Estimating the region of attraction (${\tt RoA}$) for a robot controller is essential for safe application and controller composition. Many existing methods require a closed-form expression that limit applicability to data-driven controllers. Methods that operate only over trajectory rollouts tend to be data-hungry. In prior work, we have demonstrated that topological tools based on ${\it Morse Graphs}$ (directed acyclic graphs that combinatorially represent the underlying nonlinear dynamics) offer data-efficient ${\tt RoA}$ estimation without needing an analytical model. They struggle, however, with high-dimensional systems as they operate over a state-space discretization. This paper presents ${\it Mo}$rse Graph-aided discovery of ${\it R}$egions of ${\it A}$ttraction in a learned ${\it L}$atent ${\it S}$pace (${\tt MORALS}$). The approach combines auto-encoding neural networks with Morse Graphs. ${\tt MORALS}$ shows promising predictive capabilities in estimating attractors and their ${\tt RoA}$s for data-driven controllers operating over high-dimensional systems, including a 67-dim humanoid robot and a 96-dim 3-fingered manipulator. It first projects the dynamics of the controlled system into a learned latent space. Then, it constructs a reduced form of Morse Graphs representing the bistability of the underlying dynamics, i.e., detecting when the controller results in a desired versus an undesired behavior. The evaluation on high-dimensional robotic datasets indicates data efficiency in ${\tt RoA}$ estimation.

翻译：估计机器人控制器的吸引域（${\tt RoA}$）对于安全应用和控制器组合至关重要。许多现有方法需要闭环表达式，这限制了其在数据驱动控制器上的适用性。仅基于轨迹滚动的分析方法往往数据需求量大。在先前工作中，我们证明了基于${\it Morse图}$（一种组合表示底层非线性动力学的有向无环图）的拓扑工具能够在无需解析模型的情况下实现数据高效的${\tt RoA}$估计。然而，这些方法在处理高维系统时存在困难，因为它们需要对状态空间进行离散化。本文提出了在学习的潜在空间中通过Morse图辅助发现吸引域的方法（${\tt MORALS}$）。该方法结合了自编码神经网络与Morse图。${\tt MORALS}$在估计高维系统（包括67维人形机器人和96维三指机械手）中数据驱动控制器的吸引子及其${\tt RoA}$方面展现出有前景的预测能力。它首先将受控系统的动力学投影到学习的潜在空间中，然后构建Morse图的简化形式以表征底层动力学的双稳态性，即检测控制器何时产生期望行为与非期望行为。在高维机器人数据集上的评估表明，该方法在${\tt RoA}$估计中具有数据高效性。