# Spatio-temporal Motion Planning for Autonomous Vehicles with Trapezoidal Prism Corridors and B'ezier Curves

arXiv: https://arxiv.org/abs/2209.15150 · HTML: https://mlsanity.com/paper/2209.15150/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2022.

## Built on by (most cited first, 2 of 2)

- [SIMPL: A Simple and Efficient Multi-agent Motion Prediction Baseline for Autonomous Driving](https://mlsanity.com/paper/2402.02519/) (2024)
- [A Real-time Spatio-Temporal Trajectory Planner for Autonomous Vehicles with Semantic Graph Optimization](https://mlsanity.com/paper/2502.18151/) (2025)

## Abstract (arXiv)

Safety-guaranteed motion planning is critical for self-driving cars to generate collision-free trajectories. A layered motion planning approach with decoupled path and speed planning is widely used for this purpose. This approach is prone to be suboptimal in the presence of dynamic obstacles. Spatial-temporal approaches deal with path planning and speed planning simultaneously; however, the existing methods only support simple-shaped corridors like cuboids, which restrict the search space for optimization in complex scenarios. We propose to use trapezoidal prism-shaped corridors for optimization, which significantly enlarges the solution space compared to the existing cuboidal corridors-based method. Finally, a piecewise B'ezier curve optimization is conducted in our proposed corridors. This formulation theoretically guarantees the safety of the continuous-time trajectory. We validate the efficiency and effectiveness of the proposed approach in numerical and CommonRoad simulations.