Estimating the region of attraction (${\tt RoA}$) for a robotic system's controller is essential for safe application and controller composition. Many existing methods require access to 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 Morse Graphs offer data-efficient ${\tt RoA}$ estimation without needing an analytical model. They struggle, however, with high-dimensional systems as they operate over a discretization of the state space. 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 autoencoding 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 the data efficiency of the approach in ${\tt RoA}$ estimation.

翻译：估算机器人系统控制器吸引域（${\tt RoA}$）对于安全应用和控制器组合至关重要。许多现有方法需要访问闭式表达式，这限制了它们在数据驱动控制器上的适用性。仅基于轨迹展开的方法往往数据需求量大。在先前工作中，我们已证明基于莫尔斯图的拓扑工具能在无需解析模型的情况下实现数据高效的${\tt RoA}$估算，但这些方法因依赖状态空间离散化而在高维系统中表现不佳。本文提出${\it Mo}$rse图辅助的${\it R}$egions of ${\it A}$ttraction学习潜在空间发现方法（${\tt MORALS}$），该方法结合自编码神经网络与莫尔斯图。${\tt MORALS}$在估算高维系统（包括67维人形机器人和96维三指机械手）数据驱动控制器的吸引子及其${\tt RoA}$方面展现出优异的预测能力。该方法首先将被控系统动力学投影到学习的潜在空间，然后构建简化莫尔斯图以表征底层动力学的双稳定性，即检测控制器何时产生期望行为与非期望行为。基于高维机器人数据集的评估表明，该方法在${\tt RoA}$估算中具有数据高效性。