A Single- and Multi-Dimensional Cellular Automata Approach to Robot Formation Control

One of the challenges to the realization of harvesting solar power from space is overcoming the difficulties and high cost for the transportation and construction of a large orbiting solar reflector. One approach that has received attention is using thousands of individual robots moving in formation, each with a piece of the reflector attached, to form the structure. In previous work, we demonstrate an algorithm that treats a group of robots as a 1-dimensional cellular automaton, which is able to establish formations defined by a geometric description that can be expressed as a single mathematical function. In this paper we extend the algorithm for robots to establish formations defined by multiple mathematical functions in order to form grid structures.