论文标题
使用构图操作员的全局，统一代表异源机器人动力学：Koopman直接编码方法
Global, Unified Representation of Heterogenous Robot Dynamics Using Composition Operators: A Koopman Direct Encoding Method
论文作者
论文摘要
机器人和机电系统的动态复杂性通常与动态的杂种性质有关，其中管理方程由异质方程组成，这些方程取决于系统状态。腿部机器人和操纵器机器人会经历联系 - 非接触离散过渡，从而导致控制方程的切换。由于缺乏对全球行为分析的全球统一模型，对这些系统的分析一直是一个挑战。组成运营商理论有可能通过将其转换为升起空间中的线性动力系统来提供全局，统一的表示。当前的工作提出了一种将非线性异源动力学编码为可观测值的高维空间的方法。首先，通过使用可观察功能的内部产物及其与管理状态过渡函数的内部产物，建立了一个新公式来代表希尔伯特空间中的库普曼操作员。该公式称为直接编码，允许将一类异源系统直接转换为全局统一的线性模型。与普遍的数据驱动方法不同，结果可能会根据数值数据而有所不同，而所提出的方法在全球有效，而不需要对原始动力学的数值模拟。一个简单的示例验证了理论结果，并将方法应用于多最高悬架系统。
The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and manipulator robots experience contact-noncontact discrete transitions, causing switching of governing equations. Analysis of these systems have been a challenge due to the lack of a global, unified model that is amenable to analysis of the global behaviors. Composition operator theory has the potential to provide a global, unified representation by converting them to linear dynamical systems in a lifted space. The current work presents a method for encoding nonlinear heterogenous dynamics into a high dimensional space of observables in the form of Koopman operator. First, a new formula is established for representing the Koopman operator in a Hilbert space by using inner products of observable functions and their composition with the governing state transition function. This formula, called Direct Encoding, allows for converting a class of heterogenous systems directly to a global, unified linear model. Unlike prevalent data-driven methods, where results can vary depending on numerical data, the proposed method is globally valid, not requiring numerical simulation of the original dynamics. A simple example validates the theoretical results, and the method is applied to a multi-cable suspension system.
