[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85876-en":3,"doc-seo-85876-105":28,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},85876,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","PIER Flow Physics-Informed Efficient Rectified Flow for Real-Time Mobile Robot Navigation","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.","PIER-Flow: Physics-Informed Efficient Rectified Flow for Real-Time  \nMobile Robot Navigation  \nShibo Li, Zhongcheng Wang, Jiahe Cao, Jianhua Yang, and Ke Wu  \narXiv :2607 . 10288v1 [ cs .RO] 11 Jul 2026  \nAbstract—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.  \nIndex Terms—Collision Avoidance, Machine Learning for Robot Control, Reactive Planning, Generative Models, Rectified Flow.  \nI. INTRODUCTION  \nNavigating 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] .  \nManuscript received: Month, Day, Year; Revised: Month, Day, Year; Accepted: Month, Day, Year.  \nShibo 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);  \n[chelde@mail.nwpu.edu.cn](chelde@mail.nwpu.edu.cn); [yangjianhua@nwpu.edu.cn](yangjianhua@nwpu.edu.cn)). *(Corresponding author: Jianhua Yang.)*  \nKe 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)) .  \nDigital Object Identifier (DOI): see top of this page.  \nNevertheless, conventional CBF safety filters can be locally myopic and conservative, potentially causing excessive deceleration, deadlocks, and freezing-like behaviors in cluttered environments [10], [11] .  \nBehavior 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","cbCairGKXs6Ib0U9","https://ap.wps.com/l/cbCairGKXs6Ib0U9","pdf",1156518,1,"English","en",105,"# Introduction\n## Challenges in Dense and Dynamic Navigation\n## Limits of MPC and Barrier-Function Filtering\n## Behavior Cloning and Its Failure Modes\n## Diffusion and Flow-Matching Approaches\n## Motivation for Physics-Aware Rectified Flow","[{\"question\":\"What problem does PIER-Flow address in real-time mobile robot navigation?\",\"answer\":\"It targets safe navigation in dense, dynamic environments while maintaining physically feasible control and low-latency replanning for real-time responsiveness.\"},{\"question\":\"How does PIER-Flow reduce generative inference cost compared with diffusion policies?\",\"answer\":\"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.\"},{\"question\":\"What training and architecture choices help PIER-Flow ensure feasibility and robustness?\",\"answer\":\"It uses a physics-informed training objective to enforce kinematic consistency and an asynchronous action-chunking architecture to support robust sim-to-real deployment.\"}]",1784206872,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":26},"pier-flow-physics-informed-efficient-rectified-flow-for-real-time-mobile-robot-navigation","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/pier-flow-physics-informed-efficient-rectified-flow-for-real-time-mobile-robot-navigation/85876/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What 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