基于Rodrigues参数的陀螺体受控运动

经典刚体动力学中表示刚体姿态的参数中,Euler角、Cardan角和Euler参数在工程技术中使用最为普遍．近期在航天器姿态控制问题中使用Rodrigues参数的报道也引起注意,Rodrigues参数以其表达形式简明和代数运算特点而具有独特优点．航天器姿态控制系统必须具有自适应性以适应参数的变化,建立用Rodrigues参数表达的无力矩陀螺体受控运动方程,提出基于Rodrigues参数的自适应姿态控制方案,并应用Lyapunov定理证明受控运动的渐近稳定性。

CONTROLLED ATTITUDE MOTION OF GYROSTAT BASED ON RODRIGUES PARAMETERS

Among various attitude representations of rigid body, the Euler angles, Cardan angles and Euler parameters are applied frequently in engineering. Recently the application of Rodrigues parameters in the attitude control of spacecraft attracts some attention. The Rodrigues parameters have some distinctive advantages of simplicity in representation and their algebraic calculation. In the space flight practice, it is difficult to determine the accurate value of dynamical parameters of a spacecraft in orbit, then the adaptive behavior of attitude control is required to adapt the variation of parameters. In the present paper the dynamical equations of controlled attitude motion of a torque-free gyrostat expressed by Rodrigues parameters are derived, and an adaptive approach based on Rodrigues parameters is proposed to keep a predetermined attitude under the internal disturbance. The Lyapunov theorem is used to prove the asymptotic stability of the controlled motion.