Speed planning by minimizing travel time and energy consumption

This is the authors' abstract. We don't add key points for this paper.

In this paper we address the speed planning problem for a vehicle over an assigned path with the aim of minimizing a weighted sum of travel time and energy consumption under suitable constraints (maximum allowed speed, maximum traction or braking force, maximum power consumption). The resulting mathematical model is a non-convex optimization problem. We prove that, under some mild assumptions, a convex reformulation of the non-convex problem is exact. In particular, the convex reformulation is a Second Order Cone Programming (SOCP) problem, for which efficient solvers exist. Through the numerical experiments we confirm that the convex relaxation can be solved very efficiently and, moreover, we also provide the Pareto front of the trade-off between the two objectives (travel time and energy consumption). • Nonconvex model for a speed planning problem minimizing two conflicting objectives: travel time and fuel consumption. • Convex relaxation of the nonconvex model proved to be exact under mild conditions. • Counterexample showing that exactness does not hold if the proposed conditions are not met. • Computational experiments with a focus on the Pareto front of the two objective functions for ICE and electric vehicles.