  We propose a method for open-loop stochastic optimal control of LTI systems
based on Taylor approximations of quantile functions. This approach enables
efficient computation of quantile functions that arise in chance constrained
reformulations. We are motivated by multi-vehicle planning problems for LTI
systems with norm-based collision avoidance constraints, and polytopic
feasibility constraints. Respectively, these constraints can be posed as
reverse-convex and convex chance constraints that are affine in the control and
disturbance. We show for constraints of this form, piecewise affine
approximations of the quantile function can be embedded in a
difference-of-convex program that enables use of conic solvers. We demonstrate
our method for multi-satellite coordination with Gaussian and Cauchy
disturbances, and provide a comparison with particle control.
