Speed planning by minimizing travel time and energy consumption

TL;DR

This paper presents a convex reformulation of a non-convex speed planning problem that minimizes travel time and energy consumption, enabling efficient solutions and Pareto front analysis.

Contribution

It introduces an exact convex reformulation of a complex non-convex optimization problem as an SOCP, facilitating efficient computation and trade-off analysis.

Findings

Convex reformulation is exact under mild assumptions.

Efficient solution of the reformulated problem using SOCP solvers.

Provides Pareto front for travel time and energy consumption trade-off.

Abstract

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).