Physics-Based Online Adaptive Koopman Model Predictive Attitude Control for Combined Spacecraft With Dynamic Uncertainties

Abstract

This paper proposes a physics-based adaptive Koopman Model Predictive Control (MPC) strategy for combined spacecraft attitude stabilization under inertia uncertainties and active target maneuverability. A novel, quaternion-based Koopman model is constructed from a set of analytical lifting functions derived from the quaternion kinematics, which provides a more compact and physically interpretable linear representation of the nonlinear dynamics compared with the conventional black-box EDMD and higher-dimensional DCM-based model. Leveraging the linear structure of this nominal model, a gradient descent-based update law is employed to efficiently identify time-varying inertial uncertainties from real-time input/output data. By integrating this adaptive linear model into the MPC framework, the optimal control problem reduces to a computationally efficient Quadratic Program (QP), thereby significantly lowering the online computational burden compared to nonlinear adaptive MPC. Recursive feasibility and regional input-to-state stability are formally established through the design of terminal ingredients for the MPC. The effectiveness and superiority of the proposed strategy are validated through comparative simulations of an attitude stabilization task for combined spacecraft in a high-fidelity 3D simulator. Note to Practitioners—On-orbit servicing missions such as refueling and debris removal face a critical challenge: once a spacecraft docks with another target, its inertial properties change abruptly and unpredictably. Furthermore, if the target is non-cooperative, it may also apply competitive torques that actively destabilize the combined system. Such unknown physical variations can endanger the entire mission. Conventional control schemes typically depend on complex nonlinear models of the spacecraft, which impose a heavy computational burden and fail to achieve rapid on-orbit adjustments. To overcome these limitations, this work introduces a unified, online adaptive strategy built upon Koopman operator theory and Model Predictive Control (MPC). The proposed strategy delivers a significantly faster and more precise control response under inertial uncertainty and competitive torques, as validated in high-fidelity simulations. Beyond spacecraft applications, the strategy is potentially applicable to a broader class of nonlinear dynamic systems, especially those with structured kinematics and significant parametric uncertainties. In particular, the proposed physics-enhanced Koopman-based modeling approach can be directly extended to engineering fields such as uncrewed aerial vehicle attitude control and robotic manipulator operations.