SketchMate: Agentic Geometric Reasoning for Zero-Shot Precision Insertion

Most agentic robotic systems use vision-language models (VLMs) either to orchestrate predefined skills or to directly generate actions, constraints, and control programs. The former is limited by the available skill library, while the latter requires VLMs to reason about precise geometry and contact. In this paper, we propose WorldSketch, a new paradigm for agentic robotics in which a VLM constructs a world model rather than generating robot actions. The VLM acts as an agent that actively queries perception tools to build and visually validate a minimal kinematic world model, capturing only task-relevant objects, their interaction geometry, and possible motions. A geometric planner then jointly optimizes contact and whole-body motion on the resulting model. Moreover, the world model is self-improving: execution feedback verifies outcomes, updates uncertain hypotheses, and enables the agent to revise the model when its predictions are contradicted. We demonstrate the generality of this paradigm across RoboCasa, LIBERO-PRO, and R2R-CE navigation, achieving zero-shot success rates of 91%, 97%, and 76%, respectively. On RoboCasa, WorldSketch outperforms the next-best zero-shot agent baseline by 58 percentage points while using 10 times fewer VLM input tokens; on LIBERO-PRO, it exceeds CaP-X by 82 percentage points. In navigation, it matches the success rate of step-by-step VLM agents while using 6 times fewer input tokens.

Robotic assembly in high-mixture settings requires adaptable systems that can handle diverse parts, yet current approaches typically rely on policies specialized to each insertion task. Although this can reach high success rates, it makes the process of deploying systems for new problems tedious and time consuming. We present a framework for generalizable insertion using world models that combine robot proprioceptive information with raw visual observations captured by a wrist-mounted camera. Our model-based approach trains a single world model on up to 90 insertion tasks with geometrically diverse parts, achieving 56% zero-shot success on unseen objects with unknown geometry compared to just 7% with a model-free baseline. Importantly, performance improves as more objects are included in the training dataset, demonstrating strong scalability. Lastly, finetuning the generalist model on held-out objects significantly enhances data-efficiency compared to training from scratch and, in some cases, achieves better asymptotic performance. To our knowledge, this is the first system capable of assembling unseen objects in an entirely data-driven manner, and thus represents a significant step toward scalable, generalizable robotic assembly systems.

Generalizing robotic manipulation to unseen objects remains challenging, as learning-based approaches require many demonstrations and fail in few-shot settings. Prior work transfers affordances through semantic retrieval, but semantics alone neglect geometric similarity, which is critical for manipulation. We propose GRAFT, a geometry-aware correspondence framework for zero-shot manipulation transfer using only one demonstration per object. Objects are represented as part-based graphs, where part-level descriptors support global instance retrieval and part correspondence, and vertex-level descriptors enable fine-grained contact point matching. For an unseen object, our method first retrieves the most functionally and geometrically similar instance from the demonstration buffer with aligned functional parts, and finally propagates the contact points through point-wise correspondence.