基于广义Udwadia-Kalaba方法的下肢康复机器人鲁棒约束跟随控制  

Robust Constraint Following Control of Lower Limb Rehabilitation Robots Based on the Generalized Udwadia-Kalaba Method

作　　者：孙浩[1,2] 汪新 胡澳华 马超 SUN Hao;WANG Xin;HU Aohua;MA Chao(School of Mechanical Engineering,Hefei University of Technology,Hefei 230009,P.R.China;Anhui Key Laboratory of Digit Design and Manufacture,Hefei 230009,P.R.China)

机构地区：[1]合肥工业大学机械工程学院,合肥230009 [2]数字化设计与制造安徽省重点实验室,合肥230009

出　　处：《应用数学和力学》2025年第4期451-464,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(52105093)。

摘　　要：针对下肢康复机器人系统中同时存在的等式约束和不等式约束问题,提出了一种基于广义Udwadia-Kalaba(U-K)方程的鲁棒约束跟随控制器,能够使系统同时满足等式约束和不等式约束,并解决系统中存在的不确定性,使得机器人达到很好的约束跟随效果.在机器人工作的过程中,传统的控制方法难以保证机器人的运动范围在边界条件内,可能导致患者在使用时受到二次伤害.为解决边界问题带来的影响,提出了一种控制方法,该方法利用微分同胚变换,将等式约束和不等式约束系统地纳入到U-K方程中,从数学上建立了广义U-K方程.在此基础上,提出了一种鲁棒约束跟踪策略,以确保系统在存在不确定性和各种约束的情况下,仍具有满意的性能.此外,利用Lyapunov函数对该鲁棒控制方法的稳定性进行了理论证明,并且通过仿真实验,验证了该鲁棒控制方法能够在非理想条件下实现给定轨迹的高精度跟踪控制.A robust constraint following controller based on the generalized Udwadia-Kalaba(U-K)equation was proposed for the problem of equality constraints and inequality constraints in the lower limb rehabilitation robot system,to make the system meet the equality constraints and inequality constraints at the same time,solve the uncertainty in the system,and achieve good constraint following effects on the robot.During the working process of the robot,the traditional control method is difficult to ensure that the motion range of the robot is within the boundary conditions,resulting in secondary injury to the patient during use.To solve the influence of boundary problems,a control method was proposed to use the diffeomorphism transformation to incorporate the equality constraint and inequality constraint system into the U-K equation,with the generalized U-K equation established mathematically.On this basis,a robust constraint tracking strategy was presented to ensure satisfactory performances of the system in the presence of uncertainties and various constraints.In addition,the stability of the robust control method was theoretically proved with the Lyapunov function.The simulation results show that,the robust control method has high-precision tracking control of a given trajectory under non-ideal conditions.

关 键 词：广义Udwadia-Kalaba方程 不等式约束 鲁棒控制 下肢康复机器人 

分 类 号：TH113[机械工程—机械设计及理论] TP242[自动化与计算机技术—检测技术与自动化装置]