  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.
