While spatial reasoning has made progress in object localization relationships, it often overlooks object orientation—a key factor in 6-DoF fine-grained manipulation. Traditional pose representations rely on pre-defined frames or templates, limiting generalization and semantic grounding. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a cup). To support this, we construct OrienText300K, a large-scale dataset of 3D objects annotated with semantic orientations, and develop PointSO, a general model for zero-shot semantic orientation prediction. By integrating semantic orientation into VLM agents, our SoFar framework enables 6-DoF spatial reasoning and generates robotic actions. Extensive experiments demonstrated the effectiveness and generalization of our SoFar, e.g., zero-shot 48.7\% successful rate on Open6DOR and zero-shot 74.9\% successful rate on SIMPLER-Env.

The integration of large-scale Vision-Language Models (VLMs) with embodied AI can greatly enhance the generalizability and the capacity to follow open instructions for robots. However, existing studies on object manipulation are not up to full consideration of the 6-DoF requirements, let alone establishing a comprehensive benchmark. In this paper, we propel the pioneer construction of the benchmark and approach for Open-instruction 6-DoF Object Rearrangement (Open6DOR). Specifically, we collect a synthetic dataset of 200+ objects and carefully design 5400+ Open6DOR tasks. These tasks are divided into the Position-track, Rotation-track, and 6-DoF-track for evaluating different embodied agents in predicting the positions and rotations of target objects.Besides, we also propose a VLM-based approach for Open6DOR, named Open6DOR-GPT, which empowers GPT-4V with 3D-awareness and simulation-assistance while exploiting its strengths in generalizability and instruction-following. We compare the existing embodied agents with our Open6DOR-GPT on the proposed Open6DOR benchmark and find that Open6DOR-GPT achieves the state-of-the-art performance. We further show the impressive performance of Open6DOR-GPT in diverse real-world experiments.