Stability analysis of sampled-data teleoperation systems

In a haptic teleoperation system, closed-loop stability is influenced by the human operator and the environment dynamics, which are typically uncertain, time-varying or unknown. Therefore, in lieu of stability, the passivity of a teleoperation system as a sufficient condition for stability is investigated in the literature. The rationale for this is that, if the two-port network representing the teleoperator (comprising the master, the controller and communication channel, and the slave) is passive and is terminated to any passive but otherwise arbitrary operator and environment, the overall teleoperation system will also be passive. Instead of ensuring the passivity of the teleoperator in isolation, which is an overly-conservative requirement, in this paper we study the stability of the overall teleoperation system having assumed the passivity of the operator and the environment while permitting the teleoperator to be passive or nonpassive-such relaxation of the passivity condition on the teleoperator is expected to reduce design conservatism and allow for higher teleoperation performance. The broader aim of this study is to find the conditions for the stability of a teleoperation system when its controllers are implemented in discrete-time-it is known that discretization causes energy leaks and thus does not necessarily preserve passivity or stability. The absolute stability conditions for the sampled-data teleoperator are obtained using the Small Gain Theorem. The resulting condition for stability of the sampled-data teleoperation system imposes bounds on the controller parameters, the sampling period, and the master and slave robots damping terms.