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Controllability of spacecraft systems in a central gravitationalfield

机译：中央引力场中航天器系统的可控性

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The configuration space for rigid spacecraft systems in a central gravitational field can be modeled by SO(3)× IR3, where the special orthogonal group SO(3) represents the attitude dynamics and IR3 is for the orbital motion. The attitude dynamics of the spacecraft system is affected by the orbital elements through the well-known gravity-gradient torque. On the other hand, the effects of attitude-orbit coupling can also possibly be used to alter orbital motions by controlling the attitude. This controllability property is the primary issue of this paper. The control systems for spacecraft with either reaction wheels or gas jets being used as attitude controllers are proven in this study to be controllable. Rigorously establishing these results necessitates starting with the formal definitions of controllability and Poisson stability. It is then shown that if the drift vector field of the system is weakly positively Poisson stable and the Lie algebra rank condition is satisfied, controllability can be concluded. The Hamiltonian structure of the spacecraft model provides a natural route of verifying the property of weakly positive Poisson stability. Accordingly, the controllability is obtained after confirming the Lie algebra rank condition. Developing a methodology in deriving Lie brackets in the tangent space of T(SO(3)×IR3), i.e., the second tangent bundle is thus deemed necessary. A general formula is offered for the computation of Lie brackets of second tangent vector fields in TT(SO(3)m×IRn), in light of its importance in the fields of mechanics, robotics, optimal control, and nonlinear control, among others. With these tools, the controllability results can be proved. The analysis in this paper gives some insight into the attitude-orbit coupling effects and may potentially lead towards new techniques in designing controllers for large spacecraft systems
机译：中心重力场中刚性航天器系统的配置空间可以通过SO（3）×IR3进行建模，其中特殊的正交组SO（3）代表姿态动力学，IR3用于轨道运动。航天器系统的姿态动力学会通过众所周知的重力梯度扭矩受到轨道元素的影响。另一方面，姿态-轨道耦合的影响也可以通过控制姿态来改变轨道运动。这种可控性是本文的主要问题。这项研究证明，采用反作用轮或气体喷嘴作为姿态控制器的航天器控制系统是可控的。要严格确定这些结果，就必须从可控性和泊松稳定性的正式定义开始。然后表明，如果系统的漂移矢量场具有弱的正泊松稳定并且满足李代数秩条件，则可以得出可控性。航天器模型的哈密顿结构为验证弱正泊松稳定性的性质提供了自然的途径。因此，在确定李代数秩条件之后获得可控性。因此，开发一种在T（SO（3）×IR3）的切线空间即第二个切线束中导出李括号的方法是必要的。考虑到它在力学，机器人技术，最优控制和非线性控制等领域的重要性，为在TT（SO（3）m×IRn）中第二切向量场的Lie括号的计算提供了一个通用公式。 。使用这些工具，可以证明可控性结果。本文的分析提供了对姿态-轨道耦合效应的一些见解，并可能潜在地导致设计大型航天器系统控制器的新技术

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