Causal-Geo: Neuro-Symbolic Spatial Grounding for Situated Agent Planning

Foundation Models (LLMs/VLMs) exhibit strong semantic reasoning capabilities but remain challenged by situated planning in unstructured physical environments. A key limitation is the Semantic-Geometric Gap: while models interpret linguistic and visual intent, they lack explicit grounding in continuous spatial structures, yielding physically infeasible or unsafe plans. We propose Causal-Geo, a neuro-symbolic framework that bridges this gap by integrating LLM reasoning with rigorous geometric planning. Rather than treating physical constraints heuristically, we model the environment as a continuous metric tensor field. LLMs translate high-level semantic intents into potential functions that dynamically warp this manifold via conformal scaling. This casts intent-driven planning as a geodesic optimization problem, solved efficiently via discrete graph search. Experiments across diverse domains—from a macro-scale $12.2 \text{ km}^2$ wetland digital twin to micro-scale indoor robotic navigation—demonstrate that Causal-Geo enables robust zero-shot planning. It significantly outperforms reinforcement learning in sparse-reward settings and prevents the ``physical hallucinations'' common in representative hierarchical LLM planners. Crucially, Causal-Geo acts as a rigorous physical gatekeeper, guaranteeing invariant safety against foundation model variance and demonstrating graceful degradation under contradictory prompts. These results establish continuous geometric grounding as a principled, domain-agnostic pathway toward physically consistent situated agent planning.