Heuristic Search for Path Finding With Refuelling

Abstract

This letter considers a generalization of the Path Finding (PF) problem with refuelling constraints referred to as the Gas Station Problem (GSP). Similar to PF, given a graph where vertices are gas stations with known fuel prices, and edge costs are the gas consumption between the two vertices, GSPseeks 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 GSPis polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since it requires simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This letter develops a heuristic search algorithm called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{Refuel A}^*$</tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{RF-A}^*$</tex-math></inline-formula>) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic while leveraging dominance rules for pruning during planning. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{RF-A}^*$</tex-math></inline-formula>is guaranteed to find an optimal solution and often runs 2 to 8 times faster than the existing approaches in large city maps with several hundreds of gas stations.