Environmental boundary tracking approach to close circumnavigation of a group of unknown moving targets using range measurements

A kinematically controlled robot with a finite control range travels in a plane. There is an unknown dynamic scalar field in the plane; only the field value at the current location is measured. The robot should be autonomously driven to the unsteady and deforming isoline associated with a pre-specified field value and to track this isoline afterwards. A way to this objective is offered on the basis of a novel kinematic control paradigm dissimilar from the classic idea to turn the velocity perpendicular to the gradient. Specifically, a new reactive navigation strategy is presented and shown to solve the problem by a rigorous nonlocal convergence result in a generic field; this strategy does not employ estimation of gradient or other derivative-like quantities. These findings are applied to the problem of circumnavigation of several unknown moving targets based on range-only measurements. It is required to approach the targets and then to escort them so that they are enclosed inside the robot's path and a pre-specified small distance to the currently nearest target is maintained. Applicability and performance of the proposed circumnavigation approach is demonstrated via mathematically rigorous proofs and intensive computer simulations.