Pulse-and-Glide Driving with Drivability Constraints: A Pontryagin Approach

TL;DR

This paper applies Pontryagin methods to optimize pulse-and-glide driving strategies, revealing how speed, jerk penalties, and nominal velocity influence optimal fuel-efficient driving patterns.

Contribution

It formulates a novel speed trajectory optimization problem incorporating fuel, speed, and jerk, and analyzes the conditions for optimal pulse-and-glide solutions across different speeds.

Findings

Pulse-and-glide is optimal below a jerk penalty threshold.

Infinite switching occurs without jerk penalty.

Steady-speed driving is optimal above a critical velocity.

Abstract

This paper uses Pontryagin methods to analyze pulse-and-glide driving for different nominal vehicle speeds. There is significant literature supporting the fact that pulse-and-glide has the potential to reduce fuel consumption compared to driving at a constant speed, but the benefits at a variety of nominal speeds remain relatively unexplored. Building on the literature, we formulate a speed trajectory optimization problem where the objective is a linearly-scalarized Pareto combination of fuel consumption and average vehicle speed, in addition to a quadratic penalty on jerk. By analyzing this optimization problem using Pontryagin methods, we show that (i) for each nominal speed, there is a critical penalty on jerk below which the optimal solution is pulse-and-glide, (ii) without any penalty on jerk, the optimal pulse-and-glide trajectory switches infinitely fast, and (iii) above a critical nominal velocity, the optimal solution is steady-speed driving rather than pulse-and-glide, regardless of the penalty on jerk.