UniConFlow: A Unified Constrained Flow-Matching Framework for Certified Motion Planning

TL;DR

UniConFlow introduces a unified framework for robot motion planning that effectively incorporates multiple constraints, adapts to various system models, and improves computational efficiency, leading to safer and more feasible trajectories in diverse tasks.

Contribution

It presents UniConFlow, a novel constrained flow matching framework with a prescribed-time guidance function and strategies for efficient long-horizon trajectory generation.

Findings

Outperforms state-of-the-art methods in safety and feasibility metrics.

Successfully applied to diverse tasks including pendulum control, car racing, and manipulation.

Demonstrates improved efficiency and constraint handling in certified motion planning.

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, actuation limits, and dynamic consistency, which are typically addressed individually or heuristically. In this work, we propose UniConFlow, a unified constrained flow matching-based framework for trajectory generation that systematically incorporates both equality and inequality constraints. Moreover, UniConFlow introduces a novel prescribed-time zeroing function that shapes a time-varying guidance field during inference, allowing the generation process to adapt to varying system models and task requirements. Furthermore, to further address the computational challenges of long-horizon and high-dimensional trajectory generation, we propose two practical strategies for the terminal constraint enforcement and inference process: a violation-segment extraction protocol that precisely localizes and refines only the constraint-violating portions of trajectories, and a trajectory compression method that accelerates optimization in a reduced-dimensional space while preserving high-fidelity reconstruction after decoding. Empirical validation across three experiments, including a double inverted pendulum, a real-to-sim car racing task, and a sim-to-real manipulation task, demonstrates that UniConFlow outperforms state-of-the-art generative planners and conventional optimization baselines, achieving superior performance on certified motion planning metrics such as safety, kinodynamic consistency, and action feasibility. Project page is available at: https://uniconflow.github.io.