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APCA International Conference on Automatic Control and Soft Computing

CONTROLO 2020: CONTROLO 2020 pp 363–372Cite as

A Decentralized Strategy for Variational Collision Avoidance on Complete Riemannian Manifolds

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 695))

Abstract

We introduce a variational approach for decentralized collision avoidance of multiple agents evolving on a Riemannian manifold, and we derive necessary conditions for extremal. The problem consists of finding non-intersecting trajectories of a given number of agents sharing only the information of relative positions with respect to their nearest neighbors, among a set of admissible curves, such that these trajectories are minimizers of an energy functional. The energy functional depends on covariant acceleration and an artificial potential used to prevent collision among the agents. We show the global existence of extrema for the energy functional. We apply the results to the case of agents on a compact and connected Lie group. Simulation results are shown to demonstrate the applicability of the results.

In honor to Fátima Silva Leite in her 70th birthday.

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Acknowledgments

The project that gave rise to these results received the support of a fellowship from “la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/ PI19/11690016. J. Goodman was also supported by a “La Caixa” Foundation INPhINIT Fellowship, with fellowship code LCF/BQ/DI19/11730028. This work was also partially supported by I-Link Project (Ref: linkA20079) from CSIC; Ministerio de Economía, Industria y Competitividad (MINEICO, Spain) under grant MTM2016-76702-P; “Severo Ochoa Programme for Centres of Excellence” in R&D (SEV-2015-0554).

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Authors and Affiliations

  1. Institute of Mathematical Sciences (ICMAT), Calle Nicolás Cabrera 13-15, Campus Cantoblanco, 28049, Madrid, Spain

    Leonardo J. Colombo & Jacob R. Goodman

Authors
  1. Leonardo J. Colombo
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  2. Jacob R. Goodman
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Correspondence to Leonardo J. Colombo .

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Editors and Affiliations

  1. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Bragança, Portugal

    José Alexandre Gonçalves

  2. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Bragança, Portugal

    Manuel Braz-César

  3. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Bragança, Portugal

    João Paulo Coelho

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Colombo, L.J., Goodman, J.R. (2021). A Decentralized Strategy for Variational Collision Avoidance on Complete Riemannian Manifolds. In: Gonçalves, J.A., Braz-César, M., Coelho, J.P. (eds) CONTROLO 2020. CONTROLO 2020. Lecture Notes in Electrical Engineering, vol 695. Springer, Cham. https://doi.org/10.1007/978-3-030-58653-9_35

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