Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees
Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees
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DOI：
10.1109/icra48891.2023.10160428
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Ewerton R. Vieira;A. Sivaramakrishnan;Yao Song;Edgar Granados;Marcio Gameiro;K. Mischaikow;Ying Hung;Kostas E. Bekris
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文献类型：
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作者：
Ewerton R. Vieira;A. Sivaramakrishnan;Yao Song;Edgar Granados;Marcio Gameiro;K. Mischaikow;Ying Hung;Kostas E. Bekris
本文提出了一种集成的代理建模和拓扑结构，以显着减少所需的数据量来描述底层的全局动态的机器人控制器，包括闭盒的。高斯过程（GP），在状态空间上用随机短轨迹训练，作为底层动力系统的代理模型。然后，构建组合表示并用于以有向非循环图（称为莫尔斯图）的形式描述动态。莫尔斯图能够描述系统的吸引子和它们相应的吸引区域（罗阿）。此外，在整个状态空间上的全局动态估计的逐点置信水平提供。与替代方案相比，该框架不需要估计李雅普诺夫函数，从而减轻了对GP的高预测精度的需求。该框架适用于数据驱动控制器，只要满足Lipschitz连续性，就不暴露分析模型。该方法与已建立的分析和最近的机器学习替代方案进行比较，以估计Roas，在不牺牲准确性的情况下，在数据效率方面优于它们。代码链接：https://go.rutgers.edu/49hy35en
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 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 suit-able 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 Roas, outperforming them in data efficiency without sacrificing accuracy. Link to code: https://go.rutgers.edu/49hy35en