基于四元数的刚体姿态调节问题

Attitude Regulation of a Rigid Body Using Unit Quaternion

给出了用四元数表示的刚体姿态调节问题的两种控制规律 .首先利用反馈非线性化方法 ,给出一种不含非线性扭矩项、仅由四元数和角速度的线性组合构成的控制规律 .该控制律与刚体惯性参数无关 ,因而具有一定的鲁棒性 ,并证明在一定条件下闭环系统是指数渐近稳定的 .其次重新研究了刚体姿态控制问题固有的无源性 ,并利用这种新的无源性设计了一种仅利用姿态四元数而无需用角速度测量作为反馈的控制规律 .与现有的四输入 /四输出无源系统相比 ,这里的严格无源系统的动态控制器仅是三输入 /三输出的 ,有效地减少了实时计算所需的时间 .

Two control laws are presented for attitude regulation of a rigid body expressed by unit quaternion. A kind of control law is designed using unit quaternion and angular velocity by the feedback nonlinearization approach firstly. The fact that this kind of control law assures that the closed loop system is exponentially stable is proved by consideration of modified total energy function of the rigid body. In addition, this control law does not need any inertial parameters of the rigid body, therefore, exhibits some robustness. Then a new passivity of attitude control system of a rigid body is exploited. A dynamic feedback controller without angular velocity is designed by this new passivity. Compared with the controller of four inputs and four outputs in the existing literature, this dynamic controller is three order of linear system with three inputs and three outputs.