{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T17:51:33Z","timestamp":1772301093930,"version":"3.50.1"},"reference-count":85,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2021,1,16]],"date-time":"2021-01-16T00:00:00Z","timestamp":1610755200000},"content-version":"vor","delay-in-days":366,"URL":"http:\/\/www.sagepub.com\/licence-information-for-chorus"}],"funder":[{"DOI":"10.13039\/100015599","name":"Toyota Research Institute","doi-asserted-by":"crossref","award":["N021515"],"award-info":[{"award-number":["N021515"]}],"id":[{"id":"10.13039\/100015599","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1808051"],"award-info":[{"award-number":["1808051"]}],"id":[{"id":"10.13039\/100000001","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":[[2020,3]]},"abstract":"<jats:p> Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of kinematic and contact data with measurements from an inertial measurement unit (IMU). In this work, we develop a contact-aided invariant extended Kalman filter (InEKF) using the theory of Lie groups and invariant observer design. This filter combines contact-inertial dynamics with forward kinematic corrections to estimate pose and velocity along with all current contact points. We show that the error dynamics follows a log-linear autonomous differential equation with several important consequences: (a) the observable state variables can be rendered convergent with a domain of attraction that is independent of the system\u2019s trajectory; (b) unlike the standard EKF, neither the linearized error dynamics nor the linearized observation model depend on the current state estimate, which (c) leads to improved convergence properties and (d) a local observability matrix that is consistent with the underlying nonlinear system. Furthermore, we demonstrate how to include IMU biases, add\/remove contacts, and formulate both world-centric and robo-centric versions. We compare the convergence of the proposed InEKF with the commonly used quaternion-based extended Kalman filter (EKF) through both simulations and experiments on a Cassie-series bipedal robot. Filter accuracy is analyzed using motion capture, while a LiDAR mapping experiment provides a practical use case. Overall, the developed contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in system. <\/jats:p>","DOI":"10.1177\/0278364919894385","type":"journal-article","created":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T10:07:03Z","timestamp":1579169223000},"page":"402-430","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":269,"title":["Contact-aided invariant extended Kalman filtering for robot state estimation"],"prefix":"10.1177","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4605-4333","authenticated-orcid":false,"given":"Ross","family":"Hartley","sequence":"first","affiliation":[{"name":"Robotics Institute and College of Engineering, University of Michigan, Ann Arbor, MI, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4734-4295","authenticated-orcid":false,"given":"Maani","family":"Ghaffari","sequence":"additional","affiliation":[{"name":"Robotics Institute and College of Engineering, University of Michigan, Ann Arbor, MI, USA"}]},{"given":"Ryan M","family":"Eustice","sequence":"additional","affiliation":[{"name":"Robotics Institute and College of Engineering, University of Michigan, Ann Arbor, MI, USA"}]},{"given":"Jessy W","family":"Grizzle","sequence":"additional","affiliation":[{"name":"Robotics Institute and College of Engineering, University of Michigan, Ann Arbor, MI, USA"}]}],"member":"179","published-online":{"date-parts":[[2020,1,16]]},"reference":[{"key":"bibr1-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2002.1184728"},{"key":"bibr2-0278364919894385","volume-title":"Optimal Filtering","author":"Anderson BD","year":"1979"},{"key":"bibr3-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1002\/0471221279"},{"key":"bibr4-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2011.6160733"},{"key":"bibr5-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2012.2195495"},{"key":"bibr6-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1017\/9781316671528"},{"key":"bibr7-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2014.2298059"},{"key":"bibr8-0278364919894385","volume-title":"Non-linear state error based extended Kalman filters with applications to navigation","author":"Barrau A","year":"2015"},{"key":"bibr9-0278364919894385","author":"Barrau A","year":"2015","journal-title":"arXiv preprint arXiv:1510.06263"},{"key":"bibr10-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2594085"},{"key":"bibr11-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-control-060117-105010"},{"key":"bibr12-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2019.2929112"},{"key":"bibr13-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/70.388775"},{"key":"bibr14-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1142\/S0219843615500255"},{"key":"bibr15-0278364919894385","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2013.6697236"},{"key":"bibr16-0278364919894385","volume-title":"Robotics: Science and Systems Conference (RSS 2012)","author":"Bloesch M","year":"2012"},{"key":"bibr17-0278364919894385","unstructured":"Bloesch MA (2017) State Estimation for Legged Robots\u2014Kinematics, Inertial Sensing, and Computer Vision. 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