{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T12:00:31Z","timestamp":1742644831089,"version":"3.38.0"},"reference-count":37,"publisher":"SAGE Publications","issue":"13-14","license":[{"start":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T00:00:00Z","timestamp":1666310400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"name":"Natural Sciences and Engineering Research Council (NSERC) of Canada"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2022,11]]},"abstract":" Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to their unique shape, compliance, and size. Excellent progress has been made in the mechanical design and dynamic modeling of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored. In this paper, we turn to the problem of state estimation for continuum robots that can been modeled with the common Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils, or strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for continuous-time trajectory estimation in SE(3). In our case, the continuous variable is not time but arclength and we show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a continuum robot\u2019s shape can be achieved, resulting in average end-effector errors between the estimated and ground truth shape as low as 3.5\u00a0mm and 0.016\u00b0 in simulation or 3.3\u00a0mm and 0.035\u00b0 for unloaded configurations and 6.2\u00a0mm and 0.041\u00b0 for loaded ones during experiments, when using discrete pose measurements. <\/jats:p>","DOI":"10.1177\/02783649221128843","type":"journal-article","created":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T11:21:57Z","timestamp":1666351317000},"page":"1099-1120","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":27,"title":["Continuum robot state estimation using Gaussian process regression on SE(3)"],"prefix":"10.1177","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8503-0273","authenticated-orcid":false,"given":"Sven","family":"Lilge","sequence":"first","affiliation":[{"name":"Robotics Institute, University of Toronto, Toronto, ON, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3899-631X","authenticated-orcid":false,"given":"Timothy D.","family":"Barfoot","sequence":"additional","affiliation":[{"name":"Robotics Institute, University of Toronto, Toronto, ON, Canada"},{"name":"Autonomous Space Robotics Laboratory, Institute for Aerospace Studies, University of Toronto, Toronto, ON, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9185-3970","authenticated-orcid":false,"given":"Jessica","family":"Burgner-Kahrs","sequence":"additional","affiliation":[{"name":"Robotics Institute, University of Toronto, Toronto, ON, Canada"},{"name":"Continuum Robotics Laboratory, Department of Mathematical & Computational Sciences, University of Toronto, Mississauga, 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