  In this paper, we present an efficient algorithm for solving a class of
chance constrained optimization under non-parametric uncertainty. Our algorithm
is built on the possibility of representing arbitrary distributions as
functions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation to
formulate chance constrained optimization as one of minimizing the distance
between a desired distribution and the distribution of the constraint functions
in the RKHS. We provide a systematic way of constructing the desired
distribution based on a notion of scenario approximation. Furthermore, we use
the kernel trick to show that the computational complexity of our reformulated
optimization problem is comparable to solving a deterministic variant of the
chance-constrained optimization. We validate our formulation on two important
robotic/control applications: (i) reactive collision avoidance of mobile robots
in uncertain dynamic environments and (ii) inverse dynamics based path tracking
of manipulators under perception uncertainty. In both these applications, the
underlying chance constraints are defined over highly non-linear and non-convex
functions of the uncertain parameters and possibly also decision variables. We
also benchmark our formulation with the existing approaches in terms of sample
complexity and the achieved optimal cost highlighting significant improvements
in both these metrics.
