空间碎片防撞机动设计分析框架
Analytical framework for space debris collision avoidance maneuver design
摘要：
提出了航天器与空间碎片碰撞规避机动的解析公式，包括最大偏差和最小碰撞概率情况的解。高斯行星方程和相对运动方程用于将给定时刻的机动映射到预测的近距离接近时的位移。然后扩展模型以映射两次之间的状态变化，允许传播协方差矩阵。的分析配方减少了优化问题的特征值问题，无论是最大偏差和最小的碰撞概率。对两种最大偏差情况，即总偏差和碰撞参量，对从欧洲空间局流星体和空间碎片地面环境参考（MASTER-2009）模型得出的大量航天器-碎片会合几何形状进行了比较。此外，最大碰撞参量和最小碰撞概率机动进行比较，假设协方差已知的机动时间，以评估的净影响的提前时间碰撞概率。在所有情况下，在b平面中分析解决方案，以利用其相位和几何变化效果的自然分离。在较长的前置时间内，不确定性和最大偏差都沿时间轴增长，限制了碰撞概率的降低。
英文摘要：
An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss' planetary equations and relative motion equations are used to map maneuvers at a given time to displacements at the predicted close approach. The model is then extended to map changes in state between two times, allowing one to propagate covariance matrices. The analytical formulation reduces the optimization problem to an eigenproblem, both for maximum deviation and minimum collision probability. Two maximum deviation cases, total deviation and impact parameter, are compared for a large set of spacecraft-debris conjunction geometries derived from European Space Agency's Meteoroid and Space Debris Terrestrial Environment Reference (MASTER-2009) model. Moreover, the maximum impact parameter and minimum collision probability maneuvers are compared assuming covariances known at the maneuver time, to evaluate the net effect of lead time in collision probability. In all cases, solutions are analyzed in the b-plane to leverage its natural separation of phasing and geometry change effects. Both uncertainties and maximum deviation grow along the time axis for long lead times, limiting the reduction in collision probability.
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