A macroscopic probabilistic model of adaptive foraging in swarm robotics systems

Abstract

In this paper, we extend a macroscopic probabilistic model of a swarm of foraging robots from the homogeneous to the heterogeneous case. In the swarm, each robot is capable of adjusting its searching time and resting time thresholds following the rules described in our previous paper [1]. In
\norder to model the difference between robots, private/public resting time and searching time thresholds
\nare introduced, a number of equations are then developed to work out the relationship between these private time thresholds and public time thresholds based on previously developed difference equations [2]. The extended macroscopic probabilistic model has been tested using the simulation tools Player/Stage. The results from the macroscopic probabilistic model match with those from the simulation with reasonable accuracy, not only in the final net energy of the swarm but also in the instantaneous
\nnet energy. Although the model is specific to adaptive foraging, we believe the methodology can be extended to other systems in which the heterogeneity of the system is coupled with its time parameters.