[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84078-en":3,"doc-seo-84078-105":29,"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84078,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","EAGOR Embodied Reasoning in Omni-directional","Omni-directional (360°) cameras support embodied agents with a holistic view, improving directional reasoning for navigation and object search. Existing vision-language approaches often project 360° panoramas to 2D via equirectangular projection, ignoring that the data is intrinsically spherical; this yields direction estimates that become inconsistent under camera/agent motion. EAGOR introduces a training-free, geometry-aware framework using recursive Bayesian estimation on the sphere with a Spherical Harmonic Belief Field, avoiding ERP seams and distortions, and delivering stronger active visual search and navigation performance across benchmarks and a legged robot.","EAGOR: Embodied reAsoninG in Omni-diRection  \nShriram Damodaran 1 , Soumyaratna Debnath 1 , Yan Wu2 , Wei-Yun Yau2 , Lin Wang 1 ∗ 1 EmPACT Lab, NTU Singapore 2 Institute for Infocomm Research, A*STAR Singapore  \narXiv :2607 .06 165v 1 [ cs .RO] 7 Jul 2026  \nFigure 1: EAGOR for geometry-aware embodied omni-directional reasoning (⃝ = Target)  \nAbstract: Omni-directional (360◦ ) cameras enable embodied agents with a wide and holistic view of their surroundings, making them advantageous for directional reasoning in embodied tasks, such as navigation, and object search. Existing Vision Language Models (VLMs) project 360◦ data to 2D planar images via commonly used equirectangular projection (ERP) and process them with architectures designed for perspective images. However, they overlook the fact that 360◦ data is fundamentally spherical, with each pixel encoding a direction relative to the agent’s view. As a result, existing methods often produce direction estimates that are inconsistent under camera view transformation due to agent motion. This becomes critical in map-free navigation, where the agent must continuously update it’s direction to a target in its egocentric frame as it navigates in 360◦ environment. In this paper, we propose EAGOR, a training-free and geometry-aware framework for embodied 360◦ directional reasoning. Our key idea is to reframe the dynamic agent-to-target directional relationship from 360◦ observations as recursive Bayesian estimation on the sphere, rather than as pixel-coordinate prediction in an ERP image. EAGOR therefore maintains a continuous, geometrically correct belief to a target direction on the sphere, and propagating it equivariantly under agent motion, without training the backbone VLMs. To realize this formulation, we introduce a Spherical Harmonic Belief Field (SH-BF), whose spherical harmonic representation provides a globally defined and rotation-aware basis for target direction estimation directly on the spherical manifold. As a result, EAGOR avoids the seam discontinuities, latitude distortions, and interpolation errors caused by the ERP. We evaluate EAGOR on two benchmark datasets and real-world experiments with a legged robot for multiple directional reasoning tasks. EAGOR consistently outperforms the baselines, achieving average relative gains of +34 .4% and +45 .6% on HOS and OSR-Bench, respectively, for active visual search. Notably, EAGOR improves navigation success by +14 .6%, reducing steps counts by 17. 7% and mean angular error by 24.5% .  \n Keywords: Embodied 360◦ Reasoning, Map-Free Navigation, Visual Search  \n∗ Corresponding author: [linwang@ntu.edu.sg](linwang@ntu.edu.sg)  \n1 Introduction  \nDirectional reasoning – the fundamental ability to estimate, track, and update spatial vectors relative to the agent’s own physical posture – is a cornerstone of embodied AI. Just as humans rely on a continuous, multi-sensory awareness of their surroundings to track objectives even when looking away, a physical agent, like robot, must accurately compute the egocentric direction of a target and dynamically maintain it during ego-motion [1, 2, 3] .  \nOmni-directional (360◦ ) cameras capture full surrounding environment with a 180◦ × 360◦ field-ofview (FoV), enabling agents to observe targets, landmarks, and obstacles in all directions [4, 5] . This makes them advantageous for directional reasoning in embodied AI tasks, such as map-free navigation and active visual search. In practice, spherical data is transmitted into 2D planar representations via equirectangular projection (ERP), a.k.a. panorama to preserve omni-directional information. However, ERP introduces seam discontinuities and latitude-dependent distortions, which violate the Euclidean assumptions built into the recent popular Vision-Language Models (VLMs), e.g., [6] . Consequently, it causes spatial relations and direction estimates to be inconsistent due to camera transformations or agent motion [7, 8, 9, 10, 11] .  \nCrucially,","cbCaiuLGuuKDgsx1","https://ap.wps.com/l/cbCaiuLGuuKDgsx1","pdf",14345316,1,12,"English","en",105,"# Abstract\n# Introduction\n## Directional reasoning in embodied AI\n## Limitations of equirectangular projection for 360° geometry\n## Representation requirements for consistent egocentric direction\n## Research question and proposed EAGOR framework","[{\"question\":\"What problem does EAGOR address in omni-directional directional reasoning?\",\"answer\":\"EAGOR targets inconsistency in direction estimates caused by treating spherical 360° observations as planar equirectangular images, which breaks under camera transformations and agent motion. This is especially harmful in map-free navigation where the agent must continuously update an egocentric direction in its frame.\"},{\"question\":\"How does EAGOR represent target direction for omni-directional reasoning?\",\"answer\":\"EAGOR reframes the agent-to-target directional relationship as recursive Bayesian estimation directly on the sphere. It uses a Spherical Harmonic Belief Field to provide a globally defined, rotation-aware basis for estimating target direction on the spherical manifold.\"},{\"question\":\"What benefits does EAGOR claim compared with ERP-based methods?\",\"answer\":\"EAGOR avoids seam discontinuities, latitude distortions, and interpolation errors introduced by equirectangular projection. By maintaining a geometrically correct, continuously propagated belief under agent motion, it improves navigation success and reduces steps and mean angular error.\"}]",1784192571,30,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"eagor-embodied-reasoning-in-omni-directional","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/eagor-embodied-reasoning-in-omni-directional/84078/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does EAGOR address in omni-directional directional reasoning?","Question",{"text":74,"@type":75},"EAGOR targets inconsistency in direction estimates caused by treating spherical 360° observations as planar equirectangular images, which breaks under camera transformations and agent motion. This is especially harmful in map-free navigation where the agent must continuously update an egocentric direction in its frame.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does EAGOR represent target direction for omni-directional reasoning?",{"text":79,"@type":75},"EAGOR reframes the agent-to-target directional relationship as recursive Bayesian estimation directly on the sphere. It uses a Spherical Harmonic Belief Field to provide a globally defined, rotation-aware basis for estimating target direction on the spherical manifold.",{"name":81,"@type":72,"acceptedAnswer":82},"What benefits does EAGOR claim compared with ERP-based methods?",{"text":83,"@type":75},"EAGOR avoids seam discontinuities, latitude distortions, and interpolation errors introduced by equirectangular projection. By maintaining a geometrically correct, continuously propagated belief under agent motion, it improves navigation success and reduces steps and mean angular error.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,121,126,129,133],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":28,"slug":120},"research-report",{"id":122,"doc_module":4,"doc_module_name":45,"category_name":123,"show_sort_weight":124,"slug":125},9,"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":45,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":45,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]