This work presents a geometric backstepping controller for a variable-tilt omnidirectional multirotor that explicitly accounts for both servo and rotor dynamics. Considering actuator dynamics is essential for more effective and reliable operation, particularly during aggressive flight maneuvers or recovery from sudden disturbances. While prior studies have investigated actuator-aware control for conventional and fixed-tilt multirotors, these approaches rely on linear relationships between actuator input and wrench, which cannot capture the nonlinearities induced by variable tilt angles. In this work, we exploit the cascade structure between the rigid-body dynamics of the multirotor and its nonlinear actuator dynamics to design the proposed backstepping controller and establish exponential stability of the overall system. Furthermore, we reveal parametric uncertainty in the actuator model through experiments, and we demonstrate that the proposed controller remains robust against such uncertainty. The controller was compared against a baseline that does not account for actuator dynamics across three experimental scenarios: fast translational tracking, rapid rotational tracking, and recovery from sudden disturbance. The proposed method consistently achieved better tracking performance, and notably, while the baseline diverged and crashed during the fastest translational trajectory tracking and the recovery experiment, the proposed controller maintained stability and successfully completed the tasks, thereby demonstrating its effectiveness.

翻译：本研究提出了一种几何反步控制器，用于可变倾角全向多旋翼飞行器，该控制器显式考虑了伺服机构与旋翼动力学。考虑执行器动力学对于实现更高效可靠的运行至关重要，特别是在剧烈飞行动作或突发扰动恢复过程中。虽然先前研究已针对传统及固定倾角多旋翼飞行器探索了执行器感知控制方法，但这些方法依赖于执行器输入与力/力矩之间的线性关系，无法捕捉可变倾角引起的非线性效应。本研究通过利用多旋翼刚体动力学与其非线性执行器动力学之间的级联结构，设计了所提出的反步控制器，并证明了整个系统的指数稳定性。此外，我们通过实验揭示了执行器模型中的参数不确定性，并证明所提控制器对此类不确定性具有鲁棒性。在三种实验场景下（快速平移跟踪、快速旋转跟踪及突发扰动恢复），将所提控制器与未考虑执行器动力学的基准方法进行了对比。所提方法始终获得更优的跟踪性能，特别是在最快速平移轨迹跟踪和恢复实验中，当基准方法发散并坠毁时，所提控制器仍能保持稳定性并成功完成任务，从而验证了其有效性。