A Sufficient Condition for Convex Hull Property in General Convex Spatio-Temporal Corridors
This addresses a safety and optimality issue in motion planning for autonomous vehicles, offering an incremental improvement over existing methods by supporting more complex corridor shapes.
The paper tackles the problem of ensuring the convex hull property for trajectories in time-dependent safety corridors in autonomous driving, providing a sufficient condition that reduces uncovered search space to O(1/n^2) and improves trajectory smoothness with less harsh braking in simulations.
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 $O(\frac{1}{n^2})$ 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.