Reactive Navigation of a Mobile Robot to the Moving Extremum of a Dynamic Unknown Environmental Field without Derivative Estimation

We consider a single kinematically controlled mobile robot traveling in a planar region supporting an unknown and unsteady field distribution. A single sensor provides the distribution value at the current robot location. We present a reactive navigation strategy that drives the robot to the time-varying location where the field distribution attains its spatial maximum and then keeps the robot in the pre-specified vicinity of the maximizer. The proposed control algorithm employs estimation of neither the entire field gradient nor derivative-dependent quantities, like the rate at which the available measurement evolves over time, and is non-demanding with respect to both computation and motion. Its mathematically rigorous analysis and justification are provided. Simulation results confirm the applicability and performance of the proposed guidance approach.