LGMCTS: Language-Guided Monte-Carlo Tree Search for Executable Semantic Object Rearrangement

We present LGMCTS, a framework that uniquely combines language guidance with geometrically informed sam- pling distributions to effectively rearrange objects according to geometric patterns dictated by natural language descriptions. LGMCTS uses Monte Carlo Tree Search (MCTS) to create feasible action plans that ensure executable semantic object rearrangement. We present a comprehensive comparison with leading approaches that use language to generate goal rear- rangements independently of actionable planning, including Structformer, StructDiffusion, and Code as policies. We also present a new benchmark, the Executable Language Guided Rearrangement (ELGR) Bench, containing tasks involving in- tricate geometry. With the ELGR bench, we show limitations of task and motion planning (TAMP) solutions that are purely based on Large Language Models (LLM) such as Code as Policies and Progprompt on such tasks. Our findings advo- cate for using LLMs to generate intermediary representations rather than direct action planning in geometrically complex rearrangement scenarios, aligning with perspectives from recent literature. Our code and supplementary materials are accessible at https://lgmcts.github.io/.