Switched prescribed-time sliding mode control for cooperative teleoperation systems with perturbations

This paper studies the prescribed-time sliding mode control problem for cooperative teleoperation systems under perturbations with unknown bounds, where the single-master single-slave (SMSS) and single-master multi-slave (SMMS) teleoperation systems are considered, respectively. First, based on the dynamics and kinematics differential equations, the models of SMSS and SMMS teleoperation systems are established. Then, to overcome the effect of unknown perturbations, the novel switched prescribed-time sliding mode (SPTSM) is constructed. Combined with the proposed SPTSM, a new state feedback prescribed time control (PTC) strategy is presented to guarantee the PT bounded stability of SMSS. The Lyapunov function is used to rigorously prove the effectiveness. Next, considering limited capabilities of a single slave robot, by integrating topological theory, the SPTSM based PTC strategy is designed for SMMS teleoperation systems for the first time, where the PT bounded stability with adjustable convergence bound can be obtained. Compared with existing results on sliding mode control of teleoperation systems, the SPTSM based PTC can not only guarantee the PT stability of the system, but also overcome the effect of unknown perturbations and unify the non-vanishing and vanishing perturbation cases. Finally, simulation result is put forward to illustrate the effectiveness of proposed methods.