  A formulation is developed for deterministically calculating the optimized
paths for a multi-agent system consisting of heterogeneous vehicles. The
essence of this formulation is the calculation of the shortest time for each
agent to reach every grid point from its known initial position. Such arrival
time map can be readily assessed using the Fast Marching Method (FMM), a
computational algorithm originally designed for solving boundary value problems
of the Eikonal equation. Leveraging the FMM method, we demonstrate that the
minimal time rendezvous point and paths for all member vehicles can be uniquely
determined with minimal computational concerns. To showcase the potential of
our method, we use an example of a virtual rendezvous scenario that entails the
coordination of a ship, an underwater vehicle, an aerial vehicle, and a ground
vehicle to converge at the optimal location within the Tampa Bay area in
minimal time. It illustrates the value of the developed framework in
efficiently constructing continuous path planning, while accommodating
different operational constraints of heterogeneous member vehicles.
