When a task must be executed in a remote or dangerous environment, teleoperation systems may be employed to extend the influence of the human operator. In the case of manipulation tasks, haptic feedback of the forces experienced by the remote (slave) system is often highly useful in improving an operator's ability to perform effectively. In many of these cases (especially teleoperation over the internet and ground-to-space teleoperation), substantial communication latency exists in the control loop and has the strong tendency to cause instability of the system. The first viable solution to this problem in the literature was based on a scattering/wave transformation from transmission line theory. This wave transformation requires the designer to select a wave impedance parameter appropriate to the teleoperation system. It is widely recognized that a small value of wave impedance is well suited to free motion and a large value is preferable for contact tasks. Beyond this basic observation, however, very little guidance exists in the literature regarding the selection of an appropriate value. Moreover, prior research on impedance selection generally fails to account for the fact that in any realistic contact task there will simultaneously exist contact considerations (perpendicular to the surface of contact) and quasi-free-motion considerations (parallel to the surface of contact). The primary contribution of the present work is to introduce an approximate linearized optimum for the choice of wave impedance and to apply this quasi-optimal choice to the Cartesian reality of such a contact task, in which it cannot be expected that a given joint will be either perfectly normal to or perfectly parallel to the motion constraint.

The proposed scheme selects a wave impedance matrix that is appropriate to the conditions encountered by the manipulator. This choice may be implemented as a static wave impedance value or as a time-varying choice updated according to the instantaneous conditions encountered. A Lyapunov-like analysis is presented demonstrating that time variation in wave impedance will not violate the passivity of the system. Experimental trials, both in simulation and on a haptic feedback device, are presented validating the technique. Consideration is also given to the case of an uncertain environment, in which an a priori impedance choice may not be possible.