Mathematical Model of Foraging in a Group of Robots: Effect of Interference

In multi-robot applications, such as foraging or collection tasks, interference, which results from competition for space between spatially extended robots, can significantly affect the performance of the group. We present a mathematical model of foraging in a homogeneous multi-robot system, with the goal of understanding quantitatively the effects of interference. We examine two foraging scenarios: a simplified collection task where the robots only collect objects, and a foraging task, where they find objects and deliver them to some pre-specified home location. In the first case we find that the overall group performance improves as the system size grows; however, interference causes this improvement to be sublinear, and as a result, each robot's individual performance decreases as the group size increases. We also examine the full foraging task where robots collect objects and deliver them home. We find an optimal group size that maximizes group performance. For larger group sizes, the group performance declines. However, again due to the effects of interference, the individual robot's performance is a monotonically decreasing function of the group size. We validate both models by comparing their predictions to results of sensor-based simulations in a multi-robot system and find good agreement between theory and simulations data.