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%.
Recent advancements in Large Language Models (LLMs) and Vision-Language Models (VLMs) have made them powerful tools in embodied navigation, enabling agents to leverage commonsense and spatial reasoning for efficient exploration in unfamiliar environments. Existing LLM-based approaches convert global memory, such as semantic or topological maps, into language descriptions to guide navigation. While this improves efficiency and reduces redundant exploration, the loss of geometric information in language-based representations hinders spatial reasoning, especially in intricate environments. To address this, VLM-based approaches directly process ego-centric visual inputs to select optimal directions for exploration. However, relying solely on a first-person perspective makes navigation a partially observed decision-making problem, leading to suboptimal decisions in complex environments. In this paper, we present a novel vision-language model (VLM)-based navigation framework that addresses these challenges by adaptively retrieving task-relevant cues from a global memory module and integrating them with the agent's egocentric observations. By dynamically aligning global contextual information with local perception, our approach enhances spatial reasoning and decision-making in long-horizon tasks. The proposed method surpasses previous state-of-the-art approaches by a significant margin on both the HSSD and HM3D benchmarks and demonstrates strong performance on a real robot.
City-scale outdoor navigation is currently hindered by the heavy reliance on dense maps or costly navigation supervision. In this work, we introduce a novel paradigm for leveraging directional instructions from commercial navigation tools (e.g., Google Maps). To bridge the gap between commercial instructions and executable navigation actions, while mitigating long-horizon error accumulation through robust trajectory recovery, we propose DA-Nav, a Direction-Aware vision-language Navigation framework that reformulates navigation as a discrete spatial grounding problem on the egocentric 2D image plane. To achieve trajectory recovery, DA-Nav employs a Chain-of-Thought (CoT) reasoning process encompassing deviation assessment, action prediction, and target grid selection. We further introduce ReDA, a dataset that provides direction-aware instructions and recovery trajectories to enhance spatial grounding and support CoT recovery reasoning. Extensive experiments in CARLA demonstrate that DA-Nav achieves a high success rate of 56.16% in unseen urban environments, outperforming existing State-of-The-Art (SoTA) methods while maintaining a substantially stronger recovery capability. Furthermore, without fine-tuning, DA-Nav seamlessly adapts to both quadruped and humanoid robots, enabling stable kilometer-scale closed-loop outdoor navigation in complex real world environments.
Learning-based visual navigation for legged robots typically relies on continuous goal updates from hierarchical state estimation to provide a persistent directional reference. This reliance incurs additional sensory and computational overhead and deviates from fully end-to-end mobile autonomy. Furthermore, under partial observability, policies are prone to learn myopic behaviors, easily becoming trapped in dead ends and complex structural layouts. To address these limitations, we investigate a goal-initialized navigation setting, where the target is provided only once at the beginning of an episode, requiring the robot to operate based on intrinsic spatial memory without subsequent goal updates from external modules. In this work, we propose GUIDE, a fully end-to-end reinforcement learning framework designed to cultivate internal directional awareness. Specifically, GUIDE incorporates a spatial anchor predictor that leverages multi-frequency proprioceptive history to extract egomotion representations, thereby maintaining a persistent long-horizon spatial context for navigation. Concurrently, it utilizes raw depth streams to perceive local environmental geometry. We evaluate the proposed framework across both simulation and real-world scenarios on a quadruped robot. Experiments show that GUIDE learns reliable egomotion and directional awareness, enabling a fully end-to-end deployed policy to safely navigate through dense clutter and structured mazes without subsequent goal guidance or prior maps.