Artificial vector fields for robot convergence and circulation of time-varying curves in n-dimensional spaces

This paper addresses the problem of controlling a single mobile robot to converge smoothly to a pre-specified closed curve. Once in the curve, the robot remains circulating along it. The main motivation for this is the control of unmanned airplanes, where the robot cannot converge to a single point. Our control law is based on an artificial vector field that allows for the generalization to time-varying curves defined in n-dimensional spaces. We also present results that may be used to control mobile robots moving with constant speed. We devise convergence proofs and present simulations that verify the proposed approach.