Papers › MORALS: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space
MORALS: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space
Ewerton R. Vieira, Aravind Sivaramakrishnan, Sumanth Tangirala, Edgar Granados, Konstantin Mischaikow, Kostas E. Bekris
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Estimating the region of attraction (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 Morse Graphs (directed acyclic graphs that combinatorially represent the underlying nonlinear dynamics) offer data-efficient 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 RoA estimation.
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