[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83532-en":3,"doc-seo-83532-105":30,"detail-sidebar-cat-0-en-105":84},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83532,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","From Prediction Uncertainty to Conformalized Distance Fields for Safe Motion Planning","Safe motion planning in dynamic environments requires handling uncertainty in predicted obstacle motion while preserving real-time performance. Existing conformal methods conformalize scalar aggregation scores, weakening spatial coherence and increasing computational burden as scene density grows. The proposed framework conformalizes the full predicted distance field, producing a distribution-free field-level lower bound with uniform safety certification. It leverages an empirically low-rank, approximately time-invariant residual field, enabling offline envelope fitting and efficient online adaptive updates. Integrated into a sampling-based MPC yields strong safety, feasibility, and efficiency on ETH–UCY and dense 3D quadrotor benchmarks.","arXiv :2607 .00776v 1 [ cs .RO] 1 Jul 2026  \nFrom Prediction Uncertainty to Conformalized Distance Fields for Safe Motion Planning ∗  \nJaeuk Shin, Yoonseok Ra, and Insoon Yang †‡  \nAbstract  \nSafe motion planning in dynamic environments requires reasoning about the uncertainty in predicted obstacle motion without sacrificing real-time performance. Existing conformal approaches conformalize a scalar score that aggregates per-obstacle prediction errors, losing spatial coherence and scaling poorly with scene density. We instead conformalize the entire predicted distance field at once. This functional conformal prediction (FCP) framework yields a distribution-free, field-level lower bound, from which safety follows uniformly: any trajectory satisfying the resulting constraint is certified safe, independent of how the control space is sampled. The key enabler is that the residual distance field is empirically low-rank and approximately time-invariant, which makes the bound decomposable in coefficient space. An envelope is fitted offline via functional PCA and a Gaussian-mixture inductive conformal procedure, then refined online by a lightweight adaptive functional conformal (AFCP) update on a low-dimensional vector. This keeps the per-step cost largely insensitive to obstacle count and retains long-run field coverage under distribution shift. We embed the envelope as a tightened safety constraint in a sampling-based model predictive controller, FCP-MPC. On the ETH– UCY pedestrian benchmarks and a dense 3D quadrotor task with up to 280 dynamic obstacles, FCP-MPC attains a favorable balance of safety, feasibility, and efficiency, reaching goals where pointwise and egocentric conformal baselines become too conservative or too expensive, while keeping per-step computation far below online uncertainty-reasoning baselines.  \n1 Introduction  \nAutonomous robots are increasingly asked to operate in environments shared with pedestrians, vehicles, and other moving agents, where safe behavior depends on anticipating how the surrounding world will evolve. The future occupancy of such an environment is unobservable at planning time, so it must be forecast from past observations, and any motion planner that consumes these forecasts inherits their errors. The central difficulty is therefore not prediction or planning in isolation but the coupling of the two: a controller must account for the uncertainty in predicted obstacle motion tightly enough to remain safe, yet cheaply enough to close the loop in real time and in densely populated scenes. Achieving both at once, with quantitative safety guarantees, is the problem we address.  \n∗ This work was supported in part by the Information and Communications Technology Planning and Evaluation (IITP) grants funded by MSIT No. 2022-0-00124, No. 2022-0-00480 and No. RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University), and the National Research Foundation of Korea (NRF) grant funded by MSIT No. RS-2026-25477173 .  \n†The first two authors contributed equally to this work.  \n‡All authors are with the Department of Electrical and Computer Engineering, ASRI, Seoul National University, Seoul 08826, South Korea, {sju5379, rys522, [insoonyang](insoonyang}@snu.ac.kr)[}](insoonyang}@snu.ac.kr)[@snu.ac.kr](insoonyang}@snu.ac.kr)  \nA large body of work embeds prediction uncertainty directly into the planning objective or constraints. Chance-constrained formulations bound the probability of collision [1], and risksensitive and distributionally robust planners hedge against tail events or worst-case obstacle distributions [2, 3, 4] . These methods deliver strong guarantees, but at a price. They typically require committing to an ambiguity set or a parametric/moment-based description of the prediction error, and the associated worst-case optimization is solved online, which grows costly as scene density rises. Conformal prediction (CP) [5, 6, 7] offers a complementary, distributi","cbCaiseM2lVkczSq","https://ap.wps.com/l/cbCaiseM2lVkczSq","pdf",5283113,5,1,38,"English","en",105,"# Introduction\n## Motivation: coupling prediction and planning under uncertainty\n## Existing approaches and their limitations\n## Representational insight: low-rank, time-invariant residual distance fields\n## Proposed method: functional conformal prediction over the distance field\n## Integration into FCP-MPC and experimental results","[{\"question\":\"Why is the approach computationally efficient online?\",\"answer\":\"It relies on the empirical structure that the residual distance field is low-rank and approximately time-invariant. This enables a decomposable certificate in coefficient space, with an offline envelope fit and a lightweight online adaptive functional conformal update on a low-dimensional vector.\"}]",1784188662,96,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":28},"from-prediction-uncertainty-to-conformalized-distance-fields-for-safe-motion-planning","",{"@graph":36,"@context":78},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/from-prediction-uncertainty-to-conformalized-distance-fields-for-safe-motion-planning/83532/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"Why is the approach computationally efficient online?","Question",{"text":76,"@type":77},"It relies on the empirical structure that the residual distance field is low-rank and approximately time-invariant. This enables a decomposable certificate in coefficient space, with an offline envelope fit and a lightweight online adaptive functional conformal update on a low-dimensional vector.","Answer","https://schema.org",{"og:url":52,"og:type":80,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":82,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":85},[86,90,94,98,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":87,"show_sort_weight":88,"slug":89},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":91,"show_sort_weight":92,"slug":93},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":20,"slug":130},19,"General","general"]