Discrete-time stochastic source seeking with multiple nonholonomic unicycles

Using the method of discrete-time stochastic extremum seeking, we design a single, scalar discrete-time forward velocity controller to navigate multiple nonholonomic unicycles to seek the source of an unknown, spatially distributed signal field simultaneously, while the angular velocities of unicycles are kept as different constants. We assume that the information of each unicycle's position is unavailable. Moreover, the forward velocity controller is designed by only using noisy measurements of the signal field at unicycles' position. We prove local exponential convergence, both almost surely and in probability, to a small neighbourhood near the source. A numerical example is given to illustrate the effectiveness of the controller.