A Space- and Time-Continuous Model of Self-Organizing Robot Swarms for Design Support

  Designing and implementing artificial self-organizing systems is a
  challenging task since they typically behave non-intuitive and only little
  theoretical foundations exist. Predicting a system of many components with a
  huge amount of interactions is beyond human skills. The currently common use
  of simulations for design support is not satisfying, as it is time-consuming
  and the results are most likely suboptimal.

  In this work, we present the derivation of an analytical, time-, and
  space-continuous model for a swarm of autonomous robots based on the
  Fokker-Planck equation. While the motion model is in most parts physically
  motivated, the communication model is based on a heuristic approach.
  A showcase application to a recently proposed scenario of collective
  perception in a huge swarm of robots with very limited abilities is given
  and the simulation results are compared to the model. Despite the high level
  of abstraction, the prediction discrepancies are small and the parameters
  can be mapped one-to-one from the model to the control algorithm. Finally,
  we give an outlook on the capabilities of the proposed model, discuss its
  limitations, and suggest an improvement that could reduce the number of
  empirically determined parameters.

(see doi.ieeecomputersociety.org/10.1109/SASO.2007.3 [2])