Bilateral teleoperation system stability with non-passive and strictly passive operator or environment

• Develops a new powerful stability analysis tool for a two-port network.
• Allows a passive and another strictly passive or non-passive termination.
• Studies stability of bilateral teleoperation systems with different controllers.

A bilateral teleoperation system comprises a human operator, a teleoperator, and an environment. Without exact models for the teleoperator׳s terminations (i.e., human operator and the environment), it is typically assumed that they are passive but otherwise arbitrary. Based on this assumption, the stability of the teleoperation system is investigated through Llewellyn׳s absolute stability criterion for the teleoperator. However, the assumption of passivity of the terminations is less than accurate and may be violated in practice. Using Mobius transformations, this paper develops a new powerful stability analysis tool for a two-port network coupled to a passive termination and another termination that is (a) input strictly passive (ISP), (b) output strictly passive (OSP), (c) input non-passive (INP), or (b) disc-like non-passive (DNP). While this new stability criterion is applicable to any two-port network, we apply it to bilateral teleoperation systems with position-error-based (PEB) and direct-force-reflection (DFR) controllers. Simulations and experiments are reported for a pair of Phantom haptic robots.