  While many techniques have been developed for chance constrained stochastic
optimal control with Gaussian disturbance processes, far less is known about
computationally efficient methods to handle non-Gaussian processes. In this
paper, we develop a method for solving chance constrained stochastic optimal
control problems for linear time-invariant systems with general additive
disturbances with finite moments and unimodal chance constraints. We propose an
open-loop control scheme for multi-vehicle planning, with both target sets and
collision avoidance constraints. Our method relies on the one-sided
Vysochanskij-Petunin inequality, a tool from statistics used to bound tail
probabilities of unimodal random variables. Using the one-sided
Vysochanskij-Petunin inequality, we reformulate each chance constraint in terms
of the expectation and standard deviation. While the reformulated bounds are
conservative with respect to the original bounds, they have a simple and closed
form, and are amenable to difference of convex optimization techniques. We
demonstrate our approach on a multi-satellite rendezvous problem.
