On Extending the Wave Variable Method to Multiple-DOF Teleoperation Systems

It is well known that providing a human operator with contact force information can significantly improve task performance in a teleoperation system. Unfortunately, time delay is a serious problem for such systems. Even a small time delay in a bilateral teleoperation system will generally degrade the system's performance and cause instability. Consequently, without some form of compensation for time delay, latencies in a teleoperation system would preclude the use of force feedback. Fortunately, there are approaches based on scattering theory and passivity that can compensate for time delay and allow the use of force feedback in teleoperation systems with latencies. In particular, the wave variable method is a passivity-based approach that guarantees stability for any fixed time delay. Since its introduction, the wave variable method has been augmented with predictors to compensate for variable time delay. The wave variable formalism has also been extended to multiple-DOF systems by replacing scalar damping constants with a family of impedance matrices. In this paper, the authors generalize this last approach to include a larger family of impedance matrices. The paper includes a complete derivation of the extended family of impedance matrices as well as simulation and experimental results to illustrate the approach.