For spacecraft hovering in low orbit, a high precision spacecraft relative dynamics model without any simplification and considering J₂ perturbation is established in this paper. Using the derived model, open-loop control and closed-loop control are proposed respectively. Gauss's variation equations and the coordinate transformation method are combined to deal with the relative J₂ perturbation between the two spacecraft. The sliding mode controller is adopted as the closed-loop controller for spacecraft hovering. To improve the control accuracy, the relative J₂ perturbation is regarded as a known parameter term in the closed-loop controller. The external uncertainty perturbations except J₂ perturbation are estimated by numerical difference method, and the boundary layer method is used to weaken the impact of chattering on the sliding mode controller. The open-loop control of spacecraft hovering with the relative J₂ perturbation and without the relative J₂ perturbation are simulated and compared, and the results prove that the accuracy of open-loop control with relative J₂ perturbation has been significantly improved. Similarly, the simulation of the closed-loop control are presented to validate the effectiveness of the designed sliding mode controller, and the results demonstrate that the designed sliding mode controller including the derived relative J₂ perturbation can guarantee the high accuracy and robustness of spacecraft hovering in long-term mission.

为了在低轨道上盘旋航天器，建立了一个不做任何简化并考虑J ₂摄动的高精度航天器相对动力学模型。利用推导模型，分别提出了开环控制和闭环控制。高斯的变化方程和坐标变换方法相结合，以处理两个航天器之间的相对J ₂摄动。滑模控制器被用作航天器悬停的闭环控制器。为了提高控制精度，相对J ₂摄动被认为是闭环控制器中的已知参数项。J ₂以外的外部不确定性摄动用数值差分法估计微扰，并采用边界层方法来减弱颤动对滑模控制器的影响。仿真和比较了具有相对J ₂扰动和没有相对J ₂扰动的航天器悬停的开环控制，结果证明，具有相对J ₂扰动的开环控制的精度得到了显着提高。类似地，通过闭环控制仿真验证了所设计的滑模控制器的有效性，结果表明所设计的滑模控制器包括推导的相对J _2。 扰动可以确保长期飞行中的航天器盘旋的高精度和鲁棒性。