# Trajectory Planning for Autonomous Driving in Unstructured Scenarios Based on Graph Neural Network and Numerical Optimization

arXiv: https://arxiv.org/abs/2406.08855 · HTML: https://mlsanity.com/paper/2406.08855/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Imitation-learning end-to-end planners, one of 9 directions in End-to-end autonomous driving.
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Placed in

- End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/)

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [TransFuser: Imitation with Transformer-Based Sensor Fusion for Autonomous Driving](https://mlsanity.com/paper/2205.15997/) (2022)
- [Multi-Modal Fusion Transformer for End-to-End Autonomous Driving](https://mlsanity.com/paper/2104.09224/) (2021)
- [Perceive, Predict, and Plan: Safe Motion Planning Through Interpretable Semantic Representations](https://mlsanity.com/paper/2008.05930/) (2020)
- [Learning from All Vehicles](https://mlsanity.com/paper/2203.11934/) (2022)
- [PlanT: Explainable Planning Transformers via Object-Level Representations](https://mlsanity.com/paper/2210.14222/) (2022)
- [Recent Advancements in End-to-End Autonomous Driving using Deep Learning: A Survey](https://mlsanity.com/paper/2307.04370/) (2023)
- [Urban Driving with Conditional Imitation Learning](https://mlsanity.com/paper/1912.00177/) (2019)
- [Learning by Watching](https://mlsanity.com/paper/2106.05966/) (2021)
- [Generative Adversarial Network based Heuristics for Sampling-based Path Planning](https://mlsanity.com/paper/2012.03490/) (2020)

## Built on by (most cited first, 1 of 1)

- [Evidential Uncertainty Probes for Graph Neural Networks](https://mlsanity.com/paper/2503.08097/) (2025)

## Abstract (arXiv)

In unstructured environments, obstacles are diverse and lack lane markings, making trajectory planning for intelligent vehicles a challenging task. Traditional trajectory planning methods typically involve multiple stages, including path planning, speed planning, and trajectory optimization. These methods require the manual design of numerous parameters for each stage, resulting in significant workload and computational burden. While end-to-end trajectory planning methods are simple and efficient, they often fail to ensure that the trajectory meets vehicle dynamics and obstacle avoidance constraints in unstructured scenarios. Therefore, this paper proposes a novel trajectory planning method based on Graph Neural Networks (GNN) and numerical optimization. The proposed method consists of two stages: (1) initial trajectory prediction using the GNN, (2) trajectory optimization using numerical optimization. First, the graph neural network processes the environment information and predicts a rough trajectory, replacing traditional path and speed planning. This predicted trajectory serves as the initial solution for the numerical optimization stage, which optimizes the trajectory to ensure compliance with vehicle dynamics and obstacle avoidance constraints. We conducted simulation experiments to validate the feasibility of the proposed algorithm and compared it with other mainstream planning algorithms. The results demonstrate that the proposed method simplifies the trajectory planning process and significantly improves planning efficiency.