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Stigmergy: from mathematical modelling to control.

Alain Boldini1,2,3, Martina Civitella1, Maurizio Porfiri1,2,4

  • 1Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY 11201, USA.

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Summary
This summary is machine-generated.

This study introduces a mathematical framework to design environmental modifications for swarm behavior. It enables precise control over collective actions in robotic and mixed-species swarms.

Keywords:
animal behaviourcollective behaviourcontrolswarms

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Area of Science:

  • Robotics
  • Collective Behavior
  • Artificial Intelligence

Background:

  • Stigmergy, indirect communication via environmental modification, is key to animal swarm self-organization.
  • Engineers use stigmergy for coordinating robot and mixed robot-animal swarms.
  • Current stigmergy models are algorithmic, lacking a holistic approach to environmental design.

Purpose of the Study:

  • To develop a mathematical framework for understanding the relationship between environmental modifications and swarm behavior.
  • To enable the design of specific environmental modifications for achieving desired swarm formations.
  • To provide a unified approach for implementing stigmergy in diverse swarm systems.

Main Methods:

  • Modeling swarms and environmental modifications as continua using continuification techniques.
  • Developing analytical derivations and numerical simulations in one- and two-dimensional spaces.
  • Designing environmental modifications based on the proposed mathematical framework.

Main Results:

  • The framework rigorously describes the link between environmental changes and swarm behavior.
  • It successfully determines the necessary distribution of environmental traces for desired swarm formations.
  • Demonstrated adaptability across different implementation platforms.

Conclusions:

  • The proposed mathematical framework offers a holistic approach to stigmergy.
  • It facilitates the precise engineering of environmental cues for controlled swarm behavior.
  • This work advances the application of stigmergy in robotics and mixed-agent systems.