{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:54:40Z","timestamp":1777715680704,"version":"3.51.4"},"reference-count":26,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[1999,6,1]],"date-time":"1999-06-01T00:00:00Z","timestamp":928195200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:p>This paper provides a theoretical framework for controlling a manipulator with hyper degrees of freedom (HDOF). An HDOF manipulator has the capability to achieve various kinds of tasks. To make full use of its capability, shape control is proposed here; that is, not only the tip of a manipulator, but also its whole body is controlled. To formulate control objectives for shape control, we define a shape correspondence between an HDOF manipulator and a spatial curve that prescribes a desired shape. The shape correspondence is defined by using solutions of a nonlinear optimization problem termed the shape-inverse problem. We give theorems on the existence of the solutions, and on an existence region that allows us to convert shape-control problems into more tractable ones. A shape-regulation control problem is considered first to bring an HDOF manipulator onto a given time-invariant curve. The idea of estimating the desired curve parameters is the crucial key to solving the problem by Lyapunov design. The derived shape-regulation law includes the estimator, which infers the desired curve parameters corresponding to the desired joint positions on the curve. The idea of the desired curve-parameter estimation is also effective for shape tracking where a time-varying curve is used for prescribing a moving desired shape. Considering an estimator with second-order dynamics enables us to find two shape-tracking control laws by utilizing conventional tracking methods in manipulator control. We show the simulation results of applying the derived shape-tracking control laws to a 20-DOF manipulator.<\/jats:p>","DOI":"10.1177\/02783649922066411","type":"journal-article","created":{"date-parts":[[2003,7,19]],"date-time":"2003-07-19T02:59:46Z","timestamp":1058583586000},"page":"584-600","source":"Crossref","is-referenced-by-count":53,"title":["Shape Control of Manipulators with Hyper Degrees of Freedom"],"prefix":"10.1177","volume":"18","author":[{"given":"Hiromi","family":"Mochiyama","sequence":"first","affiliation":[{"name":"School of Information Science, Japan Advanced Institute of Science and                         Technology Hokuriku, Tatsunokuchi 1-1, Ishikawa 923-1292, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Etsujiro","family":"Shimemura","sequence":"additional","affiliation":[{"name":"School of Information Science, Japan Advanced Institute of Science and                         Technology Hokuriku, Tatsunokuchi 1-1, Ishikawa 923-1292, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hisato","family":"Kobayashi","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Hosei University,                         Kajinocho 3-7-2, Koganei, Tokyo 184-8584, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1999,6,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/70.265918"},{"key":"atypb2","unstructured":"Chirikjian, G. S. 1992. Theory and applications of hyper-redundant robotic mechanisms. PhD thesis, Department of Applied Mechanics, California Institute of Technology."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/70.294209"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/70.478427"},{"key":"atypb5","unstructured":"Hirose, S. 1993. Biologically Inspired Robots: Snake-Like Locomotors and Manipulators. Oxford: Oxford Science Publications ."},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"Ivanescu, M., and Stoian, V. 1995. A variable structure controller for a tentacle manipulator . Proc. of the 1995 IEEE Intl. Conf. on Robot. and Automat., vol. 3. Washington, DC: IEEE, pp. 3155\u20133160 .","DOI":"10.1109\/ROBOT.1995.525734"},{"key":"atypb7","unstructured":"Khalil, H. 1996. Nonlinear Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall ."},{"key":"atypb8","unstructured":"Kobayashi, S. 1995. Differential Geometry of Curves and Surfaces. Tokyo:Shokabo . (In Japanese.)"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"Ma, S., and Konno, M. 1997. An obstacle avoidance scheme for hyper-redundant manipulators: Global motion planning in posture space . Proc. of the 1997 IEEE Intl. Conf. on Robot. and Automat., vol. 1. Washington, DC: IEEE, pp. 161\u2013166 .","DOI":"10.1109\/ROBOT.1997.620032"},{"key":"atypb10","unstructured":"Mochiyama, H. 1998. Shape control of manipulators with hyper degrees of freedom. PhD thesis, School of Information Science, Japan Advanced Institute of Science and Technology."},{"key":"atypb11","unstructured":"Mochiyama, H., and Kobayashi, H. Forthcoming. The shape Jacobian of a manipulator with hyper degrees of freedom . Proc. of the 1999 IEEE Intl. Conf. on Robot. and Automat. Washington, DC: IEEE."},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"Mochiyama, H., Shimemura, E., and Kobayashi, H. 1998. Direct kinematics of manipulators with hyper degrees of freedom and Frenet-Serret formula . Proc. of the 1998 IEEE Intl. Conf. on Robot. and Automat., vol. 2. Washington, DC: IEEE, pp. 1653\u20131658 .","DOI":"10.1109\/ROBOT.1998.677392"},{"key":"atypb13","unstructured":"Murray, R. M., Li, Z., and Sastry, S. S. 1994. A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press ."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620080207"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"Nilsson, M. 1997. Snake robot free climbing . Proc. of the 1997 IEEE Intl. Conf. on Robot. and Automat., vol. 4. Washington, DC: IEEE, pp. 3415\u20133420 .","DOI":"10.1109\/ROBOT.1997.606864"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"Paljug, E., Ohm, T., and Hayati, S. 1995. The JPL serpentine robot: A 12-DOF system for inspection. Proc. of the 1995 IEEE Intl. Conf. on Robot. and Automat., vol. 3. Washington, DC: IEEE , pp. 3143\u20133148.","DOI":"10.1109\/ROBOT.1995.525732"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"Salerno, R. J., Reinholts, C. F., and Dhande, S. G. 1990. Kinematics of long-chain variable geometry truss manipulators: An overview of solution techniques. Proc. of the 2nd Intl. Wkshp. on Adv. in Robot Kinemat., pp. 179\u2013187.","DOI":"10.1007\/978-3-7091-4433-6_21"},{"key":"atypb18","unstructured":"Salisbury, K. 1987. Whole arm manipulation . Proc. of the 4th Intl. Symp. on Robot. Res., pp. 183\u2013189 ."},{"key":"atypb19","unstructured":"Salisbury, K., Eberman, B., Levin, M., and Townsend, W. 1988. The design and control of an experimental wholearm manipulator . Proc. of the 5th Intl. Symp. on Robot. Res., pp. 233\u2013241 ."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1177\/027836498700600303"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1109\/37.120448"},{"key":"atypb22","unstructured":"Takanashi, N. 1995. Complete modular link with the active universal joint mechanism for 3-D hyper redundant robot . Proc. of the 34th Soc. of Instrument and Control Engineers Annual Conf., vol. 2, pp. 843\u2013844 . (In Japanese.)"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"Takegaki, M., and Arimoto, S. 1981. A new feedback method for dynamic control of manipulators . J. Dyn. Sys. Meas. Control 102: 119\u2013125 .","DOI":"10.1115\/1.3139651"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"Zanganeh, K. E., and Angeles, J. 1995. The inverse kinematics of hyper-redundant manipulators using splines. Proc. of the 1995 IEEE Intl. Conf. on Robot. and Automat., vol. 3. Washington, DC: IEEE , pp. 2797\u20132802.","DOI":"10.1109\/ROBOT.1995.525679"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"Zanganeh, K. E., Lee, R. S. K., and Hughes, P. C. 1997. A discrete model for the configuration control of hyper-redundant manipulators. Proc. of the 1997 IEEE Intl. Conf. on Robot. and Automat., vol. 1. Washington, DC: IEEE , pp. 167\u2013172.","DOI":"10.1109\/ROBOT.1997.620033"},{"key":"atypb26","unstructured":"The Zodiac [pseudonym for a 12-author group]. 1996. In Canudas de Wit, C., Siciliano, B., and Bastin, G. (eds.) Theory of Robot Control. Berlin: Springer ."}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649922066411","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649922066411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:15:53Z","timestamp":1777457753000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783649922066411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":26,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1999,6]]}},"alternative-id":["10.1177\/02783649922066411"],"URL":"https:\/\/doi.org\/10.1177\/02783649922066411","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}