{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T15:33:58Z","timestamp":1772638438214,"version":"3.50.1"},"reference-count":59,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2020,9,11]],"date-time":"2020-09-11T00:00:00Z","timestamp":1599782400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/100009011","name":"Ontario Centres of Excellence","doi-asserted-by":"publisher","award":["OCE\/SOSCIP TalentEdge Project 27901"],"award-info":[{"award-number":["OCE\/SOSCIP TalentEdge Project 27901"]}],"id":[{"id":"10.13039\/100009011","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Vector Institute for Artificial Intelligence","award":["Graduate Student Affiliation Program"],"award-info":[{"award-number":["Graduate Student Affiliation Program"]}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","award":["Sloan Research Fellowship"],"award-info":[{"award-number":["Sloan Research Fellowship"]}],"id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003400","name":"Ministry of Research and Innovation","doi-asserted-by":"publisher","award":["Early Researcher Award"],"award-info":[{"award-number":["Early Researcher Award"]}],"id":[{"id":"10.13039\/501100003400","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["Alexander Graham Bell Canada Graduate Scholarship"],"award-info":[{"award-number":["Alexander Graham Bell Canada Graduate Scholarship"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["Discovery Grant"],"award-info":[{"award-number":["Discovery Grant"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["Research Tools and Instruments Grant"],"award-info":[{"award-number":["Research Tools and Instruments Grant"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:p> High-accuracy trajectory tracking is critical to many robotic applications, including search and rescue, advanced manufacturing, and industrial inspection, to name a few. Yet the unmodeled dynamics and parametric uncertainties of operating in such complex environments make it difficult to design controllers that are capable of accurately tracking arbitrary, feasible trajectories from the first attempt (i.e., impromptu trajectory tracking). This article proposes a platform-independent, learning-based \u201cadd-on\u201d module to enhance the tracking performance of black-box control systems in impromptu tracking tasks. Our approach is to pre-cascade a deep neural network (DNN) to a stabilized baseline control system, in order to establish an identity mapping from the desired output to the actual output. Previous research involving quadrotors showed that, for 30 arbitrary hand-drawn trajectories, the DNN-enhancement control architecture reduces tracking errors by 43% on average, as compared with the baseline controller. In this article, we provide a platform-independent formulation and practical design guidelines for the DNN-enhancement approach. In particular, we: (1) characterize the underlying function of the DNN module; (2) identify necessary conditions for the approach to be effective; (3) provide theoretical insights into the stability of the overall DNN-enhancement control architecture; (4) derive a condition that supports data-efficient training of the DNN module; and (5) compare the novel theory-driven DNN design with the prior trial-and-error design using detailed quadrotor experiments. We show that, as compared with the prior trial-and-error design, the novel theory-driven design allows us to reduce the input dimension of the DNN by two thirds while achieving similar tracking performance. <\/jats:p>","DOI":"10.1177\/0278364920953902","type":"journal-article","created":{"date-parts":[[2020,9,11]],"date-time":"2020-09-11T08:11:58Z","timestamp":1599811918000},"page":"1397-1418","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["Deep neural networks as add-on modules for enhancing robot performance in impromptu trajectory tracking"],"prefix":"10.1177","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7240-546X","authenticated-orcid":false,"given":"Siqi","family":"Zhou","sequence":"first","affiliation":[{"name":"University of Toronto Institute for Aerospace Studies, Toronto, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5101-5526","authenticated-orcid":false,"given":"Mohamed K","family":"Helwa","sequence":"additional","affiliation":[{"name":"University of Toronto Institute for Aerospace Studies, Toronto, Canada"},{"name":"Electrical Power and Machines Department, Cairo University, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4012-4668","authenticated-orcid":false,"given":"Angela P","family":"Schoellig","sequence":"additional","affiliation":[{"name":"University of Toronto Institute for Aerospace Studies, Toronto, Canada"}]}],"member":"179","published-online":{"date-parts":[[2020,9,11]]},"reference":[{"key":"bibr1-0278364920953902","first-page":"879","author":"Antsaklis PJ","year":"2000","journal-title":"Proceedings of the IEEE Special Issue on Hybrid Systems: Theory and Applications"},{"key":"bibr2-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2004.01.002"},{"key":"bibr3-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2016.7798978"},{"key":"bibr4-0278364920953902","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop CM","year":"2006"},{"key":"bibr5-0278364920953902","doi-asserted-by":"publisher","DOI":"10.3182\/20110828-6-IT-1002.02327"},{"key":"bibr6-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2006.1636313"},{"key":"bibr7-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2007.01.002"},{"key":"bibr8-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/9.384214"},{"key":"bibr9-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2017.7989397"},{"key":"bibr10-0278364920953902","volume-title":"Lectures on Dynamic Systems and Control","author":"Dahleh M","year":"2004"},{"key":"bibr11-0278364920953902","first-page":"1184","volume-title":"Proceedings of the International Conference on Machine Learning (ICML)","author":"Depeweg S","year":"2018"},{"key":"bibr12-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/9.508898"},{"key":"bibr13-0278364920953902","first-page":"133","volume-title":"Proceedings of the Conference on Robot Learning (CoRL)","author":"Drews P","year":"2017"},{"key":"bibr14-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8451-9"},{"key":"bibr15-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(76)90006-6"},{"key":"bibr16-0278364920953902","volume":"3","author":"Franklin GF","year":"1994","journal-title":"Feedback Control of Dynamic Systems"},{"key":"bibr17-0278364920953902","first-page":"1050","volume-title":"Proceedings of the International Conference on Machine Learning (ICML)","author":"Gal Y","year":"2016"},{"key":"bibr18-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.813823"},{"key":"bibr19-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1117\/12.823843"},{"key":"bibr20-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2015.2411285"},{"key":"bibr21-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2015.7402117"},{"key":"bibr22-0278364920953902","author":"Helwa MK","year":"2018","journal-title":"arXiv preprint arXiv:1804.01031"},{"key":"bibr23-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2016.7798717"},{"key":"bibr24-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1979.1102181"},{"key":"bibr25-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2007.365003"},{"key":"bibr26-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(92)90053-I"},{"key":"bibr27-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.1094"},{"key":"bibr28-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-615-5"},{"key":"bibr29-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1080\/00207729408949269"},{"key":"bibr30-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00028-0"},{"key":"bibr31-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog1603_1"},{"key":"bibr32-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-88400-8.50047-9"},{"key":"bibr33-0278364920953902","author":"Kingma DP","year":"2014","journal-title":"arXiv preprint:1412.6980"},{"key":"bibr34-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.02.015"},{"key":"bibr35-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2015.7138994"},{"key":"bibr36-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2017.7989607"},{"key":"bibr37-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1002\/oca.2123"},{"key":"bibr38-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-013-9822-x"},{"key":"bibr39-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1992.4.4.590"},{"key":"bibr40-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2012.6385647"},{"key":"bibr41-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2008.4650850"},{"key":"bibr42-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2010.5509858"},{"key":"bibr43-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/AERO.2013.6496959"},{"key":"bibr44-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2016.7799164"},{"key":"bibr45-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015727715131"},{"key":"bibr46-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-012-9283-2"},{"key":"bibr47-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1177\/027836498700600303"},{"key":"bibr48-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/9.173151"},{"key":"bibr49-0278364920953902","first-page":"1929","volume":"15","author":"Srivastava N","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"bibr50-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017912319985"},{"key":"bibr51-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1051\/matecconf\/20153404004"},{"key":"bibr52-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/9.45159"},{"key":"bibr53-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-control-060117-105149"},{"key":"bibr54-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2004.01.026"},{"key":"bibr55-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2013.2275948"},{"key":"bibr56-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2016.7487175"},{"key":"bibr57-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2015.2461001"},{"key":"bibr58-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2017.8264430"},{"key":"bibr59-0278364920953902","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2018.2801471"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364920953902","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0278364920953902","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364920953902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T14:34:28Z","timestamp":1740839668000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364920953902"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,11]]},"references-count":59,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["10.1177\/0278364920953902"],"URL":"https:\/\/doi.org\/10.1177\/0278364920953902","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,11]]}}}