Tight Collision Avoidance for Stochastic Optimal Control: with Applications in Learning-based, Interactive Motion Planning
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912676054040576 |
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| author | Börve, Erik Murgovski, Nikolce Laine, Leo |
| author_facet | Börve, Erik Murgovski, Nikolce Laine, Leo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tight Collision Avoidance for Stochastic Optimal Control: with Applications in Learning-based, Interactive Motion Planning Börve, Erik Murgovski, Nikolce Laine, Leo Systems and Control 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. |
| title | Tight Collision Avoidance for Stochastic Optimal Control: with Applications in Learning-based, Interactive Motion Planning |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2510.25324 |