{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T13:17:18Z","timestamp":1792156638876,"version":"4.4.0"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T00:00:00Z","timestamp":1675296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"FCT, through IDMEC, under LAETA","doi-asserted-by":"publisher","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Soft continuum robots are compliant mechanisms that rely on a deformable structure in order to achieve a desired posture. One of the challenges in designing and controlling this type of robot is to obtain the necessary proprioceptive information without resorting to external sensors, like cameras or 3D positioning devices. This requires a reliable and repeatable sensor that can be embedded in the highly deformable structure, distributed along its length, without imposing a significant change to the overall stiffness. This paper presents design considerations and practical results of estimating the tip position of a soft continuum manipulator module using embedded linear magnetic encoders. Three flexible scales with incremental tracks and a magnetic pole pitch of 2 mm are embedded in the robot structure as passive tendons, and six pairs of Hall effect linear sensors are used to measure the relative displacement between points along the outer surface of the structure. The curvature and tip position are then estimated from these measurements. Results are compared with the ground truth measurement of the tip position provided by a commercial optical tracker system. Average error estimates lower than 2.0 mm, with 8.7 mm peak value, were obtained for a robot module with a motion span of approximately 100 mm.<\/jats:p>","DOI":"10.3390\/s23031647","type":"journal-article","created":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T05:44:45Z","timestamp":1675316685000},"page":"1647","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["End-Point Position Estimation of a Soft Continuum Manipulator Using Embedded Linear Magnetic Encoders"],"prefix":"10.3390","volume":"23","author":[{"given":"Carlos F. R.","family":"Costa","sequence":"first","affiliation":[{"name":"Departamento de Engenharia Mec\u00e2nica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7586-6269","authenticated-orcid":false,"given":"Jo\u00e3o C. P.","family":"Reis","sequence":"additional","affiliation":[{"name":"Instituto de Engenharia Mec\u00e2nica\u2014IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,2]]},"reference":[{"key":"ref_1","unstructured":"Robinson, G., and Davies, J.B.C. (1999, January 10\u201315). Continuum robots-a state of the art. Proceedings of the 1999 IEEE International Conference on Robotics and Automation (Cat. 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