{"ID":6023531,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T11:13:51.816948337Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06165","arxiv_id":"2607.06165","title":"EAGOR: Embodied Reasoning in Omni-direction","abstract":"Omni-directional (360°) cameras provide embodied agents with a holistic view of their surroundings, making them suited for directional reasoning in tasks such as navigation and object search. Existing Vision Language Models (VLMs) project 360° observations to 2D equirectangular projection (ERP) images and process them using architectures designed for perspective images. However, they ignore the spherical nature of 360° observations, where each pixel represents a viewing direction relative to the agent. Consequently, their direction estimates often become inconsistent under camera view transformations caused by agent motion. This limitation is particularly critical for map-free navigation, where the agent must continuously estimate the target direction in its egocentric frame. We propose EAGOR, a training-free, geometry-aware framework for embodied 360° directional reasoning. Instead of predicting target directions as ERP image coordinates, EAGOR formulates directional reasoning as recursive Bayesian estimation directly on the sphere. It maintains a continuous belief over target directions and propagates it equivariantly under agent motion without training the backbone VLMs. To achieve this, we introduce the Spherical Harmonic Belief Field (SH-BF), whose spherical harmonic representation provides a globally defined, rotation-aware basis for directional estimation on the spherical manifold. This formulation eliminates ERP seam discontinuities, latitude distortions, and interpolation errors. We evaluate EAGOR on two benchmark datasets and real-world experiments with a legged robot across directional reasoning tasks. EAGOR consistently outperforms existing methods, achieving average relative gains of +34.4% and +45.6% on HOS and OSR-Bench, respectively, while improving navigation success by +14.6%, reducing step count by 17.7%, and lowering mean angular error by 24.5%.","short_abstract":"Omni-directional (360°) cameras provide embodied agents with a holistic view of their surroundings, making them suited for directional reasoning in tasks such as navigation and object search. Existing Vision Language Models (VLMs) project 360° observations to 2D equirectangular projection (ERP) images and process them...","url_abs":"https://arxiv.org/abs/2607.06165","url_pdf":"https://arxiv.org/pdf/2607.06165v1","authors":"[\"Shriram Damodaran\",\"Soumyaratna Debnath\",\"Yan Wu\",\"Wei-Yun Yau\",\"Addison Lin Wang\"]","published":"2026-07-07T11:39:57Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[\"Language Model\"]","has_code":false}