,a novel three-degree-of-freedom spherical joint,its dynamic modeling method,and motion control strategy were proposed to address its spatial motion problems.First,using Lie group and screw theory,along with the exponential product formula,the kinematic analysis and modeling of the spherical joint were completed.Next,combining screw theory with the Kane equations,the dynamics of the spherical joint were derived based on screw theory.Then,to achieve high-precision motion control of the three-degree-of-freedom spherical joint,a sliding mode control algorithm based on a saturation function approximation law was designed.Compared to conventional sliding mode control algorithms based on symbolic function approximation laws,this algorithm effectively addresses the problem of chattering that is common in traditional sliding mode control.Finally,the dynamic equations of the spherical joint were simulated to verify their correctness,and simulations and experimental verification of the proposed control strategy were conducted,confirming its feasibility and effectiveness.

关 键 词：球形关节 三自由度 旋量理论 指数积 凯恩方程 滑模控制 

分 类 号：TM351[电气工程—电机]