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

Andrea Lama1, Mario di Bernardo2,3, Sabine H L Klapp4

  • 1Modeling and Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples, Italy.

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This study introduces a new field theory framework to model complex systems driven by agent decision-making, not just simple interactions. The theory captures how individual choices influence collective behavior in multi-agent systems like robotic swarms.

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Area of Science:

  • Complex Systems Theory
  • Robotics
  • Collective Behavior

Background:

  • Traditional field theories focus on simple, reciprocal interactions.
  • Many systems involve complex decision-making, leading to nonreciprocity and many-body interactions.
  • Existing models struggle to capture these decision-driven dynamics.

Purpose of the Study:

  • Develop a theoretical framework to integrate microscopic decision-making into field theories.
  • Utilize the shepherding problem in swarm robotics as a model system.
  • Derive field equations that account for agent decision-making processes.

Main Methods:

  • Developed continuous approximations for target selection and trajectory planning.
  • Formulated nonreciprocal field equations based on these approximations.
  • Applied the framework to the multi-agent shepherding problem.

Main Results:

  • The theory reveals emergent decision-making strategies at the continuum level.
  • Observed transitions between homogeneous and confined configurations driven by these strategies.
  • Demonstrated the framework's ability to capture nonreciprocity and many-body effects.

Conclusions:

  • The developed nonreciprocal field theory provides a general approach for incorporating decision-making into continuum models.
  • This framework enhances understanding of collective behavior in systems with complex agent interactions.
  • Potential applications include robotic swarms, traffic management, and crowd dynamics.