OOWM: Structuring Embodied Reasoning and Planning via Object-Oriented Programmatic World Modeling

Standard Chain-of-Thought (CoT) prompting empowers Large Language Models (LLMs) with reasoning capabilities, yet its reliance on linear natural language is inherently insufficient for effective world modeling in embodied tasks. While text offers flexibility, it fails to explicitly represent the state-space, object hierarchies, and causal dependencies required for robust robotic planning. To address these limitations, we propose Object-Oriented World Modeling (OOWM), a novel framework that structures embodied reasoning through the lens of software engineering formalisms. We redefine the world model not as a latent vector space, but as an explicit symbolic tuple $W = \langle S, T \rangle$: a State Abstraction ($G_\text{state}$) instantiating the environmental state $S$, coupled with a Control Policy ($G_\text{control}$) representing the transition logic $T: S \times A \rightarrow S'$. OOWM leverages the Unified Modeling Language (UML) to materialize this definition: it employs Class Diagrams to ground visual perception into rigorous object hierarchies, and Activity Diagrams to operationalize planning into executable control flows. Furthermore, we introduce a three-stage training pipeline combining Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO). Crucially, this method utilizes outcome-based rewards from the final plan to implicitly optimize the underlying object-oriented reasoning structure, enabling effective learning even with sparse annotations. Extensive evaluations on the MRoom-30k benchmark demonstrate that OOWM significantly outperforms unstructured textual baselines in planning coherence, execution success, and structural fidelity, establishing a new paradigm for structured embodied reasoning.