Tight Collision Avoidance for Stochastic Optimal Control: with Applications in Learning-based, Interactive Motion Planning

TL;DR

This paper presents a novel stochastic optimal control framework for collision avoidance in dense traffic, modeling human driver behavior as a Markov Decision Process and reformulating constraints for computational efficiency.

Contribution

It introduces tight, differentiable reformulations of non-convex collision constraints and chance constraints, enabling practical, interactive motion planning in uncertain traffic scenarios.

Findings

Effective collision avoidance in dense traffic scenarios

Simulation results demonstrate improved safety and efficiency

Framework handles non-convex shapes and stochastic human behavior

Abstract

Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints. This paper introduces a stochastic optimal control framework to address these issues simultaneously, without excessively conservative approximations. We opt to model human driver decisions as a Markov Decision Process and propose a method for handling collision avoidance between non-convex vehicle shapes by imposing a positive distance constraint between compact sets. In this framework, we investigate three alternative chance constraint formulations. To ensure computational tractability, we introduce tight, continuously differentiable reformulations of both the non-convex distance constraints and the chance constraints. The efficacy of our approach is demonstrated through simulation studies of two challenging interactive scenarios: an unregulated intersection crossing and a highway lane change in dense traffic.