In this paper, a novel feedback control strategy for quadrotor trajectory tracking is designed and experimentally tested with proof of exponential stability, using the Lyapunov transformations theory. The controller is derived from an inner-outer loop control structure, namely by considering the position system coupled through an interconnection term with the attitude system. For the design of the position controller, the considered dynamics are worked on the body frame, which is uncommon in the literature, and its synthesis derives from theories such as Pontryagin’s maximum principle, Lyapunov theory, and Linear Quadratic Regulator (LQR), which ensure Input-to-state stability, steady-state optimality, and global exponential stability. The attitude system is based on an error quaternion parameterization via a nonlinear coordinate transformation matrix followed by a state input feedback, rendering the system linear and time-invariant. Under a correct transformation, LQR theory ensures almost exponential stability and steady-state optimality for the overall interconnected closed-loop systems. Experimental and simulation results illustrate the performance of the tracking system onboard a quadrotor.

本文利用李亚普诺夫变换理论，设计了一种用于四旋翼飞行器轨迹跟踪的新型反馈控制策略，并通过指数稳定性证明进行了实验测试。该控制器源自内外环控制结构，即考虑通过互连项与姿态系统耦合的位置系统。对于位置控制器的设计，所考虑的动力学作用在车身框架上，这在文献中并不常见，其综合源自庞特里亚金极大值原理、李亚普诺夫理论和线性二次调节器（LQR）等理论，确保了输入状态稳定性、稳态最优性和全局指数稳定性。姿态系统基于误差四元数参数化，通过非线性坐标变换矩阵和状态输入反馈，使系统线性且时不变。在正确的变换下，LQR理论确保了整个互连闭环系统的近指数稳定性和稳态最优性。实验和仿真结果说明了四旋翼飞行器上跟踪系统的性能。