EAGOR: Embodied Reasoning in Omni-direction

• URL: http://arxiv.org/abs/2607.06165v1
• Date: Tue, 07 Jul 2026 11:39:57 GMT
• Title: EAGOR: Embodied Reasoning in Omni-direction
• Abstract summary: We propose EAGOR, a training-free, geometry-aware framework for embodied 360 directional reasoning.<n>EAGOR consistently outperforms existing methods, achieving average relative gains of +34.4% and +45.6% on benchmark datasets.
• Score: 3.042262674701172
• License: http://creativecommons.org/licenses/by/4.0/
• 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%.

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