Stochastic source seeking for nonholonomic unicycle

We apply the recently introduced method of stochastic extremum seeking to navigate a nonholonomic unicycle towards the maximum of an unknown, spatially distributed signal field, using only the measurement of the signal at the vehicle’s location butwithout themeasurement of the vehicle’s position. Keeping the forward velocity constant and controlling only the angular velocity, we design a stochastic source seeking control lawwhich employs excitation based on filteredwhite noise, rather than sinusoidal perturbations used in the existingwork.We study stabilitywith the help of stochastic averaging theorems that we recently developed for general nonlinear continuous-time systemswith stochastic perturbations. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. We characterize the convergence speed explicitly and provide design guidelines for maximizing it, as well as forminimizing the residual set near the source.We present a detailed simulation study, including a study of the effect of saturation on the steering input. © 2010 Elsevier Ltd. All rights reserved.