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

arXiv: https://arxiv.org/abs/2510.25324 · HTML: https://mlsanity.com/paper/2510.25324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2025.

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

- [Interactive Trajectory Planning with Learning-based Distributionally Robust Model Predictive Control and Markov Systems](https://mlsanity.com/paper/2605.07768/) (2026)

## Abstract (arXiv)

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.