({\tt MORALS}\): Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space

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.