Event-Triggered Logarithmic Sliding Mode Control for Discrete-Time Lagrangian Haptic Manipulator

This brief investigates the problem involving the effective discrete-time tracking control of the accurate motion of a haptic manipulator. The model of the haptic manipulator is established by using the discrete-time Lagrangian mechanism for the accurate description of its motion on a digital computer, and its discrete-time dynamic response with a large sampling interval is approximate to the Runge-Kutta solution's response, better than that of the direct Euler-forward difference. The discrete-time logarithmic sliding mode control with parameter criteria, which is developed to refer to the discrete-time Lagrangian model, and the stable motion on the sliding surface is guaranteed by the comparison principle of monotonous difference. A discrete-time event-triggering mechanism is synthesized into the proposed logarithmic sliding mode controller to decrease the inter-execution times of commands to reduce the consumption of actuators. The effectiveness of the proposed method is verified by the simulation.