Reconfiguring Massive Particle Swarms with Limited, Global Control

  • Aaron Becker
  • Erik D. Demaine
  • Sándor P. FeketeEmail author
  • Golnaz Habibi
  • James McLurkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8243)


We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal such as gravity or a magnetic field. Upon activation of the field, each particle moves maximally in the same direction, until it hits a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom—all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. The resulting model matches ThinkFun’s Tilt puzzle.

If we are given a fixed set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration can be transformed into a desired target configuration. On the positive side, we provide constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations.


Robot swarm Nano-particles Uniform inputs Parallel motion planning Complexity Array permutations 



We acknowledge the helpful discussion and motivating experimental efforts with T. pyriformis cells by Yan Ou and Agung Julius at RPI and Paul Kim and MinJun Kim at Drexel University. This work was supported by the National Science Foundation under CPS-1035716.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Aaron Becker
    • 1
  • Erik D. Demaine
    • 2
  • Sándor P. Fekete
    • 3
    Email author
  • Golnaz Habibi
    • 1
  • James McLurkin
    • 1
  1. 1.Department of Computer ScienceRice UniversityHoustonUSA
  2. 2.Computer Science and Artificial Intelligence LaboratoryMITCambridgeUSA
  3. 3.Department of Computer ScienceTU BraunschweigBraunschweigGermany

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