Fast Marching Based Rendezvous Path Planning for a Team of Heterogeneous Vehicles

This paper presents a formulation for deterministically calculating optimized paths for a multi-agent system consisting of heterogeneous vehicles. The key idea is the calculation of the shortest time for each agent to reach every grid point from its known initial position. Such arrival time map is efficiently computed using the Fast Marching Method (FMM), a computational algorithm originally designed for solving boundary value problems of the Eikonal equation. By leveraging the FMM, we demonstrate that the minimal time rendezvous point and paths for all member vehicles can be uniquely determined with minimal computational overhead. The scalability and adaptability of the present method during online execution are investigated, followed by a comparison with a baseline method that highlights the effectiveness of the proposed approach. Then, the potential of the present method is showcased through a virtual rendezvous scenario involving the coordination of a ship, an underwater vehicle, an aerial vehicle, and a ground vehicle, all converging at the optimal location within the Tampa Bay area in minimal time. The results show that the developed framework can efficiently construct continuous paths of heterogeneous vehicles by accommodating operational constraints via an FMM algorithm.