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We recently proposed the\n                    <jats:italic toggle=\"yes\">Neural Contractive Dynamical Systems (NCDS)<\/jats:italic>\n                    , which is a neural network architecture that guarantees contractive stability. With this, learning-from-demonstrations approaches can trivially provide stability guarantees. However, our early work left several unanswered questions, which we here address. Beyond providing an in-depth explanation of NCDS, this paper extends the framework with more careful regularization, a conditional variant of the framework for handling multiple tasks, and an uncertainty-driven approach to latent obstacle avoidance. Experiments verify that the developed system has the flexibility of ordinary neural networks while providing the stability guarantees needed for autonomous robotics.\n                  <\/jats:p>","DOI":"10.1177\/02783649251366326","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T18:43:14Z","timestamp":1757097794000},"page":"714-745","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Extended neural contractive dynamical systems: On multiple tasks and Riemannian safety regions"],"prefix":"10.1177","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8170-2471","authenticated-orcid":false,"given":"Hadi","family":"Beik-Mohammadi","sequence":"first","affiliation":[{"name":"Bosch Center for Artificial Intelligence (BCAI)"},{"name":"Karlsruhe Institute of Technology (KIT)"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7223-877X","authenticated-orcid":false,"given":"S\u00f8ren","family":"Hauberg","sequence":"additional","affiliation":[{"name":"Technical University of Denmark (DTU)"}]},{"given":"Georgios","family":"Arvanitidis","sequence":"additional","affiliation":[{"name":"Technical University of Denmark (DTU)"}]},{"given":"Gerhard","family":"Neumann","sequence":"additional","affiliation":[{"name":"Karlsruhe Institute of Technology (KIT)"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5970-9135","authenticated-orcid":false,"given":"Leonel","family":"Rozo","sequence":"additional","affiliation":[{"name":"Bosch Center for Artificial Intelligence (BCAI)"}]}],"member":"179","published-online":{"date-parts":[[2025,9,5]]},"reference":[{"key":"e_1_3_5_2_1","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2021.XVII.082"},{"key":"e_1_3_5_3_1","doi-asserted-by":"publisher","DOI":"10.1177\/02783649231193046"},{"key":"e_1_3_5_4_1","volume-title":"The Twelfth International Conference on Learning Representations","author":"Beik-Mohammadi H","year":"2024","unstructured":"Beik-Mohammadi H, Hauberg S, Arvanitidis G, et al. 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