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J R Soc Interface. 2014 Nov 6;11(100):20140719. doi: 10.1098/rsif.2014.0719.

Solving the shepherding problem: heuristics for herding autonomous, interacting agents.

Author information

  • 1Department of Mathematics, Uppsala University, Uppsala 75106, Sweden
  • 2Department of Mathematics, Uppsala University, Uppsala 75106, Sweden.
  • 3Structure and Motion Laboratory, The Royal Veterinary College, University of London, Hatfield, Hertfordshire AL9 7TA, UK.
  • 4Department of Computer Science, University College of London, Gower Street, London WC1E 6BT, UK.
  • 5Department of Physiology, Development and Neuroscience, University of Cambridge, Downing Street, Cambridge CB2 3DY, UK.
  • 6Department of Biosciences, College of Science, Swansea University, Swansea SA2 8PP, UK.


Herding of sheep by dogs is a powerful example of one individual causing many unwilling individuals to move in the same direction. Similar phenomena are central to crowd control, cleaning the environment and other engineering problems. Despite single dogs solving this 'shepherding problem' every day, it remains unknown which algorithm they employ or whether a general algorithm exists for shepherding. Here, we demonstrate such an algorithm, based on adaptive switching between collecting the agents when they are too dispersed and driving them once they are aggregated. Our algorithm reproduces key features of empirical data collected from sheep-dog interactions and suggests new ways in which robots can be designed to influence movements of living and artificial agents.


agent-based model; collective motion; sheep; sheepdog

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