{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:40:24Z","timestamp":1778496024188,"version":"3.51.4"},"reference-count":60,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T00:00:00Z","timestamp":1693180800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/100008398","name":"villum fonden","doi-asserted-by":"publisher","award":["42062"],"award-info":[{"award-number":["42062"]}],"id":[{"id":"10.13039\/100008398","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["757360"],"award-info":[{"award-number":["757360"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Center for Basic Machine Learning Research in Life Sciences","award":["NNF20OC0062606"],"award-info":[{"award-number":["NNF20OC0062606"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p>In recent decades, advancements in motion learning have enabled robots to acquire new skills and adapt to unseen conditions in both structured and unstructured environments. In practice, motion learning methods capture relevant patterns and adjust them to new conditions such as dynamic obstacle avoidance or variable targets. In this paper, we investigate the robot motion learning paradigm from a Riemannian-manifold perspective. We argue that Riemannian manifolds may be learned via human demonstrations in which geodesics are natural motion skills. The geodesics are generated using a learned Riemannian metric produced by our novel variational autoencoder (VAE), which is intended to recover full-pose end-effector states and joint-space configurations. In addition, we propose a technique for facilitating on-the-fly end-effector\/multiple-limb obstacle avoidance by reshaping the learned manifold using an obstacle-aware ambient metric. The motion generated using these geodesics may naturally result in multiple-solution tasks that have not been explicitly demonstrated previously. We extensively tested our approach in task-space and joint-space scenarios using a 7-DoF robotic manipulator. We demonstrate that our method is capable of learning and generating motion skills based on complicated motion patterns demonstrated by a human operator. Additionally, we assess several obstacle-avoidance strategies and generate trajectories in multiple-mode settings.<\/jats:p>","DOI":"10.1177\/02783649231193046","type":"journal-article","created":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T21:25:00Z","timestamp":1693257900000},"page":"729-754","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Reactive motion generation on learned Riemannian manifolds"],"prefix":"10.1177","volume":"42","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), Renningen, Germany"},{"name":"Autonomous Learning Robots Lab, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7223-877X","authenticated-orcid":false,"given":"S\u00f8ren","family":"Hauberg","sequence":"additional","affiliation":[{"name":"Section for Cognitive Systems, Technical University of Denmark (DTU), Lyngby, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georgios","family":"Arvanitidis","sequence":"additional","affiliation":[{"name":"Section for Cognitive Systems, Technical University of Denmark (DTU), Lyngby, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gerhard","family":"Neumann","sequence":"additional","affiliation":[{"name":"Autonomous Learning Robots Lab, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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), Renningen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"bibr1-02783649231193046","volume-title":"Conference on Robot Learning (CoRL)","author":"Aljalbout E","year":"2020"},{"key":"bibr2-02783649231193046","volume-title":"International Conference on Learning Representations (ICLR)","author":"Arvanitidis G","year":"2018"},{"key":"bibr3-02783649231193046","first-page":"1506","volume-title":"International Conference on Artificial Intelligence and Statistics (AISTATS)","author":"Arvanitidis G","year":"2019"},{"key":"bibr4-02783649231193046","volume-title":"International Conference on Artificial Intelligence and Statistics (AISTATS)","author":"Arvanitidis G","year":"2021"},{"key":"bibr5-02783649231193046","first-page":"5058","volume-title":"Advances in Neural Information Processing Systems (NeurIPS)","author":"Bahl S","year":"2020"},{"key":"bibr6-02783649231193046","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2021.XVII.082"},{"key":"bibr7-02783649231193046","volume-title":"Workshop on Self-Organizing Maps","author":"Bishop CM","year":"1997"},{"key":"bibr8-02783649231193046","volume-title":"Texts in Applied Mathematics","author":"Bullo F","year":"2004"},{"key":"bibr9-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/s11370-015-0187-9"},{"key":"bibr10-02783649231193046","doi-asserted-by":"publisher","DOI":"10.5772\/6197"},{"key":"bibr11-02783649231193046","first-page":"1540","volume-title":"International Conference on Artificial Intelligence and Statistics (AISTATS)","author":"Chen N","year":"2018"},{"key":"bibr12-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-30484-3_45"},{"key":"bibr13-02783649231193046","volume-title":"Introduction to Algorithms","author":"Cormen TH","year":"2009"},{"key":"bibr14-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1017\/9781108679930"},{"key":"bibr15-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1145\/1273496.1273527"},{"key":"bibr16-02783649231193046","volume-title":"Expected Path Length on Random Manifolds","author":"Eklund D","year":"2019"},{"key":"bibr17-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2014.2302442"},{"key":"bibr18-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2015.7139393"},{"key":"bibr19-02783649231193046","volume-title":"Only Bayes Should Learn a Manifold","author":"Hauberg S","year":"2019"},{"key":"bibr20-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2015.2511743"},{"key":"bibr21-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1177\/0278364913482016"},{"key":"bibr22-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/s11044-018-9620-0"},{"key":"bibr23-02783649231193046","volume-title":"International Conference on Learning Representations","author":"Higgins I","year":"2017"},{"key":"bibr24-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1177\/0278364919846363"},{"key":"bibr25-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00393"},{"key":"bibr26-02783649231193046","first-page":"233","volume-title":"Conference on Robot Learning (CoRL)","author":"Jaquier N","year":"2020"},{"key":"bibr27-02783649231193046","first-page":"6789","volume-title":"International Conference on Machine Learning (ICML)","author":"Kalatzis D","year":"2020"},{"key":"bibr28-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2011.2159412"},{"key":"bibr29-02783649231193046","volume-title":"International Conference on Learning Representations (ICLR)","author":"Kingma DP","year":"2014"},{"key":"bibr30-02783649231193046","volume-title":"Optimal Control Theory: An Introduction. Networks Series","author":"Kirk D","year":"1970"},{"key":"bibr31-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/IROS47612.2022.9982127"},{"key":"bibr32-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1177\/0278364911428653"},{"key":"bibr33-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-91755-9"},{"key":"bibr34-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-017-9643-z"},{"key":"bibr35-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2018.2792531"},{"key":"bibr36-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2017.10.011"},{"key":"bibr37-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/BioRob.2012.6290923"},{"key":"bibr38-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-022-09966-y"},{"key":"bibr39-02783649231193046","volume-title":"Orocos\/Orocos\u02d9kinematics\u02d9dynamics: Orocos Kinematics and Dynamics C Library","author":"Orocos","year":"2021"},{"key":"bibr40-02783649231193046","volume-title":"Variational Autoencoder Trajectory Primitives with Continuous and Discrete Latent Codes","author":"Osa T","year":"2019"},{"key":"bibr41-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1561\/2300000053"},{"key":"bibr42-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-017-9648-7"},{"key":"bibr43-02783649231193046","first-page":"8024","volume-title":"Advances in Neural Information Processing Systems (NeurIPS)","author":"Paszke A","year":"2019"},{"key":"bibr44-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1561\/0600000029"},{"key":"bibr45-02783649231193046","volume-title":"Advances in Neural Information Processing Systems (NeurIPS)","volume":"4","author":"Prescott T","year":"1992"},{"key":"bibr46-02783649231193046","unstructured":"Rana MA, Li A, Fox D, et al. (2020) Euclideanizing flows: Diffeomorphic reduction for learning stable dynamical systems. In: Proceedings of the 2nd Conference on Learning for Dynamics and Control, Proceedings of Machine Learning Research, 2020, pp. 630\u2013639. https:\/\/proceedings.mlr.press\/v120\/rana20a.html"},{"key":"bibr47-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2009.5152817"},{"key":"bibr48-02783649231193046","volume-title":"Riemannian motion policies","author":"Ratliff ND","year":"2018"},{"key":"bibr49-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-control-100819-063206"},{"key":"bibr50-02783649231193046","unstructured":"Rozo L, Dave V (2021) Orientation probabilistic movement primitives on Riemannian manifold. In: Conference on Robot Learning (CoRL). 2021, https:\/\/proceedings.mlr.press\/v164\/rozo22a.html"},{"key":"bibr51-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/ICAR.2011.6088633"},{"key":"bibr52-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/IROS45743.2020.9341570"},{"key":"bibr53-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA48506.2021.9561362"},{"key":"bibr54-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.2002.1258"},{"key":"bibr55-02783649231193046","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2019.XV.071"},{"key":"bibr56-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1109\/CVPRW.2018.00071"},{"key":"bibr57-02783649231193046","volume-title":"Applied Directional Statistics","author":"Sra S","year":"2018","edition":"1"},{"key":"bibr58-02783649231193046","doi-asserted-by":"publisher","DOI":"10.1017\/S026357471900078X"},{"key":"bibr59-02783649231193046","volume-title":"Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning Robotics: Science and Systems","author":"Urain J","year":"2021"},{"key":"bibr60-02783649231193046","volume-title":"Programming by Demonstration on Riemannian Manifolds","author":"Zeestraten M","year":"2018"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649231193046","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/02783649231193046","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649231193046","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:17:00Z","timestamp":1777457820000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783649231193046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,28]]},"references-count":60,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["10.1177\/02783649231193046"],"URL":"https:\/\/doi.org\/10.1177\/02783649231193046","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,28]]}}}