基于反步法的柔性关节空间机器人预定时间跟踪控制  

Predefined-time tracking control of a flexible-joint space robot based on backstepping technique

作　　者：刘辽雪 王璐[1] 郭毓[1] 郭健 Liu Liaoxue;Wang Lu;Guo Yu;Guo Jian(School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学自动化学院,江苏南京210094

出　　处：《南京理工大学学报》2024年第5期547-555,共9页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(62403242,61973167);江苏省自然科学基金(BK20241459);江苏省卓越博士后计划(2023ZB186)。

摘　　要：针对一类柔性关节空间机器人的高阶非线性系统轨迹跟踪控制问题,该文提出一种具有预定时间收敛性能的控制器设计方案。基于预定时间控制理论,采用反步法设计了控制律,并构造新型非线性滤波器处理反步法中虚拟控制律多次求导所造成的微分项膨胀问题。在此基础上,设计了一种避奇异辅助函数,解决了预定时间控制算法框架中对分数次幂项求导所产生的奇异问题。通过Lyapunov稳定性理论证明了闭环控制系统的半全局预定时间一致最终有界。仿真结果验证了所设计控制方案能够有效抑制柔性关节振动,使跟踪误差在预定时间内收敛,且避免了因奇异问题导致的控制力矩抖振现象。Aiming at the problem of high-order nonlinear system trajectory tracking control of flexible-joint space robots,this paper proposes a controller design scheme that can realize convergence within a predefined time.Based on the predefined-time control theory,the control law is designed by backstepping technique,and a novel nonlinear filter is constructed to deal with the problem of differential term expansion caused by multiple derivations of the virtual control law in the backstepping technique.On this basis,a singularity-free auxiliary function is designed to solve the singularity problem arising from the derivation of fractional power terms in the framework of the predefined-time control algorithm.The semi-global predefined-time uniformly ultimately bounded of the closed-loop system is proved by Lyapunov stability theory.Simulation results indicate that the proposed control scheme can effectively suppress the vibration of flexible-joints,make the tracking error converge within a predefined time,and avoid the chattering of control torque caused by the singularity problem.

关 键 词：空间机器人 反步法 非线性滤波器 预定时间控制 避奇异辅助函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]