Abstract
A kinematically controlled robot with a finite control range has access only to the distance to every member of a group of moving targets. It is required to approach and escort them, with maintaining a given distance to the currently nearest target, so that all targets are enclosed inside the robot’s path. Via representing the path of tight circumnavigation as an isoline of a scalar field artificially built from the distance measurements, the problem is shaped into tracking an isoline of an unknown dynamic scalar field based on point-wise access only to its value at the current location. In the case of a generic field, a novel reactive navigation law is presented that drives the robot to the targeted isoline and then ensures its tracking. This law follows a novel paradigm, which is distinct from the conventional imperative of turning the velocity perpendicular to the field gradient in order to trace the isoline and does not employ any field derivatives. Then this law is applied to solve the circumnavigation mission. Nonlocal convergence of the proposed laws is justified by mathematically rigorous results and is confirmed by computer simulations.
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