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Besides, in order to determine the condition of using the improved discretization method, energy of framed space curve is introduced originally to estimate the shape complexity of the backbone curve. At last, based on degree elevation of the B\u00e9zier curve, an obstacle avoidance strategy of the head-raising motion was proposed and validated through simulation.<\/jats:p>","DOI":"10.1017\/s0263574720000533","type":"journal-article","created":{"date-parts":[[2020,6,30]],"date-time":"2020-06-30T07:49:31Z","timestamp":1593503371000},"page":"503-523","source":"Crossref","is-referenced-by-count":5,"title":["Head-Raising Method of Snake Robots Based on the B\u00e9zier Curve"],"prefix":"10.1017","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3532-9477","authenticated-orcid":false,"given":"Yunhu","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanfei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fenglei","family":"Ni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,6,30]]},"reference":[{"key":"S0263574720000533_ref10","unstructured":"[10] Ye, C. , Ma, S. , Li, B. and Wang, Y. , \u201cHead-Raising Motion of Snake-Like Robots,\u201d IEEE International Conference on Robotics and Biomimetics, Shenyang, China (2004) pp. 595\u2013600."},{"key":"S0263574720000533_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-009-9175-2"},{"key":"S0263574720000533_ref27","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/aa644c"},{"key":"S0263574720000533_ref21","volume-title":"Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable","author":"Edelsbrunner","year":"2008"},{"key":"S0263574720000533_ref33","unstructured":"[33] Zacharias, F. , Borst, C. and Hirzinger, G. , \u201cCapturing Robot Workspace Structure: Representing Robot Capabilities,\u201d IEEE\/RSJ International Conference on Intelligent Robots & Systems, San Diego, CA, USA (2007) pp. 3229\u20133236."},{"key":"S0263574720000533_ref29","unstructured":"[29] Takemori, T. , Tanaka, M. and Matsuno, F. , \u201cGait Design of a Snake Robot by Connecting Simple Shapes,\u201d IEEE International Symposium on Safety, Security, and Rescue Robotics, Lausanne, Switzerland (2016) pp. 189\u2013194."},{"key":"S0263574720000533_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S026357471300091X"},{"key":"S0263574720000533_ref8","unstructured":"[8] Zhen, W. , Gong, C. and Choset, H. , \u201cModeling Rolling Gaits of a Snake Robot,\u201d IEEE International Conference on Robotics and Automation, Seattle, WA, USA (2015) pp. 3741\u20133746."},{"key":"S0263574720000533_ref4","doi-asserted-by":"publisher","DOI":"10.3390\/app8112011"},{"key":"S0263574720000533_ref31","unstructured":"[31] Kamegawa, T. , Baba, T. and Gofuku, A. , \u201cV-shift Control for Snake Robot Moving the Inside of a Pipe with Helical Rolling Motion,\u201d IEEE International Symposium on Safety, Security, and Rescue Robotics, Kyoto, Japan (2011) pp. 1\u20136."},{"key":"S0263574720000533_ref17","first-page":"867","article-title":"Generating optimal reference kinematic configurations for hyper-redundant parallel robots","volume":"229","author":"Chibani","year":"2015","journal-title":"P. 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Y. , Stavdahl, \u00d8. and Gravdahl, J. T. , \u201cA Control Framework for Snake Robot Locomotion Based on Shape Control Points Interconnected by B\u00e9zier Curves,\u201d IEEE\/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Portugal (2012) pp. 3111\u20133118."},{"key":"S0263574720000533_ref20","unstructured":"[20] Yamada, H. and Hirose, S. , \u201cApproximations to Continuous Curves of Active Cord Mechanism Made of Arc-Shaped Joints or Double Joints,\u201d IEEE International Conference on Robotics and Automation, Anchorage, AK, USA (2010) pp. 703\u2013708."},{"key":"S0263574720000533_ref11","unstructured":"[11] Xiao, X. , Cappo, E. , Zhen, W. , Dai, J. , Sun, K. , Gong, C. , Travers, M.J. and Choset, H. , \u201cLocomotive Reduction for Snake Robots,\u201d IEEE International Conference on Robotics and Automation, Seattle, WA, USA (2015) pp. 3735\u20133740."},{"key":"S0263574720000533_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574708005195"},{"key":"S0263574720000533_ref19","doi-asserted-by":"publisher","DOI":"10.7210\/jrsj.26.110"},{"key":"S0263574720000533_ref32","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016280811626"},{"key":"S0263574720000533_ref12","doi-asserted-by":"publisher","DOI":"10.1002\/rob.21549"},{"key":"S0263574720000533_ref34","doi-asserted-by":"publisher","DOI":"10.1109\/MRA.2011.2181749"},{"key":"S0263574720000533_ref5","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/aa7725"},{"key":"S0263574720000533_ref3","doi-asserted-by":"publisher","DOI":"10.1177\/1687814017721854"},{"key":"S0263574720000533_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-013-9866-y"},{"key":"S0263574720000533_ref26","unstructured":"[26] Kamegawa, T. , Harada, T. and Gofuku, A. , \u201cRealization of Cylinder Climbing Locomotion with Helical form by a Snake Robot with Passive Wheels,\u201d IEEE International Conference on Robotics and Automation, Kobe, Japan (2009) pp. 3067\u20133072."},{"key":"S0263574720000533_ref6","doi-asserted-by":"publisher","DOI":"10.1080\/01691864.2015.1118409"},{"key":"S0263574720000533_ref16","unstructured":"[16] Zanganeh, K. 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