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SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions

Jeongyong Yang, Seunghwan Jang, SooJean Han

TL;DR

SafeFlowMatcher is presented, a planning framework that couples FM with control barrier functions (CBFs) to achieve both real-time efficiency and certified safety, and proves a barrier certificate for the resulting flow system.

Abstract

Generative planners based on flow matching (FM) can produce high-quality paths in one or a few ODE steps, but their sampling dynamics offer no formal safety guarantees and can yield incomplete paths near constraints. We present SafeFlowMatcher, a planning framework that couples FM with control barrier functions (CBFs) to achieve both real-time efficiency and certified safety. SafeFlowMatcher uses a two-phase prediction-correction (PC) integrator: (i) a prediction phase integrates the learned FM once (or a few steps) to obtain a candidate path without intervention; (ii) a correction phase refines this path with a vanishing time-scaled vector field and a CBF-based quadratic program that minimally perturbs the vector field. We prove a barrier certificate for the resulting flow system, establishing forward invariance of a robust safe set and finite-time convergence to the safe set. By enforcing safety only on the executed path (rather than on all intermediate latent paths), SafeFlowMatcher avoids distributional drift and mitigates local trap problems. Across maze navigation and locomotion benchmarks, SafeFlowMatcher attains faster, smoother, and safer paths than diffusion- and FM-based baselines. Extensive ablations corroborate the contributions of the PC integrator and the barrier certificate.

SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions

TL;DR

SafeFlowMatcher is presented, a planning framework that couples FM with control barrier functions (CBFs) to achieve both real-time efficiency and certified safety, and proves a barrier certificate for the resulting flow system.

Abstract

Generative planners based on flow matching (FM) can produce high-quality paths in one or a few ODE steps, but their sampling dynamics offer no formal safety guarantees and can yield incomplete paths near constraints. We present SafeFlowMatcher, a planning framework that couples FM with control barrier functions (CBFs) to achieve both real-time efficiency and certified safety. SafeFlowMatcher uses a two-phase prediction-correction (PC) integrator: (i) a prediction phase integrates the learned FM once (or a few steps) to obtain a candidate path without intervention; (ii) a correction phase refines this path with a vanishing time-scaled vector field and a CBF-based quadratic program that minimally perturbs the vector field. We prove a barrier certificate for the resulting flow system, establishing forward invariance of a robust safe set and finite-time convergence to the safe set. By enforcing safety only on the executed path (rather than on all intermediate latent paths), SafeFlowMatcher avoids distributional drift and mitigates local trap problems. Across maze navigation and locomotion benchmarks, SafeFlowMatcher attains faster, smoother, and safer paths than diffusion- and FM-based baselines. Extensive ablations corroborate the contributions of the PC integrator and the barrier certificate.

Paper Structure

This paper contains 8 sections, 5 theorems, 16 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work & Preliminaries
  3. FlowMatcher: Flow Matching for Planning
  4. Control Barrier Functions
  5. SafeFlowMatcher
  6. Prediction-Correction Integrator
  7. Control Barrier Certificate for SafeFlowMatcher
  8. Conclusion

Key Result

Lemma 1

Define CBF $b$ as in Definition def:finite_time_cbf, such that the initial state satisfies $b({\bf x}_0) \geq 0$. Any Lipschitz continuous controller ${\bf u}_t$ that satisfies condition (eq:finite_time_cbf) ensures forward invariance of the safe set $\mathcal{C}$, i.e., $b({\bf x}_t) \geq 0$ for al

Figures (2)

  • Figure 1: Directly constraining intermediate samples during generation (top) can cause paths to be distorted or trapped, whereas SafeFlowMatcher (bottom) decouples generation and certification, producing a complete and certified-safe path.
  • Figure 2: Example of a local trap in maze environment.

Theorems & Definitions (9)

  • Definition 1: Finite-Time Convergence CBF
  • Lemma 1: Forward Invariance of the Safe Set
  • Definition 2: Local Trap
  • Lemma 2
  • Lemma 3
  • Definition 3: Finite-Time Flow Invariance
  • Theorem 1: Forward Invariance for SafeFlowMatcher
  • Proposition 1: Finite Convergence Time for SafeFlowMatcher
  • Remark 1