Decoupled Dynamic Modeling by Decomposing the Cross-Coupled Dynamics and Tube-Based LPV-MPC Control Scheme for Aerial Manipulation

In this paper, we provide a decoupled method for modeling and controlling unmanned aerial manipulators (UAMs) to improve trajectory tracking by addressing challenges arising from the cross-coupled dynamics of the UAV and manipulator. Existing methods are: 1) estimating reaction torque and force (ERTF); and 2) modeling the cross-coupled dynamics via changing the UAV's inertia matrix and center of mass (CoM), but they suffer from high tracking errors or ineffective handling of inertia parameter derivatives during fast trajectory tracking. In this work, we systematically decompose and represent the reaction force and torque in UAM states, facilitating effective adjustments to the dynamic model for both the UAV and manipulator while addressing all cross-coupled effects. This decoupling enables the development of individual controllers for both the UAV and the manipulator. Additionally, We partition the translational and rotational components of the UAV's dynamics, and then we design a linear MPC controller for the translational dynamics, aiming to achieve a desired rotational trajectory by expressing reaction forces in relation to the UAV's force vector. We develop linear parameter-varying (LPV) dynamic models for both the UAV's rotational dynamics and the manipulator, followed by designing tube-based LPV-MPC controllers for them, considering varying parameters as uncertainties. This approach ensures system feasibility, stability, and robustness. This is achieved by computing robust positively invariant (RPI) terminal sets and incorporating state and control input constraints through reachable sets over prediction horizons. The proposed approach's performance is validated through simulations. Furthermore, we show that our approach outperforms the ERTF in trajectory tracking