{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:51:15Z","timestamp":1760161875590,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,3]],"date-time":"2021-01-03T00:00:00Z","timestamp":1609632000000},"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>Kinematic redundancy of manipulators is a well-understood topic, and various methods were developed for the redundancy resolution in order to solve the inverse kinematics problem, at least for serial manipulators. An important question, with high practical relevance, is whether the inverse kinematics solution is cyclic, i.e., whether the redundancy solution leads to a closed path in joint space as a solution of a closed path in task space. This paper investigates the cyclicity property of two widely used redundancy resolution methods, namely the projected gradient method (PGM) and the augmented Jacobian method (AJM), by means of examples. Both methods determine solutions that minimize an objective function, and from an application point of view, the sensitivity of the methods on the initial configuration is crucial. Numerical results are reported for redundant serial robotic arms and for redundant parallel kinematic manipulators. While the AJM is known to be cyclic, it turns out that also the PGM exhibits cyclicity. However, only the PGM converges to the local optimum of the objective function when starting from an initial configuration of the cyclic trajectory.<\/jats:p>","DOI":"10.3390\/robotics10010009","type":"journal-article","created":{"date-parts":[[2021,1,3]],"date-time":"2021-01-03T19:54:46Z","timestamp":1609703686000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Investigation of Cyclicity of Kinematic Resolution Methods for Serial and Parallel Planar Manipulators"],"prefix":"10.3390","volume":"10","author":[{"given":"Maurizio","family":"Ruggiu","sequence":"first","affiliation":[{"name":"Department of Mechanical, Chemical and Materials Engineering, University of Cagliari, Via Marengo, 2, 09123 Cagliari, Italy"}]},{"given":"Andreas","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Institut for Robotics, Johannes Kepler University, Altenberger Stra\u00dfe, 69-4040 Linz, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1002\/rob.4620060607","article-title":"Redundancy Resolution through Local Optimization: A Review","volume":"6","author":"Nenchev","year":"1989","journal-title":"J. Robot. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF00126069","article-title":"Kinematic Control of Redundant Robot Manipulators: A Tutorial","volume":"3","author":"Siciliano","year":"1990","journal-title":"J. Lntelligent Robot. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1109\/9.14412","article-title":"Repeatability of Redundant Manipulators: Mathematical Solution of the Problem","volume":"33","author":"Shamir","year":"1988","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/70.88043","article-title":"The nature of drift in pseudo-inverse control of kinematically redundant manipulators","volume":"RA-5","author":"Klein","year":"1989","journal-title":"IEEE Trans. Robot. 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Proceedings of the IEEE International Conference on Robot and Automation, St. Louis, MO, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"020913","DOI":"10.1115\/1.4042514","article-title":"A Technique Based on Adaptive Extended Jacobians for Improving the Robustness of the Inverse Numerical Kinematics of Redundant Robots","volume":"11","author":"Simas","year":"2019","journal-title":"J. Mech. Robot."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"020019","DOI":"10.1063\/1.5029595","article-title":"An Efficient Approach for Inverse Kinematics and Redundancy Resolution Scheme of Hyper-Redundant Manipulators","volume":"1943","author":"Chembuly","year":"2018","journal-title":"AIP Conf. Proc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.simpat.2010.08.001","article-title":"Geometrical Approach of Planar Hyper-Redundant Manipulators: Inverse Kinematics, Path Planning and Workspace","volume":"19","author":"Yahya","year":"2011","journal-title":"Simul. Modell. Pract. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Perrusqu\u00eda, A., Yu, W., and Li, X. (2020). Multi-agent reinforcement learning for redundant robot control in task-space. Int. J. Mach. Learn. Cybern.","DOI":"10.1007\/s13042-020-01167-7"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/JRA.1987.1087114","article-title":"A closed-form solution for inverse kinematics of robot manipulators","volume":"3","author":"Chang","year":"1987","journal-title":"IEEE J. Robot. Automat."},{"key":"ref_13","unstructured":"Boothby, W.M. (2003). 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Autom."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/10\/1\/9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:06:28Z","timestamp":1760159188000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/10\/1\/9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,3]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["robotics10010009"],"URL":"https:\/\/doi.org\/10.3390\/robotics10010009","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2021,1,3]]}}}