﻿ 基于虚拟中心引力场方法的航天器转移轨道设计
«上一篇
 文章快速检索 高级检索

 力学学报  2015, Vol. 47 Issue (1): 180-184  DOI: 10.6052/0459-1879-14-112 0

### 引用本文 [复制中英文]

[复制中文]
Yuan Jianping, Sun Chong, Fang Qun. SPACECRAFT'S TRANSFER ORBIT DESIGN BASED ON THE VIRTUAL CENTRAL GRAVITY FIELD METHOD[J]. Chinese Journal of Ship Research, 2015, 47(1): 180-184. DOI: 10.6052/0459-1879-14-112.
[复制英文]

### 文章历史

2014-05-08收稿
2014-08-01录用
2014-12-12网络版发表

1. 西北工业大学航天学院,西安 710072;
2. 航天飞行动力学技术国家级重点实验室,西安 710072

1 虚拟中心引力场的定义

2 轨道动力学建模与虚拟中心引力场设计 2.1 动力学建模

 $\dfrac{d^2{\pmb r}_1 }{d t^2} + \dfrac{{\pmb\mu}_1 }{|{\pmb r}_1 |^3} \times {\pmb r}_1 = {\pmb a}_{\rm t}$ (1)

 $\dfrac{d^2({\pmb r}_1 - {\pmb r}_0 )}{d t^2} + \Big(\dfrac{{\pmb\mu}_2 }{ | {\pmb r}_1 - {\pmb r}_0 |^3}\Big) \times ({\pmb r}_1 - {\pmb r}_0 ) = {\bf 0}$ (2)

r2=r1-r0,在特定虚拟中心引力场中，r0为定值，则(r0)' = 0,r'2 = r'1 - r'0 = r'1. 地心惯性坐标系下航天器位置和速度与虚拟中心引力场坐标系下位置和速度转化关系为

 ${\pmb r}_2 = {\pmb r}_1 - {\pmb r}_0 \,,\ \ {\pmb v}_2 = {\pmb v}_1$ (3)

 $\dfrac{d^2{\pmb r}_2 }{d t^2} + \dfrac{\mu _2 }{ |{\pmb r}_2 |^3} {\pmb r}_2 = 0$ (4)

 ${\pmb a}_{\rm t} = \dfrac{d^2{\pmb r}_1 }{d t^2} + \dfrac{\mu _1 }{ | {\pmb r}_1 | ^3}{\pmb r}_1 - \dfrac{d^2{\pmb r}_2 }{d t^2} -\dfrac{\mu _2 }{ |{\pmb r}_2 | ^3}{\pmb r}_2 = \dfrac{\mu_1 }{ |{\pmb r}_1 | ^3}{\pmb r}_1 - \dfrac{\mu _2 }{ | {\pmb r}_2 | ^3}{\pmb r}_2$ (5)

2.2 虚拟中心引力场设计

 $\left. \begin{array}{l} {r_{a2}} = {r_{a1}} + {r_0}\\ {r_{b2}} = {r_{b1}} + {r_0}\\ {h_2} = {r_{a2}} \times {V_{a2}} = {r_{b2}} \times {V_{b2}} \end{array} \!\! \right\}$ (6)
 图 1 在虚拟中心引力场中的转移轨道及受力分析 Fig. 1 Transfer orbit and force analysis using VCGF

 $\left. \begin{array}{l} {r_{a2}} = \frac{{h_2^2}}{{{\mu _2}}}\frac{1}{{1 + {e_2}\cos ({f_{a2}})}}\\ {r_{b2}} = \frac{{h_2^2}}{{{\mu _2}}}\frac{1}{{1 + {e_2}\cos ({f_{b2}})}}\\ {f_{b2}} = {f_{a2}} + \Delta f \end{array} \! \right\}$ (7)

 $a_1 r_{0x}-b_1r_{0y}=c_1$ (8)

 图 4 三维空间机动轨道(VCGF和SB) Fig. 4 Transfer orbits using VCGF and SB method
 图 5 采用VCGF(a)和形状方法(b)所需推力 Fig. 5 Thrust profile using VCGF (a) and SB methods (b)
5 结 论

(1) 虚拟中心引力场方法将航天器转移轨道设计问题转化为2个参数寻优问题. 大大减少了轨道设计参数，简化了求解转移轨道设计过程；

(2) VCGF方法能够适用于一般情况，扩大了航天器机动范围. 在同样条件下，相比形状方法，虚拟中心引力场方法在实现轨道转移时所需推力以及所需能量较小.

 [1] 李俊峰,蒋方华,连续小推力航天器的深空探测轨道优化方法综述,力学与实践,2011, 33(3): 1-6 (Li Junfeng, Jiang Fanghua. Survey of low-thrust trajectory optimization methods for deep space exploration. Mechanics and Engineering, 2011, 33(3): 1-6 (in Chinese)) [2] 汤国建,张洪波. 小推力轨道机动动力学与控制,北京:科学出版社,2013 (Tang Guojian, Zhang Hongbo. Dynamics and Control of Low-thrust Orbital Maneuver. Beijing: Science Press,2013 (in Chinese)) [3] Tisen H. Take-off from satellite orbit. Journal of the American Rocket Society, 1953, 23(4): 233-236 [4] Boltz FW. Orbit motion under continuous radial thrust. Journal of Guidance, Control, and Dynamics, 1991, 14(3): 667-670; [5] Petropoulos AE, Longuski JM. Automated design of low-thrust gravity-assist trajectories. Journal of Spacecraft and Rockets, 2004, 41(5): 787-796 [6] Bradley W. Shape-based approximation method for low-thrust trajectory optimization. AIAA 2008-6616, 2008. 1-9 [7] Wall BJ, Conway BA. Shape-based approach to low-thrust rendezvous trajectory design. Journal of Guidance, Control, and Dynamics, 2009, 32 (1): 95-101 [8] Hudson J, Scheeres D. Fourier coefficient selection for low-thrust control shaping. Journal of Guidance, Control, and Dynamics, 2013, 36 (6): 1783-1786 [9] 潘峰，李位星. 粒子群优化算法与多目标优化. 北京： 北京理工大学出版社， 2013(Pan Feng, Li Weixing. Particle Swarm Optimization Algorithm and Multiply Variables Optimization. Beijing: Beijing Institute of Technology Press, 2013 (in Chinese))
SPACECRAFT'S TRANSFER ORBIT DESIGN BASED ON THE VIRTUAL CENTRAL GRAVITY FIELD METHOD
Yuan Jianping, Sun Chong, Fang Qun
1. College of Astronautics,Northwestern Polytechnic University,Xi'an 710072,China;
2. National Key Laboratory of Aerospace Flight Dynamics,Xi'an 710072,China
Fund: The project was supported by the National Natural Science Foundation of China (11272255).
Abstract: The space maneuver technology is the basis of space mission operation. In this paper,a novel method named virtual central gravitational field method for continuous thrust maneuver trajectory design for the spacecraft is proposed,which can decrease the number of trajectories' parameters. Because there is no assumption in this approach,it can be used in general case. This approach applies in orbit transfer in both 2-D and 3-D spaces,and the results show that in the same condition,the required thrust acceleration and energy cost are smaller than that of shape-based methods.
Key words: trajectory maneuver    transfer orbit    continuous thrust    central gravitational field