An Analytical and Spatial Model of Foraging in a Swarm of Robots

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2007
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Wörn, Heinz
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ŞAHIN, Erol, ed., William M. SPEARS, ed., Alan F. T. WINFIELD, ed.. Swarm Robotics : second international workshop, SAB 2006, Rome, Italy, September 30 - October 1, 2006 ; revised selected papers. Berlin: Springer, 2007, pp. 43-55. Lecture Notes in Computer Science. 4433. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-540-71540-5. Available under: doi: 10.1007/978-3-540-71541-2_4
Zusammenfassung

The foraging scenario is important in robotics, because it has many different applications and demands several fundamental skills from a group of robots, such as collective exploration, shortest path finding, and efficient task allocation. Particularly for large groups of robots emergent behaviors are desired that are decentralized and based on local information only. But the design of such behaviors proved to be difficult because of the absence of a theoretical basis. In this paper, we present a macroscopic model based on partial differential equations for the foraging scenario with virtual pheromones as the medium for communication. From the model, the robot density, the food flow and a quantity describing qualitatively the stability of the behavior can be extracted. The mathematical model is validated in a simulation with a large number of robots. The predictions of the model correspond well to the simulation.

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macroscopic model, foraging, swarm robotics, mathematical analysis
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2nd International Workshop (SAB 2006), 30. Sept. 2006 - 1. Okt. 2006, Rome, Italy
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ISO 690HAMANN, Heiko, Heinz WÖRN, 2007. An Analytical and Spatial Model of Foraging in a Swarm of Robots. 2nd International Workshop (SAB 2006). Rome, Italy, 30. Sept. 2006 - 1. Okt. 2006. In: ŞAHIN, Erol, ed., William M. SPEARS, ed., Alan F. T. WINFIELD, ed.. Swarm Robotics : second international workshop, SAB 2006, Rome, Italy, September 30 - October 1, 2006 ; revised selected papers. Berlin: Springer, 2007, pp. 43-55. Lecture Notes in Computer Science. 4433. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-540-71540-5. Available under: doi: 10.1007/978-3-540-71541-2_4
BibTex
@inproceedings{Hamann2007Analy-59907,
  year={2007},
  doi={10.1007/978-3-540-71541-2_4},
  title={An Analytical and Spatial Model of Foraging in a Swarm of Robots},
  number={4433},
  isbn={978-3-540-71540-5},
  issn={0302-9743},
  publisher={Springer},
  address={Berlin},
  series={Lecture Notes in Computer Science},
  booktitle={Swarm Robotics : second international workshop, SAB 2006, Rome, Italy, September 30 - October 1, 2006 ; revised selected papers},
  pages={43--55},
  editor={Şahin, Erol and Spears, William M. and Winfield, Alan F. T.},
  author={Hamann, Heiko and Wörn, Heinz}
}
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