{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T12:10:48Z","timestamp":1768997448648,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,10,2]],"date-time":"2007-10-02T00:00:00Z","timestamp":1191283200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Dyn Control Syst"],"published-print":{"date-parts":[[2007,10,23]]},"DOI":"10.1007\/s10883-007-9027-3","type":"journal-article","created":{"date-parts":[[2007,10,1]],"date-time":"2007-10-01T08:27:45Z","timestamp":1191227265000},"page":"467-502","source":"Crossref","is-referenced-by-count":55,"title":["On the Geometry of Rolling and Interpolation Curves on S n , SO n , and Grassmann Manifolds"],"prefix":"10.1007","volume":"13","author":[{"given":"K.","family":"H\u00fcper","sequence":"first","affiliation":[]},{"given":"F.","family":"Silva Leite","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,10,2]]},"reference":[{"key":"9027_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-06404-7","volume-title":"Control theory from the geometric viewpoint","author":"A. A. Agrachev","year":"2004","unstructured":"A. A. Agrachev and Yu. L. Sachkov, Control theory from the geometric viewpoint. Springer-Verlag, Berlin (2004)."},{"key":"9027_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/b97376","volume-title":"Nonholonomic mechanics and control","author":"A. M. Bloch","year":"2003","unstructured":"A. M. Bloch, Nonholonomic mechanics and control. Springer-Verlag, New York (2003)."},{"key":"9027_CR3","unstructured":"M. Camarinha, The geometry of cubic polynomials on Riemannian manifolds. Ph.D. thesis, University of Coimbra, Portugal (1996)."},{"key":"9027_CR4","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1093\/imamci\/12.4.399","volume":"12","author":"M. Camarinha","year":"1995","unstructured":"M. Camarinha, F. Silva Leite, and P. Crouch, Splines of class $\\mathcal{C}^{k}$ on non-Eulidean spaces. J. Math. Control Inform. 12 (1995), 399\u2013410.","journal-title":"J. Math. Control Inform."},{"issue":"3","key":"9027_CR5","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1023\/A:1021770717822","volume":"5","author":"P. Crouch","year":"1999","unstructured":"P. Crouch, G. Kun, and F. Silva Leite, The De Casteljau algorithm on Lie groups and spheres. J. Dynam. Control Systems 5 (1999), No. 3, 397\u2013429.","journal-title":"J. Dynam. Control Systems"},{"key":"9027_CR6","doi-asserted-by":"crossref","unstructured":"P. Crouch and F. Silva Leite, Geometry and the dynamic interpolation problem. In: Proc. American Control Conference, Boston (1991), pp. 1131\u20131136.","DOI":"10.23919\/ACC.1991.4791552"},{"issue":"2","key":"9027_CR7","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF02254638","volume":"1","author":"P. Crouch","year":"1995","unstructured":"P. Crouch and F. Silva Leite, The dynamic interpolation problem on Riemannian manifolds, Lie groups, and symmetric spaces. J. Dynam. Control Systems 1 (1995), No. 2, 177\u2013202.","journal-title":"J. Dynam. Control Systems"},{"key":"9027_CR8","unstructured":"P. De Casteljau, Outillages m\u00e9thodes calcul. Technical report, A. Citroen, Paris (1959)."},{"key":"9027_CR9","volume-title":"Curves and surfaces for CAGD: a practical guide","author":"G. Farin","year":"2002","unstructured":"G. Farin, Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann, San Francisco (2002)."},{"key":"9027_CR10","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1093\/imamci\/19.4.445","volume":"19","author":"R. Giamb\u00f3","year":"2002","unstructured":"R. Giamb\u00f3, F. Giannoni, and P. Piccione, An analytical theory for Riemannian cubic polynomials. IMA J. Math. Control Inform. 19 (2002), 445\u2013460.","journal-title":"IMA J. Math. Control Inform."},{"key":"9027_CR11","volume-title":"Lie groups, Lie algebras, and some of their applications","author":"R. Gilmore","year":"1974","unstructured":"R. Gilmore, Lie groups, Lie algebras, and some of their applications. Wiley, New York (1974)."},{"key":"9027_CR12","unstructured":"U. Helmke, K. H\u00fcper, and J. Trumpf, Newton\u2019s method on Grassmann manifolds. (in press)."},{"key":"9027_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-3467-1","volume-title":"Optimization and dynamical systems","author":"U. Helmke","year":"1994","unstructured":"U. Helmke and J. B. Moore, Optimization and dynamical systems. CCES, Springer-Verlag, London (1994)."},{"key":"9027_CR14","unstructured":"K. H\u00fcper, M. Kleinsteuber, and F. Silva Leite, Rolling Stiefel manifolds. Int. J. Systems Sci. (to appear)."},{"key":"9027_CR15","unstructured":"K. H\u00fcper and F. Silva Leite, Smooth interpolating curves with applications to path planning. In: 10th IEEE Mediterranean Conference on Control and Automation, Instituto Superior T\u00e9cnico, Lisboa, Portugal, July, 9\u201312, 2002 (on CDROM)."},{"key":"9027_CR16","unstructured":"K. H\u00fcper and F. Silva Leite, On the geometry of rolling and interpolation curves on S n , SO n , and Grassmann manifolds. Technical Report SISSA 56\/2005\/M, Int. School for Adv. Stud., Trieste, Italy (2005)."},{"issue":"1","key":"9027_CR17","doi-asserted-by":"crossref","first-page":"34","DOI":"10.2307\/2347843","volume":"36","author":"P. E. Jupp","year":"1987","unstructured":"P. E. Jupp and J. T. Kent, Fitting smooth paths to spherical data. Appl. Statist. 36 (1987), No. 1, 34\u201346.","journal-title":"Appl. Statist."},{"key":"9027_CR18","volume-title":"Geometric control theory","author":"V. Jurdjevic","year":"1997","unstructured":"V. Jurdjevic, Geometric control theory. Cambridge Univ. Press, Cambridge (1997)."},{"key":"9027_CR19","volume-title":"Foundations of differential geometry, Vol. I","author":"S. Kobayashi","year":"1996","unstructured":"S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. I. Wiley, New York (1996)."},{"key":"9027_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/b98852","volume-title":"Riemannian manifolds: An introduction to curvature","author":"J. M. Lee","year":"1997","unstructured":"J. M. Lee, Riemannian manifolds: An introduction to curvature. Springer-Verlag, New York (1997)."},{"key":"9027_CR21","series-title":"Ann. Math. Stud.","volume-title":"Morse theory. Based on lecture notes by M. Spivak and R. Wells","author":"J. W. Milnor","year":"1963","unstructured":"J. W. Milnor, Morse theory. Based on lecture notes by M. Spivak and R. Wells. Ann. Math. Stud. 51, Princeton Univ. Press, Princeton, New Jersey (1963)."},{"key":"9027_CR22","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1093\/imamci\/6.4.465","volume":"6","author":"L. Noakes","year":"1989","unstructured":"L. Noakes, G. Heinzinger, and B. Paden, Cubic splines on curved spaces. IMA J. Math. Control Inform. 6 (1989), 465\u2013473.","journal-title":"IMA J. Math. Control Inform."},{"key":"9027_CR23","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1115\/1.2826114","volume":"117","author":"F. C. Park","year":"1995","unstructured":"F. C. Park and B. Ravani, B\u00e9zier curves on Riemannian manifolds and Lie groups with kinematics applications. ASME J. Mech. Design 117 (1995), 36\u201340.","journal-title":"ASME J. Mech. Design"},{"key":"9027_CR24","volume-title":"Differential geometry","author":"R. W. Sharpe","year":"1996","unstructured":"R. W. Sharpe, Differential geometry. Springer-Verlag, New York (1996)."},{"key":"9027_CR25","unstructured":"Y. Shen and K. H\u00fcper, Optimal joint trajectory planning for manipulator robot performing constrained motion tasks. In: Australasian Conf. on Robotics and Automation, Canberra, December 2004 (on CDROM)."},{"key":"9027_CR26","doi-asserted-by":"crossref","unstructured":"Y. Shen and K. H\u00fcper, Optimal joint trajectory planning of manipulators subject to motion constraints. In: Int. Conf. on Advanced Robotics (ICAR 2005), Seattle, July 2005 (on CDROM).","DOI":"10.1109\/ICAR.2005.1507384"},{"key":"9027_CR27","unstructured":"Y. Shen, K. H\u00fcper, and F. Silva Leite, Smooth interpolation of orientation by rolling and wrapping for robot motion planning. In: IEEE Int. Conf. on Robotics and Automation (ICRA 2006), Orlando, Florida, USA (2006), pp. 113\u2013118."},{"key":"9027_CR28","unstructured":"S. T. Smith, Geometric optimization methods for adaptive filtering. Ph.D. thesis, Harvard University, Cambridge (1993)."},{"key":"9027_CR29","first-page":"113","volume-title":"Hamiltonian and gradient flows, algorithms and control","author":"S. T. Smith","year":"1994","unstructured":"S. T. Smith, Optimization techniques on Riemannian manifolds. In: Hamiltonian and gradient flows, algorithms and control (A. Bloch, ed.), Fields Inst. Commun. Amer. Math. Soc., Providence (1994), pp. 113\u2013136."},{"key":"9027_CR30","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/s00498-004-0143-2","volume":"17","author":"J. A. Zimmerman","year":"2005","unstructured":"J. A. Zimmerman, Optimal control of the sphere S n rolling on E n . Math. Control Signals Systems 17 (2005), 14\u201337.","journal-title":"Math. Control Signals Systems"}],"container-title":["Journal of Dynamical and Control Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10883-007-9027-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10883-007-9027-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10883-007-9027-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:33:04Z","timestamp":1559262784000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10883-007-9027-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10,2]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,10,23]]}},"alternative-id":["9027"],"URL":"https:\/\/doi.org\/10.1007\/s10883-007-9027-3","relation":{},"ISSN":["1079-2724","1573-8698"],"issn-type":[{"value":"1079-2724","type":"print"},{"value":"1573-8698","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,10,2]]}}}