论文标题
空间碎片碰撞避免操作设计的分析框架
Analytical framework for space debris collision avoidance maneuver design
论文作者
论文摘要
提出了涉及航天器和空间碎屑的碰撞避免操作的分析公式，包括用于最大偏差和最小碰撞概率情况的解决方案。高斯的行星方程和相对运动方程用于在给定时间绘制动作，以在预测的近距离接近方法下进行位移。然后将模型扩展到状态的映射两次之间的映射变化，从而允许一个传播协方差矩阵。分析公式将优化问题降低到本本特征，无论是最大的偏差还是最小碰撞概率。比较了欧洲航天局的Meteoroid和太空碎片陆地环境参考（Master-2009）模型的大量航天器结合几何形状（Master-2009）模型，比较了两个最大偏差情况，即总偏差和影响参数。此外，比较了假设在操纵时间已知的协方差，以评估碰撞概率中提前时间的净效应，比较了最大冲击参数和最小碰撞概率操纵。在所有情况下，在B平面中分析溶液，以利用其自然分离的定相和几何变化效应。不确定性和最大偏差沿时间轴长期长时间的交货时间增长，从而限制了碰撞概率的降低。
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.
