U-OBCA: Uncertainty-Aware Optimization-Based Collision Avoidance via Wasserstein Distributionally Robust Chance Constraints

TL;DR

This paper introduces U-OBCA, a novel optimization-based collision avoidance method that explicitly handles uncertainties with Wasserstein distributionally robust chance constraints, improving navigation safety and efficiency in cluttered environments.

Contribution

The paper extends OBCA to explicitly incorporate polygon-shaped robot and obstacle uncertainties using Wasserstein distributionally robust chance constraints, reducing conservatism and enhancing navigation performance.

Findings

U-OBCA reduces conservatism compared to traditional methods.

The approach achieves higher navigation efficiency in narrow environments.

Validated through simulations and real-world experiments.

Abstract

Uncertainties arising from localization error, trajectory prediction errors of the moving obstacles and environmental disturbances pose significant challenges to robot's safe navigation. Existing uncertainty-aware planners often approximate polygon-shaped robots and obstacles using simple geometric primitives such as circles or ellipses. Though computationally convenient, these approximations substantially shrink the feasible space, leading to overly conservative trajectories and even planning failure in narrow environments. In addition, many such methods rely on specific assumptions about noise distributions, which may not hold in practice and thus limit their performance guarantees. To address these limitations, we extend the Optimization-Based Collision Avoidance (OBCA) framework to an uncertainty-aware formulation, termed \emph{U-OBCA}. The proposed method explicitly accounts for the collision risk between polygon-shaped robots and obstacles by formulating OBCA-based chance constraints, and hence avoiding geometric simplifications and reducing unnecessary conservatism. These probabilistic constraints are further tightened into deterministic nonlinear constraints under mild distributional assumptions, which can be solved efficiently by standard numerical optimization solvers. The proposed approach is validated through theoretical analysis, numerical simulations and real-world experiments. The results demonstrate that U-OBCA significantly mitigates the conservatism in trajectory planning and achieves higher navigation efficiency compared to existing baseline methods, particularly in narrow and cluttered environments.