Trajectory planning for energy-efficient vehicles with communications constraints

A new problem of optimizing a wireless mobile terminal trajectory under a given communication constraint is introduced. The mobile or vehicle has to move from a given starting point to a target point while uploading/downloading a given amount of data; this contrasts with the classical mobile communications paradigm where the communication and motion aspects are assumed to be independent. To reach the two aforementioned objectives, the mobile has to move sufficiently close to the wireless base station, while accounting for the energy cost due to motion. This setup is formalized here and leads us to determining non-trivial trajectories for the mobile. Remarkably, a counterpart of the Snell-Descartes law for the light propagation is exhibited (see Prop. 2) for the optimal trajectory of the mobile when the latter crosses zones in which the available data rates are different.