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.

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