Minimum time rendezvous for multi-vehicle with non-identical velocity constraints

Abstract

We solve the minimum time rendezvous problem for Dubins' vehicles with non-identical velocity constraint in this paper. To solve this problem, the vehicle's determining region is proposed through Apollonius circles, which provides a planar partition method. According to the partition, we show that the minimum time rendezvous point (MTRP) uniquely exists and locates on the boundary of some vehicle's determining region. Moreover, the minimum time rendezvous point for any number of vehicles is determined by only either two or three vehicles among them. Based on the theory, our algorithm mainly concentrates on the search for those critical two or three vehicles avoiding global searching. The simulation results are worked out to verify the correctness of the theory and illustrate the effectiveness of the algorithm.