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Herding by caging: a formation-based motion planning framework for guiding mobile agents

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Abstract

We propose a solution to the problem of herding by caging: given a set of mobile robots (called herders) and a group of moving agents (called sheep), we guide the sheep to a target location without letting them escape from the herders along the way. We model the interaction between the herders and the sheep by defining virtual “repulsive forces” pushing the sheep away from the herders. This enables the herders to partially control the motion of the sheep. We formalize this behavior topologically by applying the notion of caging, a concept used in robotic manipulation. We demonstrate that our approach is provably correct in the sense that the sheep cannot escape from the robots under our assumed motion model. We propose an RRT-based path planning algorithm for herding by caging, demonstrate its probabilistic completeness, and evaluate it in simulations as well as on a group of real mobile robots.

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Notes

  1. The number of robots n does not depend on m, but, in our work, should not be smaller than 3 in the case of a 2D workspace. Robots are all the same and indistinguishable to the sheep.

  2. By interior of a closed curve in \({\mathbb {R}}^2\) we mean the union of bounded connected components in its complement. Note that the term “connected components” is used in the topological sense, and a closed curve can potentially have self-intersections.

  3. We assume that the robots do not move slower than at their maximum speed until they reach their final positions, so we assume that it is fixed and equal to \({\mathrm {v}}_{{\mathrm {r}}}\).

  4. We compute homology with coefficients in \({\mathbb {Z}}_2\).

  5. https://www.vicon.com/.

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Acknowledgements

This research work was supported by the Innovation and Technology Fund of the Government of the Hong Kong Special Administrative Region (Project No. ITS/104/19FP), Knut and Alice Wallenberg Foundation, Swedish Research Council, and European Research Council (Project 884807 BIRD).

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Author notes

  1. Haoran Song and Anastasiia Varava have contributed equally in this work.

Authors and Affiliations

  1. Robotics Institute, Hong Kong University of Science and Technology, Hong Kong, China

    Haoran Song & Michael Yu Wang

  2. Robotics, Perception and Learning Lab, KTH Royal Institute of Technology, Stockholm, Sweden

    Anastasiia Varava, Oleksandr Kravchenko, Danica Kragic & Florian T. Pokorny

  3. Department of Mechanical Engineering and Material Science, Yale University, New Haven, USA

    Kaiyu Hang

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  1. Haoran Song
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  2. Anastasiia Varava
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  3. Oleksandr Kravchenko
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  4. Danica Kragic
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  5. Michael Yu Wang
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  6. Florian T. Pokorny
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  7. Kaiyu Hang
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Correspondence to Haoran Song.

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This is one of the several papers published in Autonomous Robots comprising the Special Issue on Topological Methods in Robotics.

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Song, H., Varava, A., Kravchenko, O. et al. Herding by caging: a formation-based motion planning framework for guiding mobile agents. Auton Robot 45, 613–631 (2021). https://doi.org/10.1007/s10514-021-09975-8

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  • DOI: https://doi.org/10.1007/s10514-021-09975-8

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