Probabilistic modeling of swarming systems

This chapter provides on overview on probabilistic modeling of swarming systems. We first showhow population dynamics models can be derived from the master equation in physics. We then present models with increasing complexity and with varying degrees of spatial dynamics. We will first introduce a model for collaboration and show how macroscopic models can be used to deriveoptimal policies for the individual robot analytically. We then introduce two models for collective decisions; first modeling spatiality implicitly by tracking the number of robots at specific sites and then explicitly using a Fokker-Planck equation. The chapter is concluded withopen challenges in combining non-spatial with spatial probabilistic modeling techniques.