A framework for boltzmann-type models of robotic swarms

We introduce a new model framework to describe the temporal evolution of the macroscopic location probability of a robotic swarm in two dimensions based on the Boltzmann equation from statistical physics. The framework features a strong connection between the microscopic behavior of the robots and the macroscopic effects of this behavior. It is distinguished from other existing models by the inclusion of the robots velocities into the model. Therefore it is able to correctly describe the behavior of the robots even in regions with low robot densities or high ratios of deterministic movement of the robots. The model is validated against results from simulations of two simple test-scenarios. A short introduction to the numerics used to evaluate the model is given.