基于对偶四元数的卫星主从式编队姿轨跟踪的优化控制

在对偶四元数的框架下研究了主从式编队卫星相对姿态和相对位置跟踪控制的优化问题.首先,给出了用对偶四元数描述的编队卫星六自由度的相对运动模型.接着,把系统模型拆分为标称系统和扰动系统,对于标称系统,使用李雅普诺夫优化控制技术和轨迹跟踪优化的方法来得到非线性系统的次优解,而对于扰动系统,利用滑模控制来确保闭环系统的鲁棒性,为此把最优控制和滑模控制结合起来提出了一种优化的积分滑模控制器,并通过李雅普诺夫方法严格地证明了整个闭环系统的全局渐近稳定性.最后,通过数学仿真来验证设计方法的有效性和可行性,结果表明本文的方法能够实现编队卫星姿轨跟踪的精确控制,收敛速度较快,得到的性能指标更小,且对模型参数不确定性和外部有界干扰具有较强鲁棒性.

Optimized tracking-control for attitude and orbit of satellite formation flying using dual quaternion

This paper investigates the optimized tracking-control problem of the relative attitude and relative position between two satellites of a leader-follower satellite formation, in the framework of dual quaternion. First, a six degreesof-freedom relative motion model of satellite formation flying (SFF) is introduced with dual quaternion. Then, the system model is divided into the nominal part and the disturbed part. For the nominal part, the Lyapunov optimizing control technique and the trajectory-following optimization are utilized to obtain a sub-optimal result of the nonlinear system. For the disturbed part, the sliding-mode control is adopted to ensure the robustness of the closed-loop system. Thus, an optimized integral sliding-mode controller that combines optimal control and sliding-mode control is developed. The resulting closed-loop system is proved to be globally asymptotically stable by using Lyapunov method. Numerical simulations are performed to demonstrate the effectiveness and validity of the proposed controller; the results indicate that the proposed controller can realize accurate tracking-control of the relative attitude and relative position for SFF with fast convergence rate, small performance indices, and robustness to model uncertainties and bounded external disturbances.