Solution Algorithms for the Bounded Acceleration Shortest Path Problem

The purpose of this article is to introduce and characterize the bounded acceleration shortest path problem (BASP), a generalization of the shortest path problem (SP). This problem is associated to a graph: nodes represent positions of a mobile vehicle and arcs are associated to preassigned geometric paths that connect these positions. The BASP consists in finding the minimum-time path between two nodes. Differently from the SP, the vehicle has to satisfy bounds on maximum and minimum acceleration and speed, which depend on the vehicle's position on the currently traveled arc. Even if the BASP is NP-hard in the general case, we present a solution algorithm that achieves polynomial time-complexity under some additional hypotheses on problem data.