Asymptotic Stability for Force Reflecting Teleoperators with Time Delay

A bilateral system consists of a local master manipulator and a remotely located slave manipulator. Velocity commands are sent forward from the master to the slave, and force information is "re flected "back from the slave to the master. Often there is a transmission delay when communicating between the two subsys tems, which causes instability in the force-reflecting teleoperator. Recently, a solution for this instability problem was found, based on mimicking the behavior of a lossless transmission line. Al though the resulting control law was shown to stabilize an actual single-DOF teleoperator system, and although the control law is intuitively stable because of its passivity properties, stability for the system has not yet been proven. In this article we extend these results to a nonlinear n-DOF system and prove its stability. Non linear, multidimensional networks are used to characterize the nonlinear equations for the master and slave manipulators, the time-delayed communication systems, the human operator, and the environment. Tellegen's theorem and the Lyapunov theory are then applied to prove that the master and slave subsystems have asymp totically stable velocities. In addition, we show how gain scaling can be used without disturbing the stability of the system.