PIER Flow Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation

Jul 16, 2026

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Autonomous navigation in dense, highly dynamic environments demands physically feasible control and low-latency replanning. Model Predictive Control (MPC) handles kinematics and safety constraints but can be too expensive for real-time use, while behavior cloning is efficient yet limited in multimodal avoidance and diffusion methods are multimodal but slow. PIER-Flow (Physics-Informed Efficient Rectified Flow) distills an MPC expert into a continuous-time ODE to enable single-step action generation. Physics-informed training enforces kinematic consistency and an asynchronous action-chunking design supports sim-to-real transfer. Simulations show a 98.85% success rate with zero collisions, ~1.29 ms inference, and major acceleration versus MPC and diffusion baselines, with stable edge deployment at ~5.3 ms.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

Introduction

Challenges in Dense and Dynamic Navigation

Limits of MPC and Barrier-Function Filtering

Behavior Cloning and Its Failure Modes

Diffusion and Flow-Matching Approaches

Motivation for Physics-Aware Rectified Flow

PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation Shibo Li, Zhongcheng Wang, Jiahe Cao, Jianhua Yang, and Ke Wu arXiv :2607 . 10288v1 [ cs .RO] 11 Jul 2026 Abstract—Autonomous navigation in dense and highly dynamic environments requires both physically feasible control and lowlatency replanning. Optimization-based methods such as Model Predictive Control (MPC) explicitly handle robot kinematics and safety constraints, but repeated nonlinear optimization can limit real-time responsiveness. Deterministic behavior-cloning policies enable efficient inference but may fail to represent multimodal avoidance behaviors, whereas diffusion policies capture multimodality at the cost of time-consuming iterative denoising. We propose PIER-Flow (Physics-Informed Efficient Rectified Flow), a lightweight navigation policy for mobile robots. By distilling an MPC expert into a continuous-time Ordinary Differential Equation (ODE), PIER-Flow achieves single-step action generation through parallel latent sampling and lightweight feasibility selection. We introduce a physics-informed training objective to enforce kinematic consistency, paired with an asynchronous action chunking architecture for robust sim-to-real deployment. Extensive simulations demonstrate that PIER-Flow achieves a 98.85% success rate and zero collisions, with an average inference of ∼1.29 ms, which accelerates planning by 37.2× compared to MPC and over 800× against standard diffusion models. Crucially, real-world deployment on a resource-constrained edge computer further achieves an approximately stable inference latency of ∼5.3 ms, avoiding the latency spikes and freezing events observed with planning baselines. Index Terms—Collision Avoidance, Machine Learning for Robot Control, Reactive Planning, Generative Models, Rectified Flow. I. INTRODUCTION Navigating a mobile robot safely through dense and dynamic environments remains a fundamental challenge in robotics [1]–[3] . Model Predictive Control (MPC) addresses this problem by optimizing a finite-horizon trajectory subject to robot kinematics and collision constraints, providing valuable look-ahead capability in complex interactions [4]–[6] . However, repeatedly solving a nonlinear program becomes increasingly expensive as the prediction horizon and obstacle count grow, while sensitivity to initialization may introduce variable convergence time and delayed control [7] . Control Barrier Function (CBF) quadratic programs provide a computationally lighter alternative by minimally modifying a nominal command to enforce forward-invariance conditions [8], [9] . Manuscript received: Month, Day, Year; Revised: Month, Day, Year; Accepted: Month, Day, Year. Shibo Li, Zhongcheng Wang, Jiahe Cao, and Jianhua Yang are with the School of Automation, Northwestern Polytechnical University, Xi’an, China (e-mail: [lishibo97@mail.nwpu.edu.cn](lishibo97@mail.nwpu.edu.cn); [wangzhongcheng@mail.nwpu.edu.cn](wangzhongcheng@mail.nwpu.edu.cn); [chelde@mail.nwpu.edu.cn](chelde@mail.nwpu.edu.cn); [yangjianhua@nwpu.edu.cn](yangjianhua@nwpu.edu.cn)). *(Corresponding author: Jianhua Yang.)* Ke Wu is with the Department of Robotics, Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi SE45 05, United Arab Emirates (e-mail: [ke.wu@mbzuai.ac.ae](ke.wu@mbzuai.ac.ae)) . Digital Object Identifier (DOI): see top of this page. Nevertheless, conventional CBF safety filters can be locally myopic and conservative, potentially causing excessive deceleration, deadlocks, and freezing-like behaviors in cluttered environments [10], [11] . Behavior Cloning (BC) provides an efficient alternative by learning a direct observation-to-action policy from expert demonstrations through supervised learning [12], [13] . Action-sequence prediction and action chunking further improve temporal consistency and reduce error accumulation [14] . However, explicit BC policies trained with pointwise regression

FAQs

What problem does PIER-Flow address in real-time mobile robot navigation?

It targets safe navigation in dense, dynamic environments while maintaining physically feasible control and low-latency replanning for real-time responsiveness.

How does PIER-Flow reduce generative inference cost compared with diffusion policies?

It distills an MPC expert into a continuous-time ODE based on rectified flow, enabling single-step action generation through parallel latent sampling and lightweight feasibility selection rather than iterative denoising.

What training and architecture choices help PIER-Flow ensure feasibility and robustness?

It uses a physics-informed training objective to enforce kinematic consistency and an asynchronous action-chunking architecture to support robust sim-to-real deployment.

Jul 16, 2026

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