# A Sufficient Condition for Convex Hull Property in General Convex Spatio-Temporal Corridors

arXiv: https://arxiv.org/abs/2110.00065 · HTML: https://mlsanity.com/paper/2110.00065/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2021.

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

- [Validity Learning on Failures: Mitigating the Distribution Shift in Autonomous Vehicle Planning](https://mlsanity.com/paper/2406.01544/) (2024)
- [A Real-time Spatio-Temporal Trajectory Planner for Autonomous Vehicles with Semantic Graph Optimization](https://mlsanity.com/paper/2502.18151/) (2025)

## Abstract (arXiv)

Motion planning is one of the key modules in autonomous driving systems to generate trajectories for self-driving vehicles to follow. A common motion planning approach is to generate trajectories within semantic safe corridors. The trajectories are generated by optimizing parametric curves (e.g. Bezier curves) according to an objective function. To guarantee safety, the curves are required to satisfy the convex hull property, and be contained within the safety corridors. The convex hull property however does not necessary hold for time-dependent corridors, and depends on the shape of corridors. The existing approaches only support simple shape corridors, which is restrictive in real-world, complex scenarios. In this paper, we provide a sufficient condition for general convex, spatio-temporal corridors with theoretical proof of guaranteed convex hull property. The theorem allows for using more complicated shapes to generate spatio-temporal corridors and minimizing the uncovered search space to O(frac1n2) compared to O(1) of trapezoidal corridors, which can improve the optimality of the solution. Simulation results show that using general convex corridors yields less harsh brakes, hence improving the overall smoothness of the resulting trajectories.