Stochastic source seeking for mobile robots in environments with obstacles via the SPSA method

Eduardo Ramírez-Llanos and Sonia Martínez
IEEE Transactions on Automatic Control, 64 (4) (2019) 1732-1739

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 it is required measurements of the signal at the robot location and information of a contact sensor. 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 of size depending on the step-size that contains the location of the source. The novelty of our approach is that we consider nondifferentiable convex functions, a fixed step-size, and the environment may contain obstacles. Our proof methods employ nonsmooth Lyapunov theory, tools from convex analysis, and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithms in 2D scenarios for the source seeking problem.

File: (local copy)

Bib-tex entry:

@article{ER-SM:19-tac,
author = {E. Ram{\'\i}rez-Llanos and S. Mart{\'\i}nez},
title = {Stochastic source seeking for mobile robots in environments with obstacles via the SPSA method},
journal= {IEEE Transactions on Automatic Control},
year = {2019},
volume = 64,
number = 4,
pages = {1732--1739}
}