  Chance-constrained motion planning requires uncertainty in dynamics to be
propagated into uncertainty in state. When nonlinear models are used, Gaussian
assumptions on the state distribution do not necessarily apply since almost all
random variables propagated through nonlinear dynamics results in non-Gaussian
state distributions. To address this, recent works have developed moment-based
approaches for enforcing chance-constraints on non-Gaussian state
distributions. However, there still lacks fast and accurate moment propagation
methods to determine the necessary statistical moments of these state
distributions. To address this gap, we present a framework that, given a
stochastic dynamical system, can algorithmically search for a new dynamical
system in terms of moment state that can be used to propagate moments of
disturbance random variables into moments of the state distribution. The key
algorithm, TreeRing, can be applied to a large class of nonlinear systems which
we refer to as trigonometric polynomial systems. As an example application, we
present a distributionally robust RRT (DR-RRT) algorithm that propagates
uncertainty through the nonlinear Dubin's car model without linearization.
