Optimal Path Planning for a Convoy-Support Vehicle Pair Through a Repairable Network

In this article, we consider a multi-agent path planning problem in a partially impeded environment. The impeded environment is represented by a graph with select road segments (edges) in disrepair impeding vehicular movement in the road network. A primary vehicle, which we refer to as a convoy, wishes to travel from a starting location to a destination while minimizing some accumulated cost. The convoy may traverse an impeded edge for an additional cost (associated with repairing the edge) than if it were unimpeded. A support vehicle, which we refer to as a service vehicle, is simultaneously deployed to assist the convoy by repairing edges, reducing the cost for the convoy to traverse those edges. The convoy is permitted to wait at any vertex to allow the service vehicle to complete repairing an edge. The service vehicle is permitted to terminate its path at any vertex. The goal is then to find a pair of paths so the convoy reaches its destination while minimizing the total time (cost) the two vehicles are active, including any time the convoy waits. We refer to this problem as the Assisted Shortest Path Problem (ASPP). We present a generalized permanent labeling algorithm (GPLA) to find an optimal solution for the ASPP. We also introduce additional modifications to the labeling algorithm to significantly improve the computation time and refer to the modified labeling algorithm as GPLA*. Computational results are presented to illustrate the effectiveness of GPLA* in solving the ASPP. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —One motivation for this work is to improve the efficiency of autonomous warehouse operations, where multiple robots need to coordinate their plans. Take for example two robots operating in a warehouse where one robot is moving goods and the second robot is making repairs or clearing obstructions (fallen goods, objects left by workers, etc.) along the way. The presented algorithm’s underlying structure is relatively simple and the algorithm itself does not require special software or solvers. The algorithm generates sub-optimal solutions as it progresses and terminates with the optimal solution. A large class of problems involving asynchronous actions between two or more agents can be handled using the presented algorithm or an extension of it. In this paper we restrict ourselves to two agents. A limitation of the presented algorithm and its possible extensions is the memory required as the graph representing the problem grows in size. We compare our work against an algorithm with similar approach (centralized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A^*$</tex-math> </inline-formula> ) and show that the presented algorithm is superior in both memory and computational time. We also present results on relatively large graphs to show the algorithm has practical value. This work can also be applied to rescue missions for people to escape wildfires, flooding or other natural disasters. A robotic agent can scout ahead for impacted pathways and assist victim(s) find the best path to escape to safety.