Absolute Stability Analysis of Sampled-Data Scaled Bilateral Teleoperation Systems

Stability of a bilateral teleoperation system may be jeopardized by controller discretization, which has been shown to involve energy leaks. This paper proposes a novel approach to analyzing the absolute stability of sampled-data bilateral teleoperation systems consisting of discrete-time controllers and continuous-time master, slave, operator, and environment. The proposed stability analysis permits scaling and delay in the master and the slave positions and forces. The absolute stability conditions reported here impose bounds on the gains of the discrete-time controller, the damping terms of the master and the slave, and the sampling time. A design-related application of these results is in proper selection of various control parameters and the sampling rate for stable teleoperation under discrete-time control. To explore the trade-off between the control gains and the sampling time, it is studied how large sampling times, which require low control gains for maintaining stability, can lead to unacceptable teleoperation transparency and human task performance in a teleoperated switching task. This shows that the effect of sampling time must be taken into account because neglecting it (as in the absolute stability literature) undermines both stability and transparency of teleoperation. The resulting absolute stability condition has been verified via experiments with two Phantom Omni robots.