Adaptive Robust Task-Space Control of Bilateral Teleoperation Systems with Time Delays

The nonlinear teleoperations system has been one of the challenging topics of the last few decades. This paper considers a teleoperation system consisting of master and slave robots which interact together through a time-delayed communication channel. A robust adaptive controller applies to each robot. By defining a slide surface consisting of errors, estimation of angular acceleration is applied instead of using it directly in the controller. This strategy eliminates the instability factor. It is noteworthy that the inverse of the Jacobin matrix is not used in the design of the teleoperation system's controllers. The P + d control method is used for task space dynamics. The goal of this article is that slave tracks master in the cartesian and joint space of the sub-robot. It should be noted that the data transfer between the robots is done with varying time delays. To achieve this goal in the system, the slave has to track the master carefully. With the Lyapunov function, the proposed method will verify the validity of this matter. The robustness and stability of the proposed control method are proved by writing the dynamic model regressor form. In the proof process, we get the adaptation laws for each controller to guarantee the system stability and performance with proper gains. Finally, the validity of the stated goals is checked by simulating the teleoperations system, including master and slave robots with two degrees of freedom.