Decentralized algorithm for minimum-time rendezvous of Dubins vehicles

In this paper, we consider the problem of minimum-time rendezvous of a team of Dubins vehicle at a pre-assigned destination point starting from arbitrary initial configurations. We impose an additional constraint that the separation between arrival angles of successive team members at the destination be equal. We propose a decentralized algorithm that solves the problem up to a desired level of accuracy in finite time. The communication complexity of the algorithm is quadratic and the space complexity is constant in team size. The proposed algorithm is proved to be correct by establishing some important facts for the shortest path length of a Dubins vehicle as a function of arrival angle at the destination point.