Discrete-Time Bilateral Teleoperation Modeling And Stability Analysis

Abstract—Discretization of a stabilizing continuous-time bilateral teleoperation controller for digital implementation may not necessarily lead to stable teleoperation. While previous research has focused on the question of passivity or stability of haptic interaction with a discretely simulated virtual wall, this paper addresses the stability of master-slave teleoperation under discrete-time bilateral control. Stability regions are determined in the form of conditions involving the sampling period, control gains including the damping introduced by the controller, and environment sti ness. Among the obtained stability conditions are lower and upper bounds on the controller damping in addition to upper bounds on the sampling period and the environment stiffness, implying that as the sampling period is increased, the maximum admissible stiffness of the environment with which a slave robot can stably interact is reduced. An outcome of the paper is a set of design guidelines in terms of selection of various control parameters and the sampling rate for stable teleoperation under discrete-time control. Due to the sampling period{environment stiffness tradeoff and the stability-transparency tradeoff, the obtained stability boundaries are of particular importance for hard-contact teleoperation or when the teleoperation system has near-ideal or ideal transparency. The results of the stability analysis are confirmed by a simulation study in which the bilateral controller is realized by z-domain transfer functions while the master, the slave and the environment are simulated in the s-domain.