Hexagonal Lattice Formation in Multi-Robot Systems

We present an algorithm that arranges a multi-robot system into a regular hexagonal lattice. This configuration provides continuous coverage with the fewest number of robots required. It also has a bounded stretch over a fully-connected graph, producing an efficient multi-hop communications network. Our algorithm uses artificial forces to move each robot to local potential energy wells. A local error correction algorithm detects and corrects most local lattice errors. Both algorithms are fully distributed, requiring local network geometry information, but no global coordinates. We present analysis of the potential energy wells that form the lattice, a proof of the upper bound on the spanning ratio of a hexagonal packing, and the error detecting and correcting algorithm. Simulation results demonstrate the effectiveness of the approach for large populations of robots.