Vague objectives in many real-life scenarios pose long-standing challenges for robotics, as defining rules, rewards, or constraints for optimization is difficult. Tasks like tidying a messy table may appear simple for humans, but articulating the criteria for tidiness is complex due to the ambiguity and flexibility in commonsense reasoning. Recent advancement in Large Language Models (LLMs) offers us an opportunity to reason over these vague objectives: learned from extensive human data, LLMs capture meaningful common sense about human behavior. However, as LLMs are trained solely on language input, they may struggle with robotic tasks due to their limited capacity to account for perception and low-level controls. In this work, we propose a simple approach to solve the task of table tidying, an example of robotic tasks with vague objectives. Specifically, the task of tidying a table involves not just clustering objects by type and functionality for semantic tidiness but also considering spatial-visual relations of objects for a visually pleasing arrangement, termed as visual tidiness. We propose to learn a lightweight, image-based tidiness score function to ground the semantically tidy policy of LLMs to achieve visual tidiness. We innovatively train the tidiness score using synthetic data gathered using random walks from a few tidy configurations. Such trajectories naturally encode the order of tidiness, thereby eliminating the need for laborious and expensive human demonstrations. Our empirical results show that our pipeline can be applied to unseen objects and complex 3D arrangements.

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