{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/euclideanizing-flows-diffeomorphic-reduction","title":"Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems","arxiv_id":"2005.13143","date":"2020-05-27","proceeding":"L4DC 2020 6","authors":["Muhammad Asif Rana","Anqi Li","Dieter Fox","Byron Boots","Fabio Ramos","Nathan Ratliff"],"abstract":"Robotic tasks often require motions with complex geometric structures. We present an approach to learn such motions from a limited number of human demonstrations by exploiting the regularity properties of human motions e.g. stability, smoothness, and boundedness. The complex motions are encoded as rollouts of a stable dynamical system, which, under a change of coordinates defined by a diffeomorphism, is equivalent to a simple, hand-specified dynamical system. As an immediate result of using diffeomorphisms, the stability property of the hand-specified dynamical system directly carry over to the learned dynamical system. Inspired by recent works in density estimation, we propose to represent the diffeomorphism as a composition of simple parameterized diffeomorphisms. Additional structure is imposed to provide guarantees on the smoothness of the generated motions. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.","url_abs":"https://arxiv.org/abs/2005.13143v2","url_pdf":"https://arxiv.org/pdf/2005.13143v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"euclideanizing-flows-diffeomorphic-reduction","repo_url":"https://github.com/mrana6/euclideanizing_flows","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"euclideanizing-flows-diffeomorphic-reduction","repo_url":"https://github.com/nash169/learn-diffeomorphism","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2005.13143","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2005.13143"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/mrana6/euclideanizing_flows","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/nash169/learn-diffeomorphism","reach":{"status":"ok","spdx":"GPL-3.0"}}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"46608ec44c561960","entry":"get_jacobian","repo":"mrana6/euclideanizing_flows","repo_kind":"official","path":"euclideanizing_flows/flows.py","file_url":"https://github.com/mrana6/euclideanizing_flows/blob/HEAD/euclideanizing_flows/flows.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"46608ec44c561960"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}