Multi-level Spatial Modeling for Stochastic Distributed Robotic Systems

We propose a combined spatial and non-spatial probabilistic modeling methodology motivated by an inspection task performed by a group of miniature robots. Our models explicitly consider spatiality and yield accurate predictions on system performance. An agent's spatial distribution over time is modeled by the Fokker-Planck diffusion model and complements current non-spatial microscopic and macroscopic models that model the discrete state distribution of a distributed robotic system. We validate our models on a microscopic level based on submicroscopic, embodied robot simulations as well as real robot experiments. Subsequently, using the validated microscopic models as our template, abstraction is raised to the level of macroscopic dierence equations. We discuss the depen- dency of the modeling performance on the distance from the robot origin (drop-off location) and temporal convergence of the team distribution. Also, using an asymmetric setup, we show the necessity of spatial modeling methodologies for environments where the robotic platform underlies drift phenomena.