{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T12:38:47Z","timestamp":1766579927480,"version":"build-2065373602"},"reference-count":81,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Piecewise constant curvature soft actuators can generate various types of movements. These actuators can undergo extension, bending, rotation, twist, or a combination of these. Proprioceptive sensing provides the ability to track their movement or estimate their state in 3D space. Several proprioceptive sensing solutions were developed using soft strain sensors. However, current mathematical models are only capable of modelling the length of the soft sensors when they are attached to actuators subjected to extension, bending, and rotation movements. Furthermore, these models are limited to modelling straight sensors and incapable of modelling spiral sensors. In this study, for both the spiral and straight sensors, we utilise concepts in geodesics and covering spaces to present a mathematical length model that includes twist. This study is limited to the Piecewise constant curvature actuators and demonstrates, among other things, the advantages of our model and the accuracy when including and excluding twist. We verify the model by comparing the results to a finite element analysis. This analysis involves multiple simulation scenarios designed specifically for the verification process. Finally, we validate the theoretical results with previously published experimental results. Then, we discuss the limitations and possible applications of our model using examples from the literature.<\/jats:p>","DOI":"10.3390\/robotics12060164","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T03:58:02Z","timestamp":1701403082000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Length Modelling of Spiral Superficial Soft Strain Sensors Using Geodesics and Covering Spaces"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4319-1284","authenticated-orcid":false,"given":"Abdullah","family":"Al-Azzawi","sequence":"first","affiliation":[{"name":"Australian Centre for Field Robotics (ACFR), The University of Sydney, Sydney, NSW 2006, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5672-8971","authenticated-orcid":false,"given":"Peter","family":"Stadler","sequence":"additional","affiliation":[{"name":"e:fs Techhub GmbH, 85080 Gaimersheim, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1382-4186","authenticated-orcid":false,"given":"He","family":"Kong","sequence":"additional","affiliation":[{"name":"Shenzhen Key Laboratory of Control Theory and Intelligent Systems, and the Guangdong Provincial Key Laboratory of Human-Augmentation and Rehabilitation Robotics in Universities, Southern University of Science and Technology, Shenzhen 518055, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1173-9268","authenticated-orcid":false,"given":"Salah","family":"Sukkarieh","sequence":"additional","affiliation":[{"name":"Australian Centre for Field Robotics (ACFR), The University of Sydney, Sydney, NSW 2006, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1089\/soro.2017.0135","article-title":"Soft Robotics: Academic Insights and Perspectives through Bibliometric Analysis","volume":"5","author":"Bao","year":"2018","journal-title":"Soft Robot."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1700016","DOI":"10.1002\/adem.201700016","article-title":"Soft Robotics: Review of Fluid-Driven Intrinsically Soft Devices; Manufacturing, Sensing, Control, and Applications in Human-Robot Interaction","volume":"19","author":"Polygerinos","year":"2017","journal-title":"Adv. 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