# Safe Motion Planning against Multimodal Distributions based on a Scenario Approach

arXiv: https://arxiv.org/abs/2108.02753 · HTML: https://mlsanity.com/paper/2108.02753/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2021.

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

- [MMD-OPT : Maximum Mean Discrepancy Based Sample Efficient Collision Risk Minimization for Autonomous Driving](https://mlsanity.com/paper/2412.09121/) (2024)

## Abstract (arXiv)

We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicles reflect discrete decisions, such as turning or going straight at intersections. We develop a computationally efficient, scenario-based approach that solves the motion planning problem with high confidence given a quantifiable number of samples from the multimodal distribution. Our approach is based on two preprocessing steps, which 1) separate the samples into distinct clusters and 2) compute a bounding polytope for each cluster. Then, we rewrite the motion planning problem approximately as a mixed-integer problem using the polytopes. We demonstrate via simulation on the nuScenes dataset that our approach ensures safety with high probability in the presence of multimodal uncertainties, and is computationally more efficient and less conservative than a conventional scenario approach.