A Single Forward-Velocity Control Signal for Stochastic Source Seeking With Multiple Nonholonomic Vehicles

With a single stochastic extremum seeking control signal, we steer multiple autonomous vehicles, modeled as nonholonomic unicycles, toward the maximum of an unknown, spatially distributed signal field. The vehicles, whose angular velocities are constant and distinct, travel at the same forward velocity, which is controlled by the stochastic extremum seeking controller. To determine the vehicles’ velocity, the controller uses measurements of the signal field at the respective vehicle positions and excitation based on filtered white noise. The positions of the vehicles are not measured. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source and provide a numerical example to illustrate the effectiveness of the algorithm.