${\tt MORALS}$: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913504986923008 |
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| author | Vieira, Ewerton R. Sivaramakrishnan, Aravind Tangirala, Sumanth Granados, Edgar Mischaikow, Konstantin Bekris, Kostas E. |
| author_facet | Vieira, Ewerton R. Sivaramakrishnan, Aravind Tangirala, Sumanth Granados, Edgar Mischaikow, Konstantin Bekris, Kostas E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03246 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | ${\tt MORALS}$: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space Vieira, Ewerton R. Sivaramakrishnan, Aravind Tangirala, Sumanth Granados, Edgar Mischaikow, Konstantin Bekris, Kostas E. Robotics 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. |
| title | ${\tt MORALS}$: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space |
| topic | Robotics |
| url | https://arxiv.org/abs/2310.03246 |