This paper considers a generalization of the Path Finding (PF) with refueling constraints referred to as the Refuelling Path Finding (RF-PF) problem. Just like PF, the RF-PF problem is defined over a graph, where vertices are gas stations with known fuel prices, and edge costs depend on the gas consumption between the corresponding vertices. RF-PF seeks a minimum-cost path from the start to the goal vertex for a robot with a limited gas tank and a limited number of refuelling stops. While RF-PF is polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since the robot needs to simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This paper develops a heuristic search algorithm called Refuel A* (RF-A* ) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic function while leveraging dominance rules for state pruning during planning. RF-A* is guaranteed to find an optimal solution and runs more than an order of magnitude faster than the existing state of the art (a polynomial time algorithm) when tested in large city maps with hundreds of gas stations.

翻译：本文考虑了一种具有加油约束的路径搜索（PF）推广问题，称为加油路径搜索（RF-PF）问题。与PF问题类似，RF-PF问题在图结构上定义，其中顶点代表已知燃油价格的加油站，边成本取决于对应顶点间的燃油消耗量。RF-PF问题旨在为具有有限油箱容量和有限停车加油次数的机器人，寻找从起点到目标顶点的最小成本路径。尽管RF-PF问题可以在多项式时间内求解，但在实际中快速计算最优解仍具挑战性，因为机器人需要同时确定路径、停车位置以及每次停车加油量。本文提出了一种名为Refuel A*（RF-A*）的启发式搜索算法，该算法在规划过程中利用启发函数指导从起点到目标点的部分解路径迭代构建，同时借助支配规则进行状态剪枝。RF-A*保证找到最优解，并且在包含数百个加油站的大型城市地图测试中，其运行速度比现有最先进的算法（多项式时间算法）快一个数量级以上。