Kinematic navigation of a mobile robot for environmental extremum seeking without derivatives estimation

We consider a single kinematically controlled mobile robot traveling in a planar region supporting an unknown field distribution. A single sensor provides the distribution value at the current robot location. We present a new navigation strategy that drives the robot to the location where the field distribution attains its maximum. 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.