# EAGOR: Embodied Reasoning in Omni-direction

arXiv: https://arxiv.org/abs/2607.06165 · HTML: https://mlsanity.com/paper/2607.06165/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 40 of its 50 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 30 of 40)

- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Habitat: A Platform for Embodied AI Research](https://mlsanity.com/paper/1904.01201/) (2019)
- [Vision-and-Language Navigation: Interpreting visually-grounded navigation instructions in real environments](https://mlsanity.com/paper/1711.07280/) (2017)
- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [Habitat-Matterport 3D Dataset (HM3D): 1000 Large-scale 3D Environments for Embodied AI](https://mlsanity.com/paper/2109.08238/) (2021)
- [Beyond the Nav-Graph: Vision-and-Language Navigation in Continuous Environments](https://mlsanity.com/paper/2004.02857/) (2020)
- [Object Goal Navigation using Goal-Oriented Semantic Exploration](https://mlsanity.com/paper/2007.00643/) (2020)
- [Embodied Question Answering](https://mlsanity.com/paper/1711.11543/) (2017)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [VLFM: Vision-Language Frontier Maps for Zero-Shot Semantic Navigation](https://mlsanity.com/paper/2312.03275/) (2023)
- [Uni-NaVid: A Video-based Vision-Language-Action Model for Unifying Embodied Navigation Tasks](https://mlsanity.com/paper/2412.06224/) (2024)
- [Modelling Uncertainty in Deep Learning for Camera Relocalization](https://mlsanity.com/paper/1509.05909/) (2015)
- [GridMM: Grid Memory Map for Vision-and-Language Navigation](https://mlsanity.com/paper/2307.12907/) (2023)
- [Pano-AVQA: Grounded Audio-Visual Question Answering on 360^circ Videos](https://mlsanity.com/paper/2110.05122/) (2021)
- [DREAMWALKER: Mental Planning for Continuous Vision-Language Navigation](https://mlsanity.com/paper/2308.07498/) (2023)
- [Tangent Images for Mitigating Spherical Distortion](https://mlsanity.com/paper/1912.09390/) (2019)
- [Bending Reality: Distortion-aware Transformers for Adapting to Panoramic Semantic Segmentation](https://mlsanity.com/paper/2203.01452/) (2022)
- [ImagineNav: Prompting Vision-Language Models as Embodied Navigator through Scene Imagination](https://mlsanity.com/paper/2410.09874/) (2024)
- [Multimodal Spatial Reasoning in the Large Model Era: A Survey and Benchmarks](https://mlsanity.com/paper/2510.25760/) (2025)
- [DA2: Depth Anything in Any Direction](https://mlsanity.com/paper/2509.26618/) (2025)
- [Are Multimodal Large Language Models Ready for Omnidirectional Spatial Reasoning?](https://mlsanity.com/paper/2505.11907/) (2025)
- [Spatial Reasoning in Multimodal Large Language Models: A Survey of Tasks, Benchmarks and Methods](https://mlsanity.com/paper/2511.15722/) (2025)
- [Learning Spherical Convolution for Fast Features from 360deg Imagery](https://mlsanity.com/paper/1708.00919/) (2017)
- [PanoContext-Former: Panoramic Total Scene Understanding with a Transformer](https://mlsanity.com/paper/2305.12497/) (2023)
- [Visual Question Answering on 360deg Images](https://mlsanity.com/paper/2001.03339/) (2020)
- [Thinking in 360deg: Humanoid Visual Search in the Wild](https://mlsanity.com/paper/2511.20351/) (2025)
- [Post-hoc Probabilistic Vision-Language Models](https://mlsanity.com/paper/2412.06014/) (2024)

## Built on by (most cited first, 3 of 3)

- [AdapToPASS: Ambiguity-aware Adaptive Spherical Transformer for Panoramic Semantic Segmentation](https://mlsanity.com/paper/2608.29081/) (2026)
- [SphMind: Towards Robust, Training-Free VLM-based Spatial Reasoning with a 360 Camera](https://mlsanity.com/paper/2609.33462/) (2026)
- [UniTrackPLA: Unified Panorama-Language-Action Model for Instruction-Guided Navigation and Dynamic Person Tracking](https://mlsanity.com/paper/2610.00878/) (2026)

## Abstract (arXiv)

Omni-directional (360deg) 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 360deg observations to 2D equirectangular projection (ERP) images and process them using architectures designed for perspective images. However, they ignore the spherical nature of 360deg 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 360deg 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%.