基于对偶四元数的航天器相对位置和姿态耦合控制

针对交会对接、在轨服务等航天任务中存在的轨道和姿态动力学耦合问题,突破传统的轨道姿态分而治之模式,利用对偶四元数建立了相对位置和姿态的一体化耦合动力学模型,并分析了模型中存在的轨道和姿态耦合影响.针对此强耦合、非线性系统,基于对偶四元数的李群结构设计了误差PD（Proportional Derivative,比例微分）控制律,采用Lyapunov（李雅普诺夫）方法分析了控制系统的稳定性,并指出其相比传统的轨道和姿态分别控制方法更有优势.仿真结果表明,该控制方法能够一体化控制航天器的相对位置和姿态,相对位置控制精度在0.01m以内,相对姿态控制精度在0.05°以内,这表明所设计的控制器有效可行.

Spacecraft Attitude and Orbital Coupling Dynamics and Control Based on Dual Quaternion

A coupled relative translational and attitude dynamics model is derived using dual quaternion to meet the requirements of spacecraft rendezvous and docking missions.The relational effect between translational and attitude motion is analyzed.For highly coupling and nonlinear systems,an integrated control law including PD （Proportional Derivative） feedback and feed-forward compensation is designed based on the Lie-Group property of dual quaternion.Stability analysis of the control system is performed with Lyapunov method and its advantages are proven through comparison with the traditional method featuring separated control of orbit and attitude.Numerical simulation indicates that the proposed method is capable of integrated control of the relative position and attitude,and the relative position control accuracy is within 0.01 m and the relative attitude control accuracy is within 0.05°.