# Trajectory Prediction in Autonomous Driving with a Lane Heading Auxiliary Loss

arXiv: https://arxiv.org/abs/2011.06679 · HTML: https://mlsanity.com/paper/2011.06679/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2020.

## Built on by (most cited first, 30 of 30)

- [LaneAF: Robust Multi-Lane Detection with Affinity Fields](https://mlsanity.com/paper/2103.12040/) (2021)
- [The Integration of Prediction and Planning in Deep Learning Automated Driving Systems: A Review](https://mlsanity.com/paper/2308.05731/) (2023)
- [Towards Explainable, Safe Autonomous Driving with Language Embeddings for Novelty Identification and Active Learning: Framework and Experimental Analysis with Real-World Data Sets](https://mlsanity.com/paper/2402.07320/) (2024)
- [The Why, When, and How to Use Active Learning in Large-Data-Driven 3D Object Detection for Safe Autonomous Driving: An Empirical Exploration](https://mlsanity.com/paper/2401.16634/) (2024)
- [ActiveAnno3D -- An Active Learning Framework for Multi-Modal 3D Object Detection](https://mlsanity.com/paper/2402.03235/) (2024)
- [Language-Driven Active Learning for Diverse Open-Set 3D Object Detection](https://mlsanity.com/paper/2404.12856/) (2024)
- [doScenes: An Autonomous Driving Dataset with Natural Language Instruction for Human Interaction and Vision-Language Navigation](https://mlsanity.com/paper/2412.05893/) (2024)
- [Trajectory Prediction for Autonomous Driving: Progress, Limitations, and Future Directions](https://mlsanity.com/paper/2503.03262/) (2025)
- [On Salience-Sensitive Sign Classification in Autonomous Vehicle Path Planning: Experimental Explorations with a Novel Dataset](https://mlsanity.com/paper/2112.00942/) (2021)
- [Diverse Multiple Trajectory Prediction Using a Two-stage Prediction Network Trained with Lane Loss](https://mlsanity.com/paper/2206.08641/) (2022)
- [Safe Control Transitions: Machine Vision Based Observable Readiness Index and Data-Driven Takeover Time Prediction](https://mlsanity.com/paper/2301.05805/) (2023)
- [Robust Traffic Light Detection Using Salience-Sensitive Loss: Computational Framework and Evaluations](https://mlsanity.com/paper/2305.04516/) (2023)
- [Early Lane Change Prediction for Automated Driving Systems Using Multi-Task Attention-based Convolutional Neural Networks](https://mlsanity.com/paper/2109.10742/) (2021)
- [Pedestrian Behavior Maps for Safety Advisories: CHAMP Framework and Real-World Data Analysis](https://mlsanity.com/paper/2305.04506/) (2023)
- [Can Vision-Language Models Understand and Interpret Dynamic Gestures from Pedestrians? Pilot Datasets and Exploration Towards Instructive Nonverbal Commands for Cooperative Autonomous Vehicles](https://mlsanity.com/paper/2504.10873/) (2025)
- [Multimodal Manoeuvre and Trajectory Prediction for Automated Driving on Highways Using Transformer Networks](https://mlsanity.com/paper/2303.16109/) (2023)
- [PBP: Path-based Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/2309.03750/) (2023)
- [Natural Language Instructions for Scene-Responsive Human-in-the-Loop Motion Planning in Autonomous Driving using Vision-Language-Action Models](https://mlsanity.com/paper/2602.04184/) (2026)
- [ProIn: Learning to Predict Trajectory Based on Progressive Interactions for Autonomous Driving](https://mlsanity.com/paper/2403.16374/) (2024)
- [Risk-aware Trajectory Prediction by Incorporating Spatio-temporal Traffic Interaction Analysis](https://mlsanity.com/paper/2407.10639/) (2024)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [Perception Without Vision for Trajectory Prediction: Ego Vehicle Dynamics as Scene Representation for Efficient Active Learning in Autonomous Driving](https://mlsanity.com/paper/2405.09049/) (2024)
- [Transfer Learning from Simulated to Real Scenes for Monocular 3D Object Detection](https://mlsanity.com/paper/2408.15637/) (2024)
- [FeaXDrive: Feasibility-aware Trajectory-Centric Diffusion Planning for End-to-End Autonomous Driving](https://mlsanity.com/paper/2604.12656/) (2026)
- [Patterns of Vehicle Lights: Addressing Complexities in Curation and Annotation of Camera-Based Vehicle Light Datasets and Metrics](https://mlsanity.com/paper/2307.14521/) (2023)
- [MTR-VP: Towards End-to-End Trajectory Planning through Context-Driven Image Encoding and Multiple Trajectory Prediction](https://mlsanity.com/paper/2511.22181/) (2025)
- [When Stopping Fails: Rethinking Minimal Risk Conditions through Human-Interactive Autonomous Driving for Safe Transportation Systems](https://mlsanity.com/paper/2606.29115/) (2026)
- [What Do They See? Interpreting Complex Road Scenarios Through the Eyes of Vision-Language-Action Models for Safe and Trustworthy Autonomous Vehicle Learning](https://mlsanity.com/paper/2607.16938/) (2026)
- [Planning-Aware Diffusion Networks for Enhanced Motion Forecasting in Autonomous Driving](https://mlsanity.com/paper/2410.19639/) (2024)
- [Measuring What Matters: Scenario-Driven Evaluation for Trajectory Predictors in Autonomous Driving](https://mlsanity.com/paper/2512.12211/) (2025)

## Abstract (arXiv)

Predicting a vehicle's trajectory is an essential ability for autonomous vehicles navigating through complex urban traffic scenes. Bird's-eye-view roadmap information provides valuable information for making trajectory predictions, and while state-of-the-art models extract this information via image convolution, auxiliary loss functions can augment patterns inferred from deep learning by further encoding common knowledge of social and legal driving behaviors. Since human driving behavior is inherently multimodal, models which allow for multimodal output tend to outperform single-prediction models on standard metrics. We propose a loss function which enhances such models by enforcing expected driving rules on all predicted modes. Our contribution to trajectory prediction is twofold; we propose a new metric which addresses failure cases of the off-road rate metric by penalizing trajectories that oppose the ascribed heading (flow direction) of a driving lane, and we show this metric to be differentiable and therefore suitable as an auxiliary loss function. We then use this auxiliary loss to extend the the standard multiple trajectory prediction (MTP) and MultiPath models, achieving improved results on the nuScenes prediction benchmark by predicting trajectories which better conform to the lane-following rules of the road.