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 引用本文: 杜向南, 杨震. 航天器单脉冲机动可达域求解算法[J]. 力学学报, 2020, 52(6): 1621-1631.
Du Xiangnan, Yang Zhen. AN ALGORITHM FOR SOLVING SPACECRAFT REACHABLE DOMAIN WITH SINGLE-IMPULSE MANEUVERING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1621-1631.
 Citation: Du Xiangnan, Yang Zhen. AN ALGORITHM FOR SOLVING SPACECRAFT REACHABLE DOMAIN WITH SINGLE-IMPULSE MANEUVERING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1621-1631.

## AN ALGORITHM FOR SOLVING SPACECRAFT REACHABLE DOMAIN WITH SINGLE-IMPULSE MANEUVERING

• 摘要: 航天器轨道机动可达域是表征其在未来时间可能到达空间位置集合的有效方式,对维护航天器在轨安全、改善空间态势感知能力具有重要意义.现有关于可达域计算的方法仍然存在模型复杂、初值敏感性高导致计算效果较差等缺点,因此有必要发展更加简洁有效的可达域包络求解算法.本文基于近心点坐标系建立了基于未来可达位置矢量极值求解的可达域求解模型,首先定义任意指向的矢量描述方法并给出未来该指向位置是否可达的判据;其次,设置转移轨道面内机动方位角,将可达域求解问题转化为当前可达位置矢量方向的单变量极值求解问题,利用极值点处可达域包络面函数梯度需为零的条件确定转移轨道面机动方位角的取值,从而确定航天器的轨道机动可达域;此外根据二体轨道动力学特性,利用包络的对称性减少可达域求解计算量;最后通过蒙特卡洛打靶仿真对提出的可达域求解方法进行仿真验证.结果表明,本文方法对航天器单脉冲轨道机动可达域的计算结果与蒙特卡洛打靶仿真吻合良好,模型更加简洁且计算精度优于现有方法.

Abstract: The spacecraft reachable domain (RD) is an effective method to present the possible position boundary of a spacecraft in a future time, which is of great significance for maintaining the safety of spacecraft and improving the ability of space situational awareness. However, previous research efforts on solving RD still have some disadvantages, e.g. some RD models are relatively complicated, and some other solving methods are highly sensitive to the initial values thus result in poor computational accuracy. Therefore, it is necessary to develop a more concise and efficient RD solving algorithm. This paper develops an innovative model to solve the RD based on the extremum condition of the predicted position vector, in the pericenter coordinate frame. First, a vector description method is defined to express the spatial orientation and the criterion of accessibility for an arbitrarily given position vector. Second, the maneuvering azimuth angle in the transfer-orbit plane is used to transform the reachable domain problem to the univariate extreme value problem, at the current accessible position vector. The value of the maneuvering azimuth is determined by considering that the gradient of the describing function at the surface of RD envelope is zero, following this, the maneuvering reachable domain of the spacecraft with a single impulse can be obtained. In addition, the symmetry of the RD envelope under two-body dynamical assumption is used to reduce the computational complexity. Finally, the RD solving algorithm proposed in this paper is verified by Monte Carlo simulation. The numerical results show that the new RD algorithm proposed in this paper provides good agreement with the Monte Carlo simulation on computational accuracy. Moreover, the new RD algorithm is more concise and more accurate than the existing RD solving methods.

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