A simple algebraic criterion for stability of Bilateral Teleoperation Systems under time-varying delays

Abstract Stability analysis of Bilateral Teleoperation Systems (BTSs) is addressed, considering a control architecture subject to asymmetric time-varying delays in the communication links between the locally operated and remote robots. The manipulators are modeled as nonlinear second-order vibrating systems in generalized coordinates and are controlled by the delayed position-error feedback. The Lyapunov-Krasovskii (LK) theory is used to obtain a simple algebraic stability test. By means of this result, it is possible to compute the controller gains, given that the maximum delays in communication are known. Alternatively, if gains are known in advance, it is possible to determine the maximum delays at which the system will remain stable. Numerical experiments show that the proposed test is less conservative or provide the same results than comparable methods available in the literature. Finally, to close the paper, real-world trials illustrate the effectiveness of our result.

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