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Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation

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Abstract

In this paper we describe a novel decentralized control strategy to realize formations of mobile robots. We first describe how to design artificial potential fields to obtain a formation with the shape of a regular polygon. We provide a formal proof of the asymptotic stability of the system, based on the definition of a proper Lyapunov function. We also prove that our control strategy is not affected by the problem of local minima. Then, we exploit a bijective coordinate transformation to deform the polygonal formation, thus obtaining a completely arbitrarily shaped formation. Simulations and experimental tests are provided to validate the control strategy.

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Authors and Affiliations

  1. Department of Electronics, Computer Sciences and Systems (DEIS), University of Bologna, Bologna, Italy

    Lorenzo Sabattini

  2. Department of Sciences and Methods of Engineering (DISMI), University of Modena and Reggio Emilia, Modena and Reggio Emilia, Italy

    Cristian Secchi & Cesare Fantuzzi

Authors
  1. Lorenzo Sabattini
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  2. Cristian Secchi
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  3. Cesare Fantuzzi
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Correspondence to Lorenzo Sabattini.

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Sabattini, L., Secchi, C. & Fantuzzi, C. Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation. Auton Robot 30, 385–397 (2011). https://doi.org/10.1007/s10514-011-9225-4

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  • DOI: https://doi.org/10.1007/s10514-011-9225-4

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