Graph Neural Koopman Operator: A Structure-Aware Lifting Framework for Free-Floating Space Robot Control

This paper proposes a structure-aware system identification and control framework for free-floating space robots by integrating graph neural networks with Koopman operator theory. The FFSR is first represented as a graph, where the spacecraft base and manipulator links are modeled as nodes and their physical connections are encoded as edges. A residual graph neural network is then employed to learn a nonlinear lifting function that maps the original system state into a higher-dimensional Koopman space, explicitly preserving the topological structure of the robot. The resulting lifted linear model is integrated into a model predictive control scheme to achieve closed-loop trajectory tracking. Simulation results on a dual-arm FFSR with six joints demonstrate that the proposed GNN-Koopman model achieves lower prediction errors compared to conventional EDMDbased Koopman methods. When applied to MPC, the GNN-Koopman controller achieves tracking performance comparable to physics-based MPC with accurate physical modeling, while maintaining stable closed-loop behavior without requiring an explicit analytical model, validating the effectiveness of incorporating structural information into data-driven modeling for space robotic systems.