# tt MORALS: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space

arXiv: https://arxiv.org/abs/2310.03246 · HTML: https://mlsanity.com/paper/2310.03246/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2023.

## Built on by (most cited first, 4 of 4)

- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Verification of Unknown Dynamical Systems via Autoencoder Latent Space](https://mlsanity.com/paper/2512.13593/) (2025)
- [V-MORALS: Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space](https://mlsanity.com/paper/2602.23524/) (2026)
- [Virtues of Ordered Chaos: Planning with Topple Actions in Tabletop Stack Rearrangement](https://mlsanity.com/paper/2605.17815/) (2026)

## Abstract (arXiv)

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 Morse Graph-aided discovery of it Regions of it Attraction in a learned it Latent it Space (tt MORALS). The approach combines auto-encoding neural networks with Morse Graphs. tt MORALS shows promising predictive capabilities in estimating attractors and their tt RoAs 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.