Motion planning for formations of Dubins vehicles

This paper studies the motion planning problem for formations of n identical Dubins vehicles maintaining constant distances. We discuss three basic formations: star formations, chain formations and ring formations, from which any formation based on pairwise constant distance can be obtained. The challenge is to control such high-dimensional affine systems with drift through 1-dimensional controls whose admissible ranges depend on the configuration variables. Motion planning algorithms are designed to drive star formations and chain formations between any two configurations in their reachable sets. For ring formations, a motion planning algorithm is proposed when all vehicles have the equal direction of motion. Finally, examples of trajectories of ring formations in case of non equal directions of motion are presented.