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We consider a single kinematically controlled robot with a bounded controlrange. The robot travels in a two-dimensional region supporting an unknownunsteady scalar field. A single sensor provides the field value at the currentlocation of the robot. The paper is concerned with a reactive navigationstrategy to drive the robot to the time-varying location where the fieldattains its spatial maximum, with subsequent keeping the robot close to thislocation. This strategy is based on a novel paradigm of kinematic controldifferent from conventionally trying to align the velocity vector with thefield gradient, does not employ estimation of the entire field gradient orderivative-dependent quantities, like the rate at which the available fieldreading evolves over time, and is non-demanding with respect to bothcomputation and motion. The paper presents the proofs of the technical factsrequired to justify convergence of the proposed algorithm.

Proofs of the Technical Results Justifying an Algorithm of Extremum Seeking Navigation in Dynamic Environmental Fields