Safe operation for teleoperated robotic manipulators with restricted synchronization error via non-singular terminal sliding-mode control

•A novel sliding surface is provided to avoid the singularity problem present in the classical terminal sliding modes.•The proposed sliding surface remains bounded, implying that the synchronization error constraints are satisfied.•The synchronization error converges in a prescribed compact set asymptotically within a pre-assignable finite-time.•The synchronization error remains bounded by predefined asymmetric time-varying constraints.•An adaptive finite-time force observer is presented to estimate the human force and environmental force acting over the TRS.