基于Udwadia-Kalaba方法的并联机器人鲁棒伺服约束控制

Robust Servo Constrained Control of Parallel Robots Based on the Udwadia-Kalaba Method

针对2自由度冗余驱动并联机器人轨迹跟踪控制问题,提出了一种基于Udwadia-Kalaba方程的鲁棒伺服控制方法.在负载、外部干扰以及制造误差的影响下,无法得到机器人精确、完整的运动模型,导致机器人控制性能变差.为解决这类不确定性带来的影响,提出了一种鲁棒控制方法.该方法通过保证系统的一致有界性和一致最终有界性,使系统能够精确跟踪理想约束轨迹.此外,该方法采用Udwadia-Kalaba方程,求解控制过程中满足系统理想约束所需要的约束力.Udwadia-Kalaba方程不需要Lagrange乘子或伪广义速度等辅助变量,可以同时处理完整约束和非完整约束,且可以获得满足轨迹约束的约束力解析解.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.

For the trajectory tracking control problems of 2-DOF redundant drive parallel robots,a robust servo control method based on the Udwadia-Kalaba equation was proposed.Under the influences of load,external interference and manufacturing errors,it is impossible to obtain the accurate and complete motion model for the robot,and the control performance of the robot is poor.To solve the impacts of this type of uncertainty,a robust control method was proposed to enable the system to accurately track the ideal trajectory,and ensure the uniform boundedness and the uniform ultimate boundedness of the overall system.In addition,the Udwadia-Kalaba equation was used to solve the constraint force required by the system to meet the ideal constraint in the control process.The Udwadia-Kalaba equation does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized velocities,and can handle both complete and incomplete constraints,with analytical solutions of constraint forces satisfying the trajectory obtained.The stability of this robust control method was proved theoretically with the Lyapunov function.Simulation experiments show that,the proposed robust control method can achieve high-precision tracking control along a given trajectory under non-ideal conditions.