This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot controllers, including closed-box ones. A Gaussian Process (GP), trained with randomized short trajectories over the state-space, acts as a surrogate model for the underlying dynamical system. Then, a combinatorial representation is built and used to describe the dynamics in the form of a directed acyclic graph, known as {\it Morse graph}. The Morse graph is able to describe the system's attractors and their corresponding regions of attraction (\roa). Furthermore, a pointwise confidence level of the global dynamics estimation over the entire state space is provided. In contrast to alternatives, the framework does not require estimation of Lyapunov functions, alleviating the need for high prediction accuracy of the GP. The framework is suitable for data-driven controllers that do not expose an analytical model as long as Lipschitz-continuity is satisfied. The method is compared against established analytical and recent machine learning alternatives for estimating \roa s, outperforming them in data efficiency without sacrificing accuracy. Link to code: https://go.rutgers.edu/49hy35en
翻译:本文建议整合代用模型和地形学,以大幅减少描述机器人控制器的基本全球动态所需的数据数量,包括封闭式控制器。 一个Gaussian进程(GP),在州-空间上接受随机短轨道训练,作为基础动态系统的代用模型。然后,建立一个组合式代表制,用于描述动态,其形式为定向环流图,称为 Whit Morse 图}。Morse 图表能够描述系统的吸引器及其相应的吸引力区域(\roa) 。此外,还提供了全球动态估计在全州空间的高度信任度。相对于其他办法,该框架不需要估计Lyapunov的功能,从而减轻对GP高预测准确度的需要。框架适合于数据驱动的控制器,只要Lipschitz- continity是满意的,它们不会暴露分析模型。该方法与用于估计\roa s/hyal35 的既定分析和机器学习替代方法相比较。在不精确性数据中表现 MAG35 。