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.

翻译：针对由异构车辆组成的多智能体系统，提出了一种确定性计算优化路径的数学建模方法。该模型的核心在于计算每个智能体从已知初始位置到达所有网格点的最短时间。这种到达时间图可通过快速行进法（FMM）轻松获取，该算法最初是为求解Eikonal方程边值问题而设计的。我们证明，利用FMM方法可以唯一确定所有成员车辆的最小时间会合点及路径，且计算量极小。为展示该方法的应用潜力，我们采用虚拟会合场景进行实例验证：协调一艘船舶、一艘水下航行器、一架飞行器与一辆地面车辆，在坦帕湾区域内实现最短时间内的最优位置汇聚。该案例充分验证了所构建框架在高效生成连续路径规划方面的价值，同时兼顾了异构成员车辆的不同运行约束条件。