We present a new stability proof for cascaded geometric control used by aerial vehicles tracking time-varying position trajectories. Our approach uses sliding variables and a recently proposed quaternion-based sliding controller to demonstrate that exponentially convergent position trajectory tracking is theoretically possible. Notably, our analysis reveals new aspects of the control strategy, including how tracking error in the attitude loop influences the position loop, how model uncertainties affect the closed-loop system, and the practical pitfalls of the control architecture.

翻译：本文针对航空器跟踪时变位置轨迹所使用的级联几何控制提出了一种新的稳定性证明。我们的方法采用滑模变量与近期提出的基于四元数的滑模控制器，从理论上证明了指数收敛的位置轨迹跟踪是可能实现的。特别值得注意的是，我们的分析揭示了该控制策略的新特性，包括姿态环跟踪误差如何影响位置环、模型不确定性对闭环系统的影响，以及该控制架构在实际应用中的潜在缺陷。