An Exact Stability Condition for Bilateral Teleoperation With Delayed Communication Channel

In this correspondence paper, an exact method is developed to guarantee asymptotic stability of a bilateral teleoperation system that is subjected for a time-delayed communication. This extends the prior art of searching for the maximum upper bound of time delay. In order to improve the flexibility in controller design and obtain better performance, a fractional-order PDα controller is proposed. The exactly stable regions of delays are explored for both integral-order and fractional-order controllers. Compared with conditions in most previous works which are deduced by the Lyapunov-Krasovskii functional and rely on the solution of some linear matrix inequalities, the stability conditions proposed in this paper are established from the frequency domain point of view, and thus, the results are not only sufficient but also necessary. To illustrate accuracy of the conditions, they are simulated on a delayed teleoperation system composed of a pair of robots.

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