Stochastic Source Seeking for Mobile Robots in Obstacle Environments Via the SPSA Method

Abstract

This paper considers a class of stochastic source-seeking problems to drive a mobile robot to the minimizer of a source signal. Our approach is first analyzed in an obstacle-free scenario, where measurements of the signal at the robot location and information of a contact sensor are required. We extend our results to environments with obstacles under mild assumptions on the step size. Our approach builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithms to a ball whose size depends on the step size that contains the location of the source. The novelty relies in that we consider nondifferentiable convex functions, a fixed step size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov function theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in a two-dimensional scenarios.