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A projection-based algorithm for optimal formation and optimal matching of multi-robot system

Abstract

In this paper, the optimal formation and optimal matching of a multi-robot system are investigated with a projection-based algorithm designed to get the optimal formation moving in real time. The formation-related optimization problem is proposed under the consideration of two cases: the free formation and the formation with anchor(s). For the latter, equality constraints are formulated for the anchor, and the objective of the optimal formation is to minimize the total distance to the initial formation of the multi-robot system. Here, the objective function with mixed norm is considered to get a compact formation. Sufficient conditions on the design parameter for global convergence of the proposed algorithm are provided in the theoretical results. Furthermore, the projection particle swarm optimizer is investigated for getting the optimal matching between the initial/intermediate formation and the optimal formation. Finally, simulations on several numerical examples are presented to validate the effectiveness of the proposed method.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61876036 and Grant 61833005 and in part by the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant BM2017002.

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Correspondence to Qingshan Liu.

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Liu, Q., Wang, M. A projection-based algorithm for optimal formation and optimal matching of multi-robot system. Nonlinear Dyn 104, 439–450 (2021). https://doi.org/10.1007/s11071-020-06189-y

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  • DOI: https://doi.org/10.1007/s11071-020-06189-y

Keywords

  • Multi-robot system
  • Projection-based algorithm
  • Constrained optimization
  • Global convergence
  • Particle swarm optimizer