{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T21:14:47Z","timestamp":1772918087096,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T00:00:00Z","timestamp":1566777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Frontier Science &amp; Technology Innovation Project","award":["19-163-11-ZT-005-004-02"],"award-info":[{"award-number":["19-163-11-ZT-005-004-02"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51975070"],"award-info":[{"award-number":["51975070"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Special Cooperation Program for Higher Education Institutions Collaborative Innovation","award":["KH2016006"],"award-info":[{"award-number":["KH2016006"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2018CDGFJX0022"],"award-info":[{"award-number":["2018CDGFJX0022"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2019CDCGJX219"],"award-info":[{"award-number":["2019CDCGJX219"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents a novel CPG-based gait generation of the curved-leg hexapod robot that can enable smooth gait transitions between multi-mode gaits. First, the locomotion of the curved leg and instability during the gait transitions are analyzed. Then, a modified Hopf oscillator is applied in the CPG control, which can realize multiple gaits by adjusting a simple parameter. In addition, a smooth gait switching method is also proposed via smooth gait transition functions and gait planning. Tripod gait, quadruped gait, and wave gait are planned for the hexapod robot to achieve quick and stable gait transitions smoothly and continuously. MATLAB and ADAMS simulations and corresponding practical experiments are conducted. The results show that the proposed method can achieve smooth and continuous mutual gait transitions, which proves the effectiveness of the proposed CPG-based hexapod robot control.<\/jats:p>","DOI":"10.3390\/s19173705","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T10:54:53Z","timestamp":1566816893000},"page":"3705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["CPG-Based Gait Generation of the Curved-Leg Hexapod Robot with Smooth Gait Transition"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9410-5107","authenticated-orcid":false,"given":"Long","family":"Bai","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"},{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohong","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0054-1053","authenticated-orcid":false,"given":"Yuanxi","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoyang","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5689-1146","authenticated-orcid":false,"given":"Yuanhong","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication of Engineering, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1126\/science.1254486","article-title":"Biorobotics: Using robots to emulate and investigate agile locomotion","volume":"364","author":"Ijspeert","year":"2014","journal-title":"Science"},{"key":"ref_2","unstructured":"Arikawa, K., and Hirose, S. (1996, January 8). Development of Quadruped Walking Robot TITAN-VIII. Proceedings of the International Conference on Intelligent Robots and Systems, Osaka, Japan."},{"key":"ref_3","unstructured":"Berns, K., IIg, W., Deck, M., and Dillmann, R. (July, January 29). The mammalian-like quadrupedal walking machine BISAM. Proceedings of the International Conference on Control Applications, Coimbra, Portugal."},{"key":"ref_4","unstructured":"Ga\u00dfmann, B., and Scholl, K.U. (2001, January 8\u201312). Locomotion of LAURON III in rough terrain. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics IEEE, Como, Italy."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.asd.2004.06.003","article-title":"Mechanical aspects of legged locomotion control","volume":"33","author":"Koditschek","year":"2004","journal-title":"Arthropod Struct. Dev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1038\/nature14422","article-title":"Robots that can adapt like animals","volume":"521","author":"Cully","year":"2014","journal-title":"Nature"},{"key":"ref_7","first-page":"5001","article-title":"Dynamic Hybrid Control of a Hexapod Walking Robot: Experimental Verification","volume":"63","author":"Zhong","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1016\/S0893-6080(98)00067-7","article-title":"Walknet-a biologically inspired network to control six-legged walking","volume":"11","author":"Cruse","year":"1998","journal-title":"Neural Netw."},{"key":"ref_9","first-page":"81","article-title":"Walknet-a decentralized architecture for the control of walking behaviour based on insect studies","volume":"467","author":"Cruse","year":"2004","journal-title":"Int. Centre Mech. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1177\/02783640122067570","article-title":"Rhex: A simple and highly mobile hexapod robot","volume":"20","author":"Saranli","year":"2001","journal-title":"Int. J. Robot. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1023\/A:1012426720699","article-title":"Rhex: A biologically inspired hexapod runner","volume":"11","author":"Altendorfer","year":"2001","journal-title":"Auton. Robot."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1080\/713603737","article-title":"Efficiency, speed, and scaling of two-dimensional passive-dynamic walking","volume":"15","author":"Garcia","year":"2000","journal-title":"Dyn. Stab. Syst."},{"key":"ref_13","unstructured":"Moore, E.Z. (2002, January 11\u201315). Reliable Stair Climbing in the Simple Hexapod \u2018RHex\u2019. Proceedings of the IEEE International Conference on Robotics & Automation, Washington, DC, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Altendorfer, R., Saranli, U., and Komsuoglu, H. (2001). Evidence for spring loaded inverted pendulum running in a hexapod robot. Experimental Robotics VII, Springer.","DOI":"10.21236\/ADA438810"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1109\/TRO.2004.840898","article-title":"A Leg Configuration Measurement System for Full-Body Pose Estimates in a Hexapod Robot","volume":"21","author":"Lin","year":"2005","journal-title":"IEEE Trans. Robot."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Haynes, G.C., Pusey, J., and Knopf, R. (2012, January 23\u201327). Laboratory on Legs: An Architecture for Adjustable Morphology with Legged Robots. Proceedings of the SPIE Defense, Security, and Sensing, Baltimore, MD, USA.","DOI":"10.1117\/12.920678"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1109\/ACCESS.2013.2263192","article-title":"Legged Self-Manipulation","volume":"1","author":"Johnson","year":"2013","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Huang, K.J., and Lin, P.C. (2012, January 11\u201314). Rolling SLIP: A model for running locomotion with rolling contact. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Kachsiung, Taiwan.","DOI":"10.1109\/AIM.2012.6266018"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/TRO.2014.2376141","article-title":"Model-based development of leaping in a hexapod robot","volume":"31","author":"Chou","year":"2015","journal-title":"IEEE Trans. Robot."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chou, Y.C., Yu, W.S., Huang, K.J., and Lin, P.C. (2011, January 25\u201330). Bio-inspired step crossing algorithm for a hexapod robot. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots & Systems, San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6048161"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1720","DOI":"10.1109\/TMECH.2015.2490074","article-title":"AmphiHex-I: Locomotory performance in amphibious environments with specially designed transformable flipper legs","volume":"21","author":"Zhang","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/0166-2236(95)80008-P","article-title":"Neural networks that co-ordinate locomotion and body orientation in lamprey","volume":"18","author":"Grillner","year":"1995","journal-title":"Trends Neurosci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5488","DOI":"10.1109\/TIE.2016.2569489","article-title":"Gait generation with smooth transition using CPG-based locomotion control for hexapod walking robot","volume":"63","author":"Yu","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1016\/j.neunet.2008.03.014","article-title":"Central pattern generators for locomotion control in animals and robots: a review","volume":"21","author":"Ijspeert","year":"2008","journal-title":"Neural Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/TNNLS.2013.2280596","article-title":"A Survey on CPG-Inspired Control Models and System Implementation","volume":"25","author":"Yu","year":"2014","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF00319514","article-title":"Mechanism of frequency and pattern control in the neural rhythm generators","volume":"56","author":"Matsuoka","year":"1987","journal-title":"Biol. Cybern."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1177\/0278364907078089","article-title":"Adaptive dynamic walking of a quadruped robot on natural ground based on biological concepts","volume":"26","author":"Kimura","year":"2007","journal-title":"Int. J. Robot. Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.robot.2004.09.015","article-title":"Amphibot I: an amphibious snake-like robot","volume":"50","author":"Crespi","year":"2005","journal-title":"Robot. Autom. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s10514-009-9168-1","article-title":"Adaptive creeping locomotion of a CPG-controlled snake-like robot to environment change","volume":"28","author":"Wu","year":"2010","journal-title":"Auton. Robot."},{"key":"ref_30","unstructured":"Hu, Y., Tian, W., Liang, J., and Wang, T. (2011, January 25\u201330). Learning fish-like swimming with A CPG-based locomotion controller. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots & Systems, San Francisco, CA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1109\/TNNLS.2015.2459913","article-title":"CPG Network Optimization for a Biomimetic Robotic Fish via PSO","volume":"27","author":"Yu","year":"2016","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1177\/0278364907084980","article-title":"Learning CPG-based biped locomotion with a policy gradient method: application to a humanoid robot","volume":"27","author":"Endo","year":"2008","journal-title":"Int. J. Robot. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00422-010-0373-y","article-title":"Evaluating functional roles of phase resetting in generation of adaptive human bipedal walking with a physiologically based model of the spinal pattern generator","volume":"102","author":"Aoi","year":"2010","journal-title":"Biol. Cybern."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1007\/s00422-013-0572-4","article-title":"Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation","volume":"107","author":"Fukuoka","year":"2013","journal-title":"Biol. Cybern."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1109\/TRO.2017.2696022","article-title":"TurboQuad: A Novel Leg-Wheel Transformable Robot with Smooth and Fast Behavioral Transitions","volume":"33","author":"Chen","year":"2017","journal-title":"IEEE Trans. Robot."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.mechatronics.2016.01.003","article-title":"Prototype, control system architecture and controlling of the hexapod legs with nonlinear stick-slip vibrations","volume":"37","author":"Grzelczyk","year":"2016","journal-title":"Mechatronics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1109\/TCST.2017.2692727","article-title":"Locomotion control and gait planning of a novel hexapod robot using biomimetic neurons","volume":"26","author":"Zhong","year":"2018","journal-title":"IEEE Trans. Control Syst. Tech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"8042","DOI":"10.1109\/ACCESS.2018.2799145","article-title":"Versatile locomotion control of a hexapod robot using a hierarchical network of nonlinear oscillator circuits","volume":"6","author":"Minati","year":"2018","journal-title":"IEEE Access"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1823","DOI":"10.1109\/TSMCB.2004.828593","article-title":"An adaptive, self-organizing dynamical system for hierarchical control of bio-inspired locomotion","volume":"34","author":"Arena","year":"2004","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Frasca, M., Arena, P., and Fortuna, L. (2004). Bio-Inspired Emergent Control of Locomotion Systems. World Scientific.","DOI":"10.1142\/9789812562302"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/0025-5564(68)90090-4","article-title":"On the stability properties of quadruped creeping gaits","volume":"3","author":"McGhee","year":"1968","journal-title":"Math. Biosci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/TSMC.1979.4310180","article-title":"Adaptive locomotion of a multilegged robot over rough terrain","volume":"9","author":"Mcghee","year":"1979","journal-title":"IEEE Trans. Syst. Man Cybern."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/17\/3705\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:14:08Z","timestamp":1760188448000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/17\/3705"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,26]]},"references-count":42,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["s19173705"],"URL":"https:\/\/doi.org\/10.3390\/s19173705","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,26]]}}}