A Macroscopic Analytical Model of Collaboration in Distributed Robotic Systems

TLDR

The model assumes no explicit communication or coordination among robots, and unlike microscopic simulations, its computational cost is independent of group size. The study presents a macroscopic analytical model of collaboration among reactive robots. The model uses coupled differential equations to describe group dynamics and is applied to a stick‑pulling experiment where two robots must collaborate to extract sticks from holes. Analysis reproduces Ijspeert et al.’s qualitative findings, showing distinct dynamical regimes depending on the robot‑to‑stick ratio, optimal control parameters that maximize performance with group size, and a transition from super‑linear to sub‑linear performance as robot numbers rise. Autonomous Robots, 11:149–171.

Abstract

In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by Ijspeert et al. [Autonomous Robots, 11, 149-171]. The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of Ijspeert et al.: namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased.