针对航天器姿态跟踪任务，考虑一种配置两个独立动量交换型执行机构的欠驱动航天器，提出了一种基于横截函数的任意姿态轨迹跟踪控制律。利用三维特殊正交群SO(3)建立航天器姿态运动学方程，并基于动量守恒条件，将动力学方程与运动学统一写成以执行机构输出角动量为控制输入的降阶系统。利用横截条件与Lie代数秩条件构造基于SO(3)的横截函数，其本质为能够任意逼近平衡点的一个嵌入子流形，并基于横截函数与姿态误差建立降阶跟踪控制系统的伴随系统。针对伴随系统，提出了一种光滑静态反馈控制律，利用Morse函数证明了对于任意轨迹闭环系统的最终有界稳定性。进一步针对可行轨迹，基于零动态系统设计了横截函数的参数自调整律，使得在零动态时横截函数趋近跟踪系统的平衡点，证明了闭环系统具有指数稳定性。最后，通过数值仿真验证了提出控制器的有效性。
For the spacecraft attitude tracking task, two independent actuators of momentum exchange type are considered for an underactu-ated spacecraft and arbitrary attitude trajectory tracking control law is proposed based on the transverse function. The kinematic equations of the rigid spacecraft attitude are established using the three-dimensional special orthogonal group SO(3), and the kinematic equations are unified with the kinematics based on the momentum conservation condition as a reduced-order system with the output angular momentum of the actuator as the control input. The transverse condition is used to construct the trans-verse function based on the Lie algebraic rank condition, which is essentially an embedded submanifold that can approach the equilibrium point arbitrarily, and the adjoint system of the reduced-order tracking control system is established based on the transverse function and the attitude error. For the accompanying system, a smooth static feedback control law is proposed, and the ultimately bounded stability of the closed-loop system for arbitrary trajectories is proved by using Morse function. Furthermore, for the feasible trajectory, the parameter adjustment law of the transverse function is designed based on the zero dynamic system, so that the transverse function converges to the equilibrium point of the tracking system at zero dynamic, and the closed-loop system is proved to have exponential stability. Finally, the effectiveness of the above controller is verified by numerical simula-tion.
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