This paper analyzes the stability properties of a decentralized hybrid control system for maintaining formations. Utilizing only local sensing, the system assembles strings or “platoons” of robots that has each robot maintaining a fixed bearing to its nearest neighbor. Using these platoons, the system is able to construct more complicated geometries. A piecewise linear controller based on bidirectional controller design is utilized to ensure the stability of the system. The system is demonstrated in simulation as well as on a physical set on non-holonomic mobile robots.