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.

中文翻译：

---

非线性机会约束运动规划的矩状态动力系统

机会受限的运动规划需要将动力学中的不确定性传播为状态中的不确定性。当使用非线性模型时，状态分布的高斯假设不一定适用，因为几乎所有通过非线性动力学传播的随机变量都会导致非高斯状态分布。为了解决这个问题，最近的工作开发了基于矩的方法，用于对非高斯状态分布实施机会约束。然而，仍然缺乏快速准确的矩传播方法来确定这些状态分布的必要统计矩。为了解决这个差距，我们提出了一个框架，给定一个随机动力系统，可以在矩状态方面通过算法搜索新的动力系统，该系统可用于将扰动随机变量的矩传播到状态分布的矩中。关键算法 TreeRing 可以应用于一大类非线性系统，我们将其称为三角多项式系统。作为示例应用，我们提出了一种分布稳健的 RRT (DR-RRT) 算法，该算法通过非线性 Dubin 汽车模型传播不确定性，而无需线性化。