Exponential stability of bilateral sampled-data teleoperation systems using multirate approach

This paper develops the stability analysis for linear bilateral teleoperation systems exposed to communication constraints and multirate samplers. Dynamics of the master and slave robots are assumed to be continuous-time with discrete-time controllers. The proposed multirate design guarantees the exponential stability of the teleoperation system over a communication networks. Different sampling rates are imposed on position/velocity signals in both master and slave sides and by exerting input-delay approach, the multirate dynamics is transformed into a continuous-time system. Sufficient Krasovskii-based stability criteria are provided to preserve the exponential stability of the linear discrete-time system for asynchronously sampling intervals and update rates. This analysis is formulated as a convex optimization problem in terms of linear matrix inequalities (LMI) to calculate the longest interval between two successive sampling periods. The proposed multirate approach demonstrates that selecting adequate intervals for samplers and proper update rates for actuators has a considerable effect on the stability of the system. In order to validate the stability criteria and present the efficacy of the proposed multirate scheme, pair of two degree of freedom manipulators will be investigated and maximum allowable sampling periods and update rates are computed to preserve the exponential stability for different multirate cases.