  The purpose of this work is to introduce and characterize the Bounded
Acceleration Shortest Path (BASP) problem, a generalization of the Shortest
Path (SP) problem. This problem is associated to a graph: the nodes represent
positions of a mobile vehicle and the arcs are associated to pre-assigned
geometric paths that connect these positions. BASP consists in finding the
minimum-time path between two nodes. Differently from SP, we require that the
vehicle satisfy bounds on maximum and minimum acceleration and speed, that
depend on the vehicle position on the currently traveled arc. We prove that
BASP is NP-hard and define solution algorithm that achieves polynomial
time-complexity under some additional hypotheses on problem data.
