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Slope Considered Online Nonlinear Trajectory Planning with Differential Energy Model for Autonomous Driving

Zhaofeng Tian, Lichen Xia, Weisong Shi

TL;DR

The paper addresses energy-efficient trajectory planning for autonomous driving by embedding a differentiable fuel-rate model into online nonlinear trajectory optimization. It combines offline fuel modeling and gear optimization with online NLP-based trajectory planning within an MPC-style framework that accounts for traffic and slope predictions while enforcing hard ACC safety constraints. The approach is evaluated against model-agnostic QP baselines across multiple driving cycles and road profiles, showing notable energy improvements (e.g., up to 7.15% for trucks) with practical online solving times and broad applicability to sedans and heavy vehicles. The work also provides open-source implementations, offering a practical path to integrate energy efficiency into real-time autonomous driving systems.

Abstract

Achieving energy-efficient trajectory planning for autonomous driving remains a challenge due to the limitations of model-agnostic approaches. This study addresses this gap by introducing an online nonlinear programming trajectory optimization framework that integrates a differentiable energy model into autonomous systems. By leveraging traffic and slope profile predictions within a safety-critical framework, the proposed method enhances fuel efficiency for both sedans and diesel trucks by 3.71\% and 7.15\%, respectively, when compared to traditional model-agnostic quadratic programming techniques. These improvements translate to a potential \$6.14 billion economic benefit for the U.S. trucking industry. This work bridges the gap between model-agnostic autonomous driving and model-aware ECO-driving, highlighting a practical pathway for integrating energy efficiency into real-time trajectory planning.

Slope Considered Online Nonlinear Trajectory Planning with Differential Energy Model for Autonomous Driving

TL;DR

The paper addresses energy-efficient trajectory planning for autonomous driving by embedding a differentiable fuel-rate model into online nonlinear trajectory optimization. It combines offline fuel modeling and gear optimization with online NLP-based trajectory planning within an MPC-style framework that accounts for traffic and slope predictions while enforcing hard ACC safety constraints. The approach is evaluated against model-agnostic QP baselines across multiple driving cycles and road profiles, showing notable energy improvements (e.g., up to 7.15% for trucks) with practical online solving times and broad applicability to sedans and heavy vehicles. The work also provides open-source implementations, offering a practical path to integrate energy efficiency into real-time autonomous driving systems.

Abstract

Achieving energy-efficient trajectory planning for autonomous driving remains a challenge due to the limitations of model-agnostic approaches. This study addresses this gap by introducing an online nonlinear programming trajectory optimization framework that integrates a differentiable energy model into autonomous systems. By leveraging traffic and slope profile predictions within a safety-critical framework, the proposed method enhances fuel efficiency for both sedans and diesel trucks by 3.71\% and 7.15\%, respectively, when compared to traditional model-agnostic quadratic programming techniques. These improvements translate to a potential \$6.14 billion economic benefit for the U.S. trucking industry. This work bridges the gap between model-agnostic autonomous driving and model-aware ECO-driving, highlighting a practical pathway for integrating energy efficiency into real-time trajectory planning.

Paper Structure

This paper contains 17 sections, 23 equations, 3 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Offline Fuel Modeling and Gear Optimization
  3. Basic Dynamics
  4. Fuel Rate Modeling
  5. Nonlinear Online Trajectory Optimization
  6. Traffic and Road Profile
  7. Optimization Problem Setup
  8. QP
  9. SQP and NLP
  10. Experiments
  11. Online Trajectory Optimization Framework
  12. Experiment Setup
  13. Results Analysis
  14. Planning-Predction Horizon and Usage of Slope Prediction
  15. Solving Time
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Engine characteristic and fuel efficiency maps of the diesel truck used in this study.
  • Figure 2: Fitted fuel model and optimized gear selection with respect to $u$ and $v$ for the 7-speed truck.
  • Figure 3: Example experiments, in the velocity graph, the leading agent in the blue line represents the standard driving cycle speed profile, and shaded fill-in denotes the elevation of the leading agent w.r.t. time coordinate. Fuel consumption of QP, SQP, and NLP agents are compared by lines in different colors, where NLP agents could achieve lower consumption.