Extremum Seeking Navigation Without Derivative Estimation of a Mobile Robot in a Dynamic Environmental Field

Abstract

We consider a single kinematically controlled robot with bounded control inputs. It travels in a 2-D region supporting an unknown unsteady scalar field. A single sensor provides the field value at the current location of the robot. We present a reactive navigation strategy that drives the robot to the time-varying spatial maximum of the field, and subsequently maintains proximity to this location. This strategy is based on a novel paradigm of kinematic control, and is distinct from the conventional imperative of aligning the velocity vector with the field gradient. It does not employ estimation of any field gradient-or derivative-dependent quantities, like the rate at which the field measurement evolves over time, and is nondemanding with respect to both computation and motion. Its convergence is rigorously justified for smooth dynamic fields under some technical and partly unavoidable assumptions. Simulation results and experiments with a real wheeled robot confirm the applicability and performance of the proposed navigation approach.