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

Heiko Hamann, Heinz Wörn
in Proc. of Swarm Robotics - Second SAB 2006 International Workshop (2007), 43-55


             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 find-
ing, 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 forag-
ing scenario with virtual pheromones as the medium for communication.
From the model, the robot density, the food flow and a quantity de-
scribing 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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