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Decentralized multi-robot encirclement of a 3D target with guaranteed collision avoidance

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Abstract

We present a control framework for achieving encirclement of a target moving in 3D using a multi-robot system. Three variations of a basic control strategy are proposed for different versions of the encirclement problem, and their effectiveness is formally established. An extension ensuring maintenance of a safe inter-robot distance is also discussed. The proposed framework is fully decentralized and only requires local communication among robots; in particular, each robot locally estimates all the relevant global quantities. We validate the proposed strategy through simulations on kinematic point robots and quadrotor UAVs, as well as experiments on differential-drive wheeled mobile robots.

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Notes

  1. Note that matrix \(J_i\) is invertible whenever \(\phi _i\) is defined, i.e., unless the ith robot is exactly above the target. This zero-measure case represents a purely theoretical problem, especially considering the presence of noise in the measurements.

  2. It is a differently weighted Laplacian of the undirected ring.

  3. Note that the first-order derivative \(\dot{\varvec{p}}_i=\varvec{u}_i\) is directly given by the general expression (22), whereas the second-order derivative \(\ddot{\varvec{p}}_i(t)\) is numerically computed.

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Authors and Affiliations

  1. CNRS, LAAS, 7 Avenue du Colonel Roche, 31400, Toulouse, France

    Antonio Franchi

  2. Univ de Toulouse, LAAS, 31400, Toulouse, France

    Antonio Franchi

  3. Max Planck Institute for Biological Cybernetics, Spemanstraße 38, 72076, Tübingen, Germany

    Paolo Stegagno

  4. Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Sapienza Università di Roma, Via Ariosto 25, 00185, Rome, Italy

    Giuseppe Oriolo

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  1. Antonio Franchi
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  2. Paolo Stegagno
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  3. Giuseppe Oriolo
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Correspondence to Antonio Franchi.

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Franchi, A., Stegagno, P. & Oriolo, G. Decentralized multi-robot encirclement of a 3D target with guaranteed collision avoidance. Auton Robot 40, 245–265 (2016). https://doi.org/10.1007/s10514-015-9450-3

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