Enhanced formation graphs with projected distance matrices

Formation graphs are widely used in multi vehicle decentralized formation control area. They provide a robust and scalable control approach and tools for designing stable systems. However, current methods cannot guarantee the uniqueness of formations for every communication scheme and resulting formations depend on initial conditions. In this article, a method for forcing unique formations for multi-vehicle systems is proposed. The proposed method uses projected distance matrices in formation graphs and is successful even in loosely connected non-rigid graphs. Simulations are also implemented successfully.