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

2026-03-05

AI Summary

This work addresses the challenge of safe robotic navigation under uncertainties arising from localization errors, prediction inaccuracies of dynamic obstacles, and environmental disturbances. To this end, the authors propose U-OBCA, an uncertainty-aware optimization-based collision avoidance framework. U-OBCA introduces Wasserstein distributionally robust chance constraints into polygonal obstacle avoidance for the first time, eliminating the need for strong assumptions about noise distributions and avoiding conservative circular or elliptical approximations. The probabilistic collision-avoidance constraints are reformulated as deterministic nonlinear constraints that can be solved efficiently. Both theoretical analysis and experiments demonstrate that U-OBCA significantly reduces trajectory conservativeness and enhances navigation efficiency in narrow, complex environments, outperforming existing baseline methods.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Learning & Optimization for ROB
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• uncertainty-aware planning
• collision avoidance
• geometric simplification
• distributional assumptions
• trajectory conservatism

Innovation

• distributionally robust optimization
• chance constraints
• polygonal collision avoidance
• Wasserstein distance
• uncertainty-aware planning