# Real-Time Trajectory Planning for Autonomous Driving with Gaussian Process and Incremental Refinement

arXiv: https://arxiv.org/abs/2205.11853 · HTML: https://mlsanity.com/paper/2205.11853/

## Key facts

- Cited by 14 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 11 of its 22 references that are in the map.
- First posted on arXiv 24 May 2022.

## 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, 11 of 11)

- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Baidu Apollo EM Motion Planner](https://mlsanity.com/paper/1807.08048/) (2018)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [Robust and Efficient Quadrotor Trajectory Generation for Fast Autonomous Flight](https://mlsanity.com/paper/1907.01531/) (2019)
- [Search-based optimal motion planning for automated driving](https://mlsanity.com/paper/1803.04868/) (2018)
- [Model Predictive Contouring Control for Collision Avoidance in Unstructured Dynamic Environments](https://mlsanity.com/paper/2010.10190/) (2020)
- [Safe Trajectory Generation for Complex Urban Environments Using Spatio-temporal Semantic Corridor](https://mlsanity.com/paper/1906.09788/) (2019)
- [Fast UAV Trajectory Optimization using Bilevel Optimization with Analytical Gradients](https://mlsanity.com/paper/1811.10753/) (2018)
- [A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories](https://mlsanity.com/paper/1902.00606/) (2019)
- [TDR-OBCA: A Reliable Planner for Autonomous Driving in Free-Space Environment](https://mlsanity.com/paper/2009.11345/) (2020)
- [Alternating Minimization Based Trajectory Generation for Quadrotor Aggressive Flight](https://mlsanity.com/paper/2002.10629/) (2020)

## Built on by (most cited first, 14 of 14)

- [textitS3Gaussian: Self-Supervised Street Gaussians for Autonomous Driving](https://mlsanity.com/paper/2405.20323/) (2024)
- [DrivingRecon: Large 4D Gaussian Reconstruction Model For Autonomous Driving](https://mlsanity.com/paper/2412.09043/) (2024)
- [Rethinking Imitation-based Planner for Autonomous Driving](https://mlsanity.com/paper/2309.10443/) (2023)
- [MMFN: Multi-Modal-Fusion-Net for End-to-End Driving](https://mlsanity.com/paper/2207.00186/) (2022)
- [Instruct Large Language Models to Drive like Humans](https://mlsanity.com/paper/2406.07296/) (2024)
- [Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes](https://mlsanity.com/paper/2309.12658/) (2023)
- [Towards Deviation-Robust Agent Navigation via Perturbation-Aware Contrastive Learning](https://mlsanity.com/paper/2403.05770/) (2024)
- [B'ezierGS: Dynamic Urban Scene Reconstruction with B'ezier Curve Gaussian Splatting](https://mlsanity.com/paper/2506.22099/) (2025)
- [Street Gaussians without 3D Object Tracker](https://mlsanity.com/paper/2412.05548/) (2024)
- [FlexDrive: Toward Trajectory Flexibility in Driving Scene Reconstruction and Rendering](https://mlsanity.com/paper/2502.21093/) (2025)
- [IR-STP: Enhancing Autonomous Driving with Interaction Reasoning in Spatio-Temporal Planning](https://mlsanity.com/paper/2311.02850/) (2023)
- [Real-Time Joint Simulation of LiDAR Perception and Motion Planning for Automated Driving](https://mlsanity.com/paper/2305.06966/) (2023)
- [A Real-time Spatio-Temporal Trajectory Planner for Autonomous Vehicles with Semantic Graph Optimization](https://mlsanity.com/paper/2502.18151/) (2025)
- [Towards Safe Autonomous Driving: A Real-Time Motion Planning Algorithm on Embedded Hardware](https://mlsanity.com/paper/2601.03904/) (2026)

## Abstract (arXiv)

Real-time kinodynamic trajectory planning in dynamic environments is critical yet challenging for autonomous driving. In this letter, we propose an efficient trajectory planning system for autonomous driving in complex dynamic scenarios through iterative and incremental path-speed optimization. Exploiting the decoupled structure of the planning problem, a path planner based on Gaussian process first generates a continuous arc-length parameterized path in the Fren'et frame, considering static obstacle avoidance and curvature constraints. We theoretically prove that it is a good generalization of the well-known jerk optimal solution. An efficient s-t graph search method is introduced to find a speed profile along the generated path to deal with dynamic environments. Finally, the path and speed are optimized incrementally and iteratively to ensure kinodynamic feasibility. Various simulated scenarios with both static obstacles and dynamic agents verify the effectiveness and robustness of our proposed method. Experimental results show that our method can run at 20 Hz. The source code is released as an open-source package.