Graph-Operator World Models Generalize Robot Control Across Morphologies

Current world models for continuous control often struggle when the physical characteristics of a robot, such as link lengths or masses, change. These models are typically trained for a fixed system and degrade when morphology parameters vary, even if these parameters are provided as conditioning information. This paper proposes Graph-Operator World Models (GraphOp-WM) to address this limitation. GraphOp-WM represents robot bodies and their kinematic relationships as an attributed graph. Its core innovation is factorizing each transition into two parts: a morphology-independent local dynamics basis and a morphology-conditioned structured operator. This operator intelligently combines node-local modulation, kinematic-tree coupling, and a low-rank global correction, allowing the model to adapt to new morphologies while retaining core dynamic understanding. The architecture uses information separation, basis normalization, and paired-morphology supervision to ensure that static morphology dependence is handled by the operator. Tested on MuJoCo parameter splits for Hopper, Walker2d, and HalfCheetah, GraphOp-WM demonstrates robust generalization across interpolated, extrapolated, and held-out compositions of various physical parameters.