Jeongyong Yang

Generative planners based on Flow Matching (FM) produce high-quality paths in a single 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. In addition, by enforcing safety only on the executed path—rather than all intermediate latent paths—SafeFlowMatcher avoids distributional drift and mitigates local trap problems. Moreover, SafeFlowMatcher attains faster, smoother, and safer paths than diffusion- and FM-based baselines on maze navigation and locomotion. Extensive ablations corroborate the contributions of the PC integrator and the barrier certificate.

Real-time planning among many uncertain, dynamic obstacles is challenging because predicting every agent with high fidelity is both unnecessary and computationally expensive. We present Heterogeneous Predictor-based Risk-Aware Planning (H-PRAP), a framework that allocates prediction effort to where it matters. H-PRAP introduces the Probability-based Collision Risk Index (P-CRI), a closed-form, horizon-level collision index obtained by calibrating a Gaussian surrogate with conformal prediction. P-CRI drives a router that assigns high-risk obstacles to accurate but expensive predictors and low-risk obstacles to lightweight predictors, while preserving distribution-free coverage across heterogeneous predictors through conformal prediction. The selected predictions and their conformal radii are embedded in a chance-constrained model predictive control (MPC) problem, yielding receding-horizon policies with explicit safety margins. We analyze the safety-efficiency trade-off under a prediction compute budget: allocating more to low-fidelity predictions reduces residual risk from dropped obstacles, but at the same time induces larger conformal radii, degrades trajectory efficiency, and shrinks MPC feasibility. Extensive numerical simulations in dense, uncertain environments validate that H-PRAP attains the best balance between trajectory success rate (i.e., no collisions) and time to reach the goal (i.e., trajectory efficiency) compared to single-prediction architectures.