Shepherding control and herdability in complex multiagent systems (2307.16797v2)
Abstract: We study the shepherding control problem where a group of "herders" need to orchestrate their collective behaviour in order to steer the dynamics of a group of "target" agents towards a desired goal. We relax the strong assumptions of targets showing cohesive collective behavior in the absence of the herders, and herders owning global sensing capabilities. We find scaling laws linking the number of targets and minimum herders needed, and we unveil the existence of a critical threshold of the density of the targets, below which the number of herders needed for success significantly increases. We explain the existence of such a threshold in terms of the percolation of a suitably defined herdability graph and support our numerical evidence by deriving and analysing a PDE describing the herders dynamics in a simplified one-dimensional setting. Extensive numerical experiments validate our methodology.
- M. A. Haque, A. R. Rahmani, and M. B. Egerstedt, Biologically inspired confinement of multi-robot systems, International Journal of Bio-Inspired Computation 3, 213 (2011).
- E. Sebastián, E. Montijano, and C. Sagüés, Adaptive multirobot implicit control of heterogeneous herds, IEEE Transactions on Robotics 38, 3622 (2022).
- A. Pierson and M. Schwager, Controlling noncooperative herds with robotic herders, IEEE Transactions on Robotics 34, 517 (2017).
- R. A. Licitra, Z. I. Bell, and W. E. Dixon, Single-agent indirect herding of multiple targets with uncertain dynamics, IEEE Transactions on Robotics 35, 847 (2019).
- D. Ko and E. Zuazua, Asymptotic behavior and control of a “guidance by repulsion” model, Mathematical Models and Methods in Applied Sciences 30, 765 (2020).
- K. Fujioka, Comparison of shepherding control behaviors, in Proceedings of TENCON 2017-2017 IEEE Region 10 Conference (IEEE, 2017) pp. 2426–2430.
- P. Dolai, A. Simha, and S. Mishra, Phase separation in binary mixtures of active and passive particles, Soft Matter 14, 6137 (2018).
- S. Mohapatra and P. S. Mahapatra, Confined system analysis of a predator-prey minimalistic model, Scientific Reports 9, 11258 (2019).
- R. M. D’Souza, M. di Bernardo, and Y.-Y. Liu, Controlling complex networks with complex nodes, Nature Reviews Physics 5, 250 (2023).
- M. Casiulis, D. Hexner, and D. Levine, Self-propulsion and self-navigation: Activity is a precursor to jamming, Physical Review E 104, 064614 (2021).
- P. Romanczuk, I. D. Couzin, and L. Schimansky-Geier, Collective motion due to individual escape and pursuit response, Physical Review Letters 102, 010602 (2009).
- Z. You, A. Baskaran, and M. C. Marchetti, Nonreciprocity as a generic route to traveling states, Proceedings of the National Academy of Sciences 117, 19767 (2020).
- S. Saha, J. Agudo-Canalejo, and R. Golestanian, Scalar active mixtures: The nonreciprocal cahn-hilliard model, Physical Review X 10, 041009 (2020).
- This concept is related but not entirely equivalent to the definition of herdability of complex systems that was given independently in [34].
- K. J. Åström and R. M. Murray, Feedback systems: an introduction for scientists and engineers (Princeton university press, 2021).
- M. Barthélemy, Spatial networks, Physics Reports 499, 1 (2011).
- J. Dall and M. Christensen, Random geometric graphs, Physical review E 66, 016121 (2002).
- E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback, SIAM Journal on Control and Optimization 28, 466 (1990).
- M. Krstic and A. Smyshlyaev, Boundary control of PDEs: A course on backstepping designs (SIAM, 2008).
- S. F. Ruf, M. Egerstedt, and J. S. Shamma, Herdability of linear systems based on sign patterns and graph structures, arXiv preprint arXiv:1904.08778 (2019).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.