  Recent low-thrust space missions have highlighted the importance of designing
trajectories that are robust against uncertainties. In its complete form, this
process is formulated as a nonlinear constrained stochastic optimal control
problem. This problem is among the most complex in control theory, and no
practically applicable method to low-thrust trajectory optimization problems
has been proposed to date. This paper presents a new algorithm to solve
stochastic optimal control problems with nonlinear systems and constraints. The
proposed algorithm uses the unscented transform to convert a stochastic optimal
control problem into a deterministic problem, which is then solved by
trajectory optimization methods such as differential dynamic programming. Two
numerical examples, one of which applies the proposed method to low-thrust
trajectory design, illustrate that it automatically introduces margins that
improve robustness. Finally, Monte Carlo simulations are used to evaluate the
robustness and optimality of the solution.
