Controlling three dimensional swarms of robots

We address the problem of modeling and controlling a swarm of fully actuated point-like robots in three dimensions by generalizing the planar framework from (C. Belta and V. Kumar, 2004). We define a nine-dimensional abstraction of the swarm that has a product structure of the six-dimensional Euclidean group and a three-dimensional shape, and is independent of the number of robots. The group captures the pose of an ellipsoid spanning the swarm with semiaxes given by the shape variables. The overall abstract description is invariant to robot permutations. In addition, the shape is also invariant to left actions of the group. This description allows one to define and control the behavior of the swarm at a high level, with automatic generation of individual robot control laws. We present simulation results for controlling swarms of rotorcrafts