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Attitude and orbit control of spacecrafts for motion reconstruction of flying around and approaching the tumbling target
SUN Shihao, JIA Yingmin
The Seventh Research Division, Beihang University, Beijing 100191, China
Abstract: This paper deals with the attitude and orbit control problem for motion reconstruction of spacecrafts flying around and approaching the tumbling target during ground experiments. Firstly, a 6-DOF similarity model is established to describe the integrated attitude and orbit motion, which is suitable for the experimental verification with the practical constraints on the space size, running velocity and time involved. Secondly, the polynomial approach is used to design the motion reference trajectory that can ensure finite-time convergence and good dynamic performances, based on which, an integrated attitude and orbit control law is proposed by the back-stepping method and the corresponding closed-loop stability is proved. Finally, a numerical example is included to illustrate the effectiveness of the obtained results.
Key words: motion reconstruction     similarity     flying around     tumbling     attitude and orbit control     spacecrafts

1 运动再现系统

 图 1 地面模拟器样机示意图 Fig. 1 Schematic diagram of ground motion simulator

2 相似动力学模型建立

 图 2 坐标系示意图 Fig. 2 Several coordinate frames

2.1 追踪器本体坐标系下航天器相对姿轨模型[19]

 (1)

 (2)

 (3)
2.2 姿轨联合相似动力学模型

x1=[Δrqv]Tx2=[dΔr/dtωct]T，则联立方程(1)、(2)和(3)有姿轨联合方程：

 (4)

x2(0)=[dΔr(0)/dtωct(0)]T

λi表示系统变量i的缩比系数,即λi=im/ip，给定交会对接再现任务的长度、时间、质量3个基本量纲缩比系数λLλTλM，则根据相似理论的量纲分析法[17]，可得姿轨联合相似动力学模型为

 (5)

3 控制器设计

3.1 参考轨迹设计

 (6)

 (7)

 (8)
 (9)
 (10)
3.2 基于反步法的跟踪控制器设计

 (11)

1) e1m(0)=0e2m(0)=0

2) 参考轨迹(Δrm)r(tm)、(qvm)r(tm)二次可微；

3) 参考轨迹分别在有限时间Tqm=λTTqTrm=λTTr能够收敛到零。

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)

e1m(tm)≡0，

4 数值实验 4.1 仿真条件

 参数 数值 偏心率 0.73 半长轴/km 24 371 升交点赤经/(°) 98 轨道倾斜角/(°) 0 近地点幅角/(°) 0 初始真近点角/(°) 10

λL=1/10，λT=1/10，λm=1/1 000

K1=diag(60，60，60)，K2=diag(50，50，50)

 图 3 仿真结构框图 Fig. 3 Block diagram of simulation

 图 4 位置参考轨迹 Fig. 4 Reference trajectory of position
 图 5 姿态参考轨迹 Fig. 5 Reference trajectory of attitude
 图 6 控制器控制力和力矩 Fig. 6 The force and moment of visual controller
 图 7 跟踪误差曲线 Fig. 7 Block diagram of simulation
 图 8 0~1 000 s坐标系otixtiytizti下的运动轨迹 Fig. 8 Trajectory in otixtiytizti at time 0~1 000 s
 图 9 1 000~2 400 s坐标系otixtiytizti下的运动轨迹 Fig. 9 Trajectory in otixtiytizti at time 1 000~2 400 s
 图 10 坐标系ocxcyczc下的航天器相对轨道运动 Fig. 10 Relative orbit trajectory in ocxcyczcframe
 图 11 航天器相对姿态四元数 Fig. 11 Relative attitude quaternion
4.2 仿真结果分析

5 结束语

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DOI: 10.11992/tis.201611022

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#### 文章信息

SUN Shihao, JIA Yingmin

Attitude and orbit control of spacecrafts for motion reconstruction of flying around and approaching the tumbling target

CAAI Transactions on Intelligent Systems, 2016, 11(6): 818-826
http://dx.doi.org/10.11992/tis.201611022