We describe a new decentralized algorithm for multi-robot systems to form arbitrary repeated lattice patterns. Prior work showed how to represent a desired pattern using a directed graph in which each edge is labeled with a rigid body transformation, and proposed an algorithm that accepts this graph as input and computes destinations for each robot using only local information. In this paper, we improve upon that result by describing a new algorithm, substantially different both in message passing procedure and in movement strategy, to resolve several limitations of the existing algorithm. We prove that, by executing this algorithm, the robots will form the desired lattice pattern in a bounded amount of time. We further show that, if the robots' communication graph is connected at the start of the algorithm, it will remain connected throughout the algorithm's execution. Using a simulation, we demonstrate that this algorithm works correctly for systems with dozens of autonomous robots to form various lattice patterns. Moreover, the experiments show a significant improvement in solution quality for our new algorithm compared to the previous approach.
['Yang Song', "Jason M. O'Kane"]
Forming repeating patterns of mobile robots: A provably correct decentralized algorithm