基于HJI的移动机器人轨迹跟踪控制

Trajectory Tracking Control of Mobile Robot Based on HJI

考虑一类受外界干扰的移动机器人的轨迹跟踪控制问题,基于哈密顿-雅可比不等式(HJI)设计了前馈控制和反馈控制相结合的复合控制算法。针对移动机器人的运动学模型,利用反步法设计了运动学辅助速度控制率。针对移动机器人的动力学模型,考虑其外部扰动,基于模型设计了前馈控制器,然后将动力学误差模型改写成HJI所适用的非线性形式,基于HJI设计了反馈控制器。在此基础上,进一步利用Lyapunov稳定性理论证明了运动学控制系统的稳定性,利用HJI理论证明了动力学控制系统的稳定性。最后,仿真结果表明存在外界不确定干扰的情况下,控制算法能够使跟踪误差快速收敛,系统具有良好的抗扰性。

Considering the trajectory tracking control problem of a class of mobile robots with external disturbances, a composite control algorithm combining feedforward control and feedback control has been designed based on the HJI(Hamilton-Jacobi Inequality). Aiming at the kinematics model of the mobile robot, the kinematics-assisted speed control algorithm is designed by backstepping method. Aiming at the dynamic model of the mobile robot, considering its external disturbance, a feedforward controller is designed based on the model,and then the dynamic error model is rewritten into a nonlinear form suitable for HJI, and a feedback controller is designed based on the HJI. On this basis, the Lyapunov stability theory is further used to prove the stability of the kinematic control system, and the HJI theory is used to prove the stability of the dynamic control system. Finally,the simulation results show that the control algorithm can make the tracking error converge quickly and the control system has good disturbance immunity under the condition of external uncertain disturbance.