  A method is developed to numerically solve chance constrained optimal control
problems. The chance constraints are reformulated as nonlinear constraints that
retain the probability properties of the original constraint. The reformulation
transforms the chance constrained optimal control problem into a deterministic
optimal control problem that can be solved numerically. The new method
developed in this paper approximates the chance constraints using Markov Chain
Monte Carlo (MCMC) sampling and kernel density estimators whose kernels have
integral functions that bound the indicator function. The nonlinear constraints
resulting from the application of kernel density estimators are designed with
bounds that do not violate the bounds of the original chance constraint. The
method is tested on a non-trivial chance constrained modification of a soft
lunar landing optimal control problem and the results are compared with results
obtained using a conservative deterministic formulation of the optimal control
problem. The results show that this new method efficiently solves chance
constrained optimal control problems.
