In a nutshell, unscented trajectory optimization is the generation of optimal trajectories through the use of an unscented transform. Although unscented trajectory optimization was introduced by the authors about a decade ago, it is reintroduced in this paper as a special instantiation of tychastic optimal control theory. Tychastic optimal control theory (from \textit{Tyche}, the Greek goddess of chance) avoids the use of a Brownian motion and the resulting It\^{o} calculus even though it uses random variables across the entire spectrum of a problem formulation. This approach circumvents the enormous technical and numerical challenges associated with stochastic trajectory optimization. Furthermore, it is shown how a tychastic optimal control problem that involves nonlinear transformations of the expectation operator can be quickly instantiated using an unscented transform. These nonlinear transformations are particularly useful in managing trajectory dispersions be it associated with path constraints or targeted values of final-time conditions. This paper also presents a systematic and rapid process for formulating and computing the most desirable tychastic trajectory using an unscented transform. Numerical examples are used to illustrate how unscented trajectory optimization may be used for risk reduction and mission recovery caused by uncertainties and failures.

翻译：简而言之，无迹轨迹优化是通过使用无迹变换生成最优轨迹的方法。尽管作者在约十年前提出了无迹轨迹优化，但本文将其重新引入为τυχαστικός（希腊命运女神）最优控制理论的一个特例。τυχαστικός最优控制理论（源自希腊命运女神Tyche）避免了布朗运动的使用及由此产生的伊藤微积分，尽管它在问题公式化的全谱系中使用了随机变量。这种方法规避了与随机轨迹优化相关的巨大技术和数值挑战。此外，本文展示了如何通过无迹变换快速实例化涉及期望算子非线性变换的τυχαστικός最优控制问题。这些非线性变换在管理轨迹分散性方面尤为有用，无论是与路径约束还是终端时刻条件的目标值相关。本文还提出了一种系统且快速的过程，用于通过无迹变换公式化并计算最优的τυχαστικός轨迹。数值示例用于说明无迹轨迹优化如何在由不确定性和故障引起的风险降低与任务恢复中发挥作用。