Vector fields for robot navigation along time-varying curves in n-dimensions

Authors:
Vinícius M. Gonçalves;Luciano C. A. Pimenta;Carlos A. Maia;Bruno C. O. Dutra;Guilherme A. S. Pereira
Affiliations:
Escola de Engenharia, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil;Escola de Engenharia, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil;Escola de Engenharia, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil;Escola de Engenharia, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil;Escola de Engenharia, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
Venue:
IEEE Transactions on Robotics
Year:
2010

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Abstract

This paper presents a methodology for computation of 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 multirobot 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 time-varying 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 construction of the target curve based on a given set of its samples.