UniConFlow: A Unified Constrained Generalization Framework for Certified Motion Planning with Flow Matching Models

Abstract: Generative models have become increasingly powerful tools for robot motion generation, enabling flexible and multimodal trajectory generation across various tasks. Yet, most existing approaches remain limited in handling multiple types of constraints, such as collision avoidance and dynamic consistency, which are often treated separately or only partially considered. This paper proposes UniConFlow, a unified flow matching (FM) based framework for trajectory generation that systematically incorporates both equality and inequality constraints. UniConFlow introduces a novel prescribed-time zeroing function to enhance flexibility during the inference process, allowing the model to adapt to varying task requirements. To ensure constraint satisfaction, particularly with respect to obstacle avoidance, admissible action range, and kinodynamic consistency, the guidance inputs to the FM model are derived through a quadratic programming formulation, which enables constraint-aware generation without requiring retraining or auxiliary controllers. We conduct mobile navigation and high-dimensional manipulation tasks, demonstrating improved safety and feasibility compared to state-of-the-art constrained generative planners. Project page is available at https://uniconflow.github.io.