Stability Analysis of a Bilateral Teleoperating System

In this paper the stability of a control scheme for bilateral master-slave teleoperation is investigated. Given the nominal models of the master and slave dynamics, and using an approximate feedback linearization control, based on the earlier work of Spong and Vidyasagar, 1987, a robust closed-loop system (position and force) can be obtained with a multiloop version of the small gain theorem. It is shown that stable bilateral teleoperating systems can be achieved under the assumption that the deviation of the models from the actual systems satisfies certain norm inequalities. We also show that, using the proposed scheme, the tracking error (position/velocity and force/torque) is bounded and it can be made arbitrarily small. The control scheme is illustrated using the simulation of a three-degree-of-freedom master-slave teleoperator (three-degree-of-freedom master and three-degree-of-freedom slave).