基于四元数的四旋翼无人飞行器轨迹跟踪控制

Trajectory Tracking Control of Quad-rotor UAV Based on Quaternion

四旋翼无人飞行器具有复杂的数学模型,但现有控制方法大多是基于系统简化模型提出的.为此,该文分析了这类方法的局限性,并基于原始数学模型研究了非线性轨迹跟踪控制问题.通过期望轨迹建立跟踪误差模型,将其分解为两个相互独立的子系统,并以刚体旋转的四元数为系统状态对姿态子系统进行描述.利用backstepping方法设计时变反馈控制律使其子系统指数稳定.根据级联系统的全局稳定性判据,通过研究耦合部分的性质证明系统的全局指数稳定性.仿真结果表明,该方法能够实现四旋翼无人飞行器对期望轨迹的跟踪.

Because a complete mathematical model of a quadrotor is complicated, the controller design is usually based on a simplified model. In this paper, we analyze the limitation of such simplification, and consider nonlinear trajectory tracking control based on its original model. A tracking error control system consisting of two independent subsystems is established to track the expected trajectory. The attitude subsystem is described using the quaternion of rigid body＇s rotation as the system state. A backstepping based approach is proposed to stabilize the subsystems exponentially. Based on the global stability criterion of cascade systems and analysis of the properties of coupled parts, globally exponential stability of the system is proved. Simulation results show that the proposed method enables the quadrotor to track a trajectory.