Probabilistic Modeling of Swarming Systems

  • Nikolaus Correll
  • Heiko Hamann
Part of the Springer Handbooks book series (SHB)


This chapter provides on overview on probabilistic modeling of swarming systems. We first show how 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 derive optimal 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 with open challenges in combining non-spatial with spatial probabilistic modeling techniques.


Master Equation Langevin Equation Planck Equation Collective Decision Swarm Robotic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

partial differential equation


stochastic differential equation


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dep. Computer ScienceUniversity of Colorado at BoulderBoulderUSA
  2. 2.Dep. Computer ScienceUniverstity of PaderbornPaderbornGermany

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