Revisiting Llewellyn's Absolute Stability Criterion for Bilateral Teleoperation Systems under Non-Passive Operator or Environment

摘要

Stability of a haptic teleoperation system is influenced by the typically uncertain, time-varying and/or unknown dynamics of the operator and the environment. For a stability analysis that is independent of the operator and the environment dynamics, Llewellyn's absolute stability criterion proposes certain conditions on the two-port network representing the teleoperator (comprising the master, the controller and communication channel, and the slave) {em assuming that the terminations (i.e., the operator and the environment) are passive}. These are less-than-accurate assumptions. It is desirable to extend Llewellyn's result to the cases where the operator or the environment is non-passive. This paper revisits Llewellyn's criterion and relaxes the assumption of passivity for one of the terminations. The possibly non-passive termination is realistically assumed to have a complex impedance with an upper or lower bound on its amplitude or real part, respectively. Although the proposed stability criteria are useful for any application of two-port network systems, we specifically apply them on bilateral teleoperation systems and find the stability conditions when the operator or the environment is not passive; this is a result that Llewellyn's absolute stability criterion cannot afford.