Feedback optimization problem for master–slave teleoperation tracking in the presence of random noise in dynamics and feedback

Abstract

In this work, we study the problem of a teleoperation master–slave system with error feedback based on sampled versions of the past and present master and slave positions. The sampling interval is the teleoperation delay, and small random fluctuations in the feedback coefficients are considered apart from small random noise in the dynamics. The overall master–slave dynamical system is abstracted into a stochastic delay differential system with random fluctuations in the parameters. This system is transformed into an ordinary stochastic differential system with an infinite-dimensional state vector, and using perturbation theory, integral expressions for the state correlations are obtained in terms of the noise correlations and feedback coefficient fluctuation correlations. We then partially explain how these computations may be used in minimizing the expected value of a cost functional of the state such as the master–slave tracking error energy. Some details about how the underlying delay differential equations for the master–slave dynamics are simulated using the fourth-order Runge–Kutta algorithm are provided. Finally, the simulation experiments are carried out on hardware, i.e., using the actual PHANToM Omni robot and these demonstrate excellent master–slave tracking when sampled teleoperation feedback is given.