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Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. In addition, by leveraging a known parameterization of the constraint, we modify our method to learn parametric constraints in high dimensions. We also provide theoretical analysis on what subset of the constraint and safe set can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space.<\/jats:p>","DOI":"10.1177\/02783649211035177","type":"journal-article","created":{"date-parts":[[2021,8,13]],"date-time":"2021-08-13T05:59:26Z","timestamp":1628834366000},"page":"1255-1283","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Learning constraints from demonstrations with grid and parametric representations"],"prefix":"10.1177","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4444-3631","authenticated-orcid":false,"given":"Glen","family":"Chou","sequence":"first","affiliation":[{"name":"Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Berenson","sequence":"additional","affiliation":[{"name":"Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Necmiye","family":"Ozay","sequence":"additional","affiliation":[{"name":"Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2021,8,13]]},"reference":[{"key":"bibr1-02783649211035177","author":"Abbasi-Yadkori Y","year":"2017","journal-title":"International Conference on Artificial Intelligence and Statistics"},{"key":"bibr2-02783649211035177","author":"Abbeel P","year":"2004","journal-title":"International Conference on Machine Learning"},{"key":"bibr3-02783649211035177","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2014.7039601"},{"key":"bibr4-02783649211035177","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-016-1453-y"},{"key":"bibr5-02783649211035177","first-page":"1813","author":"Amin K","year":"2017","journal-title":"31st Conference on Neural Information Processing Systems"},{"key":"bibr6-02783649211035177","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2008.10.024"},{"key":"bibr7-02783649211035177","first-page":"1520","author":"Armesto L","year":"2017","journal-title":"International Conference on Robotics and Automation"},{"key":"bibr8-02783649211035177","doi-asserted-by":"publisher","DOI":"10.1145\/1228716.1228751"},{"key":"bibr9-02783649211035177","author":"Calinon S","year":"2008","journal-title":"International Conference on Intelligent Robots and Systems"},{"key":"bibr10-02783649211035177","first-page":"228","author":"Chou G","year":"2018","journal-title":"Algorithmic Foundations of Robotics XIII, Proceedings of the 13th Workshop on the Algorithmic Foundations of Robotics (WAFR 2018)"},{"key":"bibr11-02783649211035177","first-page":"1211","volume-title":"3rd Annual Conference on Robot Learning (CoRL 2019)","author":"Chou G","year":"2019"},{"key":"bibr12-02783649211035177","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2020.2974427"},{"key":"bibr13-02783649211035177","unstructured":"Chou G, Ozay N, Berenson D (2020b) Uncertainty-aware constraint learning for adaptive safe motion planning from demonstrations. 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