Constrained source seeking for mobile robots via simultaneous perturbation stochastic approximation

This paper considers a class of stochastic source seeking problems to drive a mobile robot to the maximizer of a source signal by only using measurements of the signal at the robot location. Our algorithm builds on the simultaneous perturbation stochastic approximation idea to obtain information of the signal field. We prove the practical convergence of the algorithm 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 can be restricted to any compact convex set. Our proof methods employ nonsmooth Lyapunov theory, tools from convex analysis and stochastic difference inclusions. Finally, we illustrate the applicability of the proposed algorithm in a 2D scenario for the source seeking problem.