Reconfiguring massive particle swarms with limited, global control

Abstract

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. © 2014 Springer-Verlag Berlin Heidelberg.