Discrete-time bilateral teleoperation: modelling and stability analysis

Discretisation of a stabilising 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, here the stability of master-slave teleoperation under discrete-time bilateral control is addressed. Stability regions are determined in the form of conditions involving the sampling period, control gains including the damping introduced by the controller and environment stiffness. 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. Because of 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 realised by z-domain transfer functions while the master, the slave and the environment are simulated in the s-domain.