Many current applications of maneuver design to astrodynamics consider a deterministic case, where statistics or uncertainty is left unquantified. When including constraints based on the probability of collision, any solution must be robust to the uncertainty of the system. This paper considers the methodology of separated representations for orbit uncertainty propagation and its subsequent application to a reliability design formulation of the maneuver design problem. Separated representations is a polynomial surrogate method that has been shown to be both efficient at propagating uncertainty when considering high stochastic dimension and accurate over long propagation times. This efficiency is leveraged to improve tractability when solving the reliability design problem using optimization under uncertainty. Two sequential, potential collisions are considered in the results of this paper, with one object able to maneuver. The optimization problem therefore seeks to avoid both collisions. The probability of each collision is estimated via large numbers of samples propagated via the separated representation. The accuracy of the surrogates is compared to that of a Monte Carlo reference, and the variability of the estimated probabilities of collision is analyzed.

机动设计在空气动力学中的许多当前应用考虑了确定性的情况，其中统计或不确定性未被量化。当包括基于碰撞概率的约束时，任何解决方案都必须对系统的不确定性具有鲁棒性。本文考虑了轨道不确定性传播的分离表示方法，并将其随后应用于机动设计问题的可靠性设计公式。分离表示法是一种多项式替代方法，已被证明在考虑高随机维数时可以有效地传播不确定性，并且可以在较长的传播时间内保持精确。当使用不确定性下的优化来解决可靠性设计问题时，可以利用这种效率来提高可处理性。两个连续 本文的结果考虑了潜在的碰撞，其中一个物体能够机动。因此，优化问题试图避免两个冲突。每次碰撞的可能性是通过大量的样本（通过分离的表示）传播来估计的。将代理的准确性与蒙特卡罗参考的准确性进行比较，并分析估计的碰撞概率的变异性。