Vector Fields for Robot Navigation Along Time-Varying Curves in n -Dimensions

This paper presents a methodology for computing artificial vector fields that allows a robot to converge to and circulate around generic curves specified in n-dimensional spaces. These vector fields may be directly applied to solve several robot navigation problems such as border monitoring, surveillance, target tracking and multi-robot pattern generation, with special application to fixed-wing aerial robots, which must keep a positive forward velocity and cannot converge to a single point. Unlike previous solutions found in the literature, the approach is based on fully continuous vector fields and is generalized to timevarying curves defined in n-dimensional spaces. We provide mathematical proofs and present simulation and experimental results that illustrate the applicability of the proposed approach. We also present a methodology for constructing the target curve based on a given set of its samples.