Chattering‐free fixed‐time sliding mode control for bilateral teleoperation under unknown time‐varying delay via disturbance and state observers

Abstract This paper proposes a new chattering‐free Fixed‐time Observer‐Based Sliding Mode Control (FOBSMC) scheme for synchronization of two bilateral teleoperations under unknown time‐varying delay. The system is subjected to unknown disturbances which are estimated in a fixed time by utilizing the Disturbance Observer‐based SMC scheme. The fixed‐time State Observer‐based SMC is designed to estimate the unmeasured velocity state, while the position state is assumed to be available. Fixed‐time stability method is used to provide the system convergence time independently of initial states. A FOBSMC scheme is first designed for master system of bilateral teleoperation under unknown time‐varying delay to track the environmental torque by the human operating torque in the presence of time delay in the communication channel, as well as estimating the unknown disturbances and unmeasured states. A FOBSMC scheme is designed to synchronize slave system to master system in the presence of time delay in the communication channel, as well as estimating disturbances and states. The stability analysis is performed for closed‐loop system of combined controller‐observer by using Lyapunov theory. The efficacy of the proposed method to fulfill a good transparency and stability under time‐varying communication delays is tested by performing numerical simulation in Simulink/MATLAB.