基于对偶四元数的航天器六自由度相对运动输入有界控制

利用对偶四元数的理论来分析航天器六自由度的相对运动,设计了一种考虑输入有界的姿轨一体化控制器。在介绍对偶数和对偶四元数的基础上推导六自由度相对运动的姿轨耦合模型;利用双曲正切函数绝对值小于1的特性来显式地构造有界控制器,分别设计两个相互耦合的自适应调节律来动态地改变控制器的输出,并基于李雅普诺夫稳定性理论严格证明了闭环系统的全局渐近稳定性;利用数学仿真实验来验证该控制器和控制力满足给定的约束条件,能够实现航天器六自由度相对运动的精确稳定控制,并且对模型参数不确定性和外界扰动具有鲁棒性。与其他方法相比,由该控制器计算得到的控制力矩器的收敛速度更快,输出的控制力矩和控制力的最大幅值更小,且消耗的能量也更少。

Control for 6-DOF Relative Motion of Spacecraft with Input Saturation Constraint Using Dual Quaternion

This paper investigates six degree-of-freedom (6-DOF) relative motion of spacecraft using dual quaternion and designs an integrated controller of attitude and orbit with input saturation constraint. First of all, dual number and dual quaternion are introduced followed by the derivation of 6-DOF relative motion of attitude and orbit coupled model. Then, an explicitly bounded controller is proposed using the property that the absolute value of hyperbolic tangent function is less than 1. Two coupled adaptive regulators are respectively designed to adjust the outputs of the controller dynamically. Moreover, it is proved by a rigorous theoretical analysis that the closed-loop system is globally and asymptotically stable. Finally, numerical simulation experiment is implemented to demonstrate the validity and effectiveness of the proposed controller. Also, the presented method is compared with another method. The experimental results show that both the obtained control torque and control force satisfy the given constraints, 6-DOF relative motion of spacecraft can be controlled accurately and the method is robust to parameter uncertainties and external disturbance. Compared with another method, the new one has the following advantages: 1) faster convergence rate can be obtained. 2) the max magnitude of output control torque and control force are both smaller. 3) the consumed energy is less.