Safe Motion Planning against Multimodal Distributions based on a Scenario Approach

TL;DR

This paper introduces a scenario-based motion planning algorithm for autonomous vehicles that efficiently handles multimodal uncertainties, ensuring safety with high confidence while reducing conservativeness and computational load.

Contribution

The paper proposes a novel, computationally efficient scenario approach that clusters multimodal uncertainties and formulates the problem as a mixed-integer program for safe motion planning.

Findings

Ensures high-probability safety in simulations with multimodal uncertainties.

More computationally efficient than traditional scenario methods.

Less conservative, providing practical real-time applicability.

Abstract

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.