论文标题
非线性机会受限运动计划的力矩状态动力系统
Moment State Dynamical Systems for Nonlinear Chance-Constrained Motion Planning
论文作者
论文摘要
偶然受限的运动计划要求动态的不确定性在状态下传播到不确定性。当使用非线性模型时，对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力矩的方法，用于在非高斯州分布上执行机会构成。但是，仍然缺乏快速，准确的力矩传播方法来确定这些状态分布的必要统计矩。为了解决这一差距，我们提出了一个框架，鉴于随机动力学系统，可以从矩状状态中算法搜索新的动态系统，该系统可用于将干扰随机变量的矩传入状态分布的矩中。关键算法（Treeering）可以应用于我们称为三角多项式系统的大型非线性系统。作为示例应用程序，我们提出了一个分布鲁棒的RRT（DR-RRT）算法，该算法在没有线性化的情况下通过非线性Dubin的CAR模型传播不确定性。
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.
