针对欠驱动六自由度垂直起降无人驾驶飞行器的轨迹跟踪控制问题,设计使跟踪误差全局K指数收敛的控制器。建立基于修正的罗德里格参数的系统非线性误差模型,基于分级控制的思想,使用反步法分别设计使飞行器位置和姿态子系统指数稳定的控制器;考虑到该系统稳定性分析的复杂性,通过刚体旋转的罗德里格斯定理建立子系统间耦合项与修正的罗德里格参数间的内在联系,并最终得到闭环误差系统的全局K指数稳定的结论。仿真分析表明:本文提出的控制方法能够有效实现飞行器对于复杂轨迹的快速和精确跟踪。
In order to solve the trajectory tracking control problem of the six degrees of freedom vertical take-off and landing unmanned aerial vehicles, a controller which is capable of stabilizing the trajectory tracking error K-exponentially was designed. Firstly, a nonlinear error model was established based on the modified rodrigues parameters. Considering the thought of hierarchical control, the position and attitude controller for the translational and orientation dynamics were designed based on the backstepping approach, respectively. Due to the complexity stability analysis of this system, the Rodrigues theory was applied to analyze the internal contact between the coupled term and the modified rodrigues parameters, and hence the global K-exponential stability of the closed-loop system was proved. Simulation results show that the proposed control scheme enables the aircraft to track a complex trajectory lastly and accurately.