V-MORALS: Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space

TL;DR

V-MORALS introduces a novel approach for estimating regions of attraction in robotic systems using only sensor data, leveraging learned latent spaces and Morse graphs to enhance safety analysis without full state knowledge.

Contribution

It extends MORALS by enabling ROA estimation solely from sensor measurements, eliminating the need for full state information or large datasets.

Findings

Successfully estimates ROAs using only image data.

Generates Morse graphs for various systems and controllers.

Operates without requiring known system dynamics.

Abstract

Reachability analysis has become increasingly important in robotics to distinguish safe from unsafe states. Unfortunately, existing reachability and safety analysis methods often fall short, as they typically require known system dynamics or large datasets to estimate accurate system models, are computationally expensive, and assume full state information. A recent method, called MORALS, aims to address these shortcomings by using topological tools to estimate Regions of Attraction (ROA) in a low-dimensional latent space. However, MORALS still relies on full state knowledge and has not been studied when only sensor measurements are available. This paper presents Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space (V-MORALS). V-MORALS takes in a dataset of image-based trajectories of a system under a given controller, and learns a latent space for reachability analysis. Using this learned latent space, our method is able to generate well-defined Morse Graphs, from which we can compute ROAs for various systems and controllers. V-MORALS provides capabilities similar to the original MORALS architecture without relying on state knowledge, and using only high-level sensor data. Our project website is at: https://v-morals.onrender.com.