Fixed-time Coordination Control for Bilateral Telerobotics System with Asymmetric Time-varying Delays

Fixed-time coordination in dynamical systems means system trajectories converge to the desired trajectories in determined time which is independent of the system initial states. In this paper, a novel fixed-time coordination control approach for nonlinear telerobotics system with asymmetric time-varying delays is proposed to provide faster convergence rate and higher convergence precision. The neural networks (NNs) and the parameter adaptive method are combined to approximate the uncertain model of the teleoperator, the upper bound of the NNs estimation errors and the external disturbances. Then the corresponding adaptive NNs fixed-time controller is designed without using the derivatives of the time-varying delays. Dynamic surface control (DSC) is employed to avoid the singularity. Moreover, considering the nonpassive human operator and remote environment insert forces, the stability criterion for the closed-loop system is also developed. Then by choosing proper Lyapunov functions, the master-slave coordination errors converging into a deterministic domain in fixed-time with the new controller is proved in the presence of the exogenous forces from human operator and remote environment. Furthermore, the exact convergence time is presented only with the designed parameters. Some comparisons are conducted in simulation to show the superior performance of the proposed control approach. Finally, experimental results are also given to demonstrate the effectiveness of the new control method.