Hidden convexity property of a speed planning problem

In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the problem, we introduce a convex relaxation of the model and show that, after the application of a suitable feasibility-based bound tightening procedure, the convex relaxation shares the same optimal value and solution of the non-convex problem. We also establish that the feasible region of the non-convex problem is a lattice and, through that, a necessary and sufficient condition for the non-emptiness of the feasible region.