Nonreciprocal field theory for decision-making in multi-agent control systems

Andrea Lama, Mario di Bernardo () and Sabine. H. L. Klapp ()
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Andrea Lama: Scuola Superiore Meridionale
Mario di Bernardo: Scuola Superiore Meridionale
Sabine. H. L. Klapp: Technische Universität Berlin

Nature Communications, 2025, vol. 16, issue 1, 1-12

Abstract: Abstract Field theories for complex systems traditionally focus on collective behaviours emerging from simple, reciprocal pairwise interaction rules. However, many natural and artificial systems exhibit behaviours driven by microscopic decision-making processes that introduce both nonreciprocity and many-body interactions, challenging these conventional approaches. We develop a theoretical framework to incorporate decision-making into field theories using the shepherding problem from swarm robotics as a paradigmatic example of a multi-agent control system, where agents, the herders, must coordinate to confine another group of agents, the targets, within a prescribed region. By introducing continuous approximations of two key decision-making elements - target selection and trajectory planning - we derive field equations that capture the essential features of this distributed control problem. Our theory reveals that different decision-making strategies emerge at the continuum level, from average attraction to highly selective choices, and from undirected to goal-oriented motion, driving transitions between homogeneous and confined configurations. The resulting nonreciprocal field theory not only describes the shepherding problem but provides a general framework for incorporating decision-making into continuum theories of collective behaviour, with implications for applications ranging from robotic swarms to traffic and crowd management systems.

Date: 2025
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DOI: 10.1038/s41467-025-63071-4

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