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We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization problem on Lie groups. A gradient descent optimization algorithm is presented to tackle the optimization numerically. Our algorithm is scalable, and applicable to any finite-dimensional Lie group, including matrix Lie groups. By representing the system at the Lie algebra level, we reduce the computational cost of the gradient computation. In an extensive example, optimal potential energy shaping for control of a rigid body is treated. The optimal control problem is phrased as an optimization of a neural ODE on the Lie group SE(3), and the controller is iteratively optimized. The final controller is validated on a state-regulation task.<\/jats:p>","DOI":"10.1177\/02783649241256044","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T19:17:00Z","timestamp":1718392620000},"page":"2221-2244","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimal potential shaping on SE(3) via neural ordinary differential equations on Lie groups"],"prefix":"10.1177","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3002-4479","authenticated-orcid":false,"given":"Yannik P.","family":"Wotte","sequence":"first","affiliation":[{"name":"RaM, University of Twente, Enschede, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"Califano","sequence":"additional","affiliation":[{"name":"RaM, University of Twente, Enschede, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8212-7387","authenticated-orcid":false,"given":"Stefano","family":"Stramigioli","sequence":"additional","affiliation":[{"name":"RaM, University of Twente, Enschede, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"key":"bibr1-02783649241256044","doi-asserted-by":"publisher","DOI":"10.1016\/J.SYSCONLE.2021.104956"},{"key":"bibr2-02783649241256044","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-2675-8_2"},{"key":"bibr3-02783649241256044","volume-title":"Geometric Deep Learning","author":"Bronstein MM","year":"2021"},{"key":"bibr4-02783649241256044","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-control-042920-020211"},{"key":"bibr5-02783649241256044","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-7276-7"},{"key":"bibr6-02783649241256044","volume-title":"Proportional Derivative (PD) Control on the Euclidean Group","author":"Bullo F","year":"1995"},{"key":"bibr7-02783649241256044","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00520-0"},{"key":"bibr8-02783649241256044","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.12.031"},{"key":"bibr9-02783649241256044","unstructured":"Chen RTQ, Rubanova Y, Bettencourt J, et al. 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