{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T04:56:51Z","timestamp":1696309011715},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2011,10,11]],"date-time":"2011-10-11T00:00:00Z","timestamp":1318291200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Control Signals Syst."],"published-print":{"date-parts":[[2011,12]]},"DOI":"10.1007\/s00498-011-0067-6","type":"journal-article","created":{"date-parts":[[2011,10,10]],"date-time":"2011-10-10T20:02:12Z","timestamp":1318276932000},"page":"177-197","source":"Crossref","is-referenced-by-count":1,"title":["On the transversality of functions at the core of the transverse function approach to control"],"prefix":"10.1007","volume":"23","author":[{"given":"David A.","family":"Liz\u00e1rraga","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,10,11]]},"reference":[{"key":"67_CR1","first-page":"181","volume-title":"Differential geometric control theory. Progress in Mathematics, vol 27","author":"RW Brockett","year":"1983","unstructured":"Brockett RW (1983) Asymptotic stability and feedback stabilization. In: Brockett RW, Millman RS, Sussmann HJ (eds) Differential geometric control theory. Progress in Mathematics, vol 27. Birkh\u00e4user, Boston, pp 181\u2013191"},{"key":"67_CR2","first-page":"121","volume-title":"Recent trends in mobile robots. Series in Robotics and Automated Systems, vol 11","author":"C Canudasde Wit","year":"1994","unstructured":"Canudasde Wit C, Khennouf H, Samson C, S\u00f8rdalen OJ (1994) Nonlinear control design for mobile robots. In: Zheng YF (eds) Recent trends in mobile robots. Series in Robotics and Automated Systems, vol 11. World Scientific Publ Co., Singapore, pp 121\u2013156"},{"key":"67_CR3","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0167-6911(90)90017-O","volume":"14","author":"J-M Coron","year":"1990","unstructured":"Coron J-M (1990) A necessary condition for feedback stabilization. Syst Control Lett 14: 227\u2013232","journal-title":"Syst Control Lett"},{"key":"67_CR4","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF01211563","volume":"5","author":"J-M Coron","year":"1992","unstructured":"Coron J-M (1992) Global asymptotic stabilization for controllable systems without drift. Math Control Signals Syst 5: 295\u2013312","journal-title":"Math Control Signals Syst"},{"key":"67_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-7904-5","volume-title":"Stable mappings and their singularities. Graduate Texts in Mathematics, vol 14","author":"M Golubitsky","year":"1973","unstructured":"Golubitsky M, Guillemin VW (1973) Stable mappings and their singularities. Graduate Texts in Mathematics, vol 14. Springer, New York"},{"key":"67_CR6","volume-title":"Differential topology","author":"V Guillemin","year":"1974","unstructured":"Guillemin V, Pollack A (1974) Differential topology. Prentice Hall, Inc., Englewood Cliffs"},{"key":"67_CR7","unstructured":"Gurvits L, Li ZX (1992) Smooth time-periodic feedback solutions for nonholonomic motion planning. In: Li V, Canny JF (eds) Nonholonomic motion planning. Kluwer Acad Publ, pp 53\u2013108"},{"key":"67_CR8","doi-asserted-by":"crossref","unstructured":"Hardy M (2006) Combinatorics of partial derivatives. Electron J Combin 13:#R1","DOI":"10.37236\/1027"},{"key":"67_CR9","volume-title":"Differential topology. Graduate Texts in Mathematics, vol 33","author":"MW Hirsch","year":"1976","unstructured":"Hirsch MW (1976) Differential topology. Graduate Texts in Mathematics, vol 33. Springer, New York"},{"issue":"1","key":"67_CR10","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s002080050007","volume":"316","author":"S Illman","year":"2000","unstructured":"Illman S, Kankaanrinta M (2000) A new topology for the set C \u221e, g (m, n) of G-equivariant smooth maps. Math Ann 316(1): 139\u2013168","journal-title":"Math Ann"},{"key":"67_CR11","doi-asserted-by":"crossref","unstructured":"Ishikawa M, Morin P, Samson C (2009) Tracking control of the trident snake robot with the transverse function approach. In: IEEE Conference on Decision and Control (CDC). Shanghai, pp 4137\u20134143","DOI":"10.1109\/CDC.2009.5399958"},{"key":"67_CR12","doi-asserted-by":"crossref","unstructured":"Jiang Z-P, Nijmeijer H (1997) Backstepping-based tracking control of nonholonomic chained systems. In: European Control Conference (ECC), Brussels","DOI":"10.23919\/ECC.1997.7082510"},{"key":"67_CR13","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/(SICI)1099-1239(20000415)10:4<243::AID-RNC472>3.0.CO;2-P","volume":"10","author":"E Lefeber","year":"2000","unstructured":"Lefeber E, Robertsson A, Nijmeijer H (2000) Linear controllers for exponential tracking of systems in chained-form. Int J Robust Nonlinear Control 10: 243\u2013263","journal-title":"Int J Robust Nonlinear Control"},{"key":"67_CR14","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s00498-003-0140-x","volume":"16","author":"DA Liz\u00e1rraga","year":"2003","unstructured":"Liz\u00e1rraga DA (2003) Obstructions to the existence of universal stabilizers for smooth control systems. Math Control Signals Syst 16: 255\u2013277","journal-title":"Math Control Signals Syst"},{"issue":"6","key":"67_CR15","doi-asserted-by":"crossref","first-page":"2172","DOI":"10.1137\/S0363012902405571","volume":"42","author":"DA Liz\u00e1rraga","year":"2004","unstructured":"Liz\u00e1rraga DA, Aneke NPI, Nijmeijer H (2004) Robust point-stabilization of underactuated mechanical systems via the extended chained form. SIAM J Control Optim 42(6): 2172\u20132199","journal-title":"SIAM J Control Optim"},{"key":"67_CR16","doi-asserted-by":"crossref","unstructured":"Liz\u00e1rraga DA, Morin P, Samson C (1999) Non-robustness of continuous homogeneous stabilizers for affine control systems. In: IEEE Conference on Decision and Control (CDC), vol 1, Phoenix, pp 855\u2013860","DOI":"10.1109\/CDC.1999.832897"},{"key":"67_CR17","doi-asserted-by":"crossref","unstructured":"Liz\u00e1rraga DA, Sosa JM (2005) Vertically transverse functions as an extension of the transverse function control approach for second-order systems. In: IEEE Conference on Decision and Control and European Control Conference ECC, Sevilla, pp 7290\u20137295","DOI":"10.1109\/CDC.2005.1583337"},{"issue":"4","key":"67_CR18","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s00498-008-0026-z","volume":"20","author":"DA Liz\u00e1rraga","year":"2008","unstructured":"Liz\u00e1rraga DA, Sosa JM (2008) Control of mechanical systems on Lie groups based on vertically transverse functions. Math Control Signals Syst 20(4): 111\u2013133","journal-title":"Math Control Signals Syst"},{"key":"67_CR19","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1109\/9.580865","volume":"42","author":"RT M\u2019Closkey","year":"1997","unstructured":"M\u2019Closkey RT, Murray RM (1997) Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Trans Autom Control 42: 614\u2013628","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"67_CR20","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1137\/S0363012997315427","volume":"38","author":"P Morin","year":"1999","unstructured":"Morin P, Pomet J-B, Samson C (1999) Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of Lie brackets in closed loop. SIAM J Control Optim 38(1): 22\u201349","journal-title":"SIAM J Control Optim"},{"key":"67_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/cocv:1999101","volume":"4","author":"P Morin","year":"1999","unstructured":"Morin P, Samson C (1999) Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics. Control Optim Calc Var (COCV) 4: 1\u201335","journal-title":"Control Optim Calc Var (COCV)"},{"issue":"4","key":"67_CR22","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1137\/S0363012900366054","volume":"40","author":"P Morin","year":"2001","unstructured":"Morin P, Samson C (2001) A characterization of the Lie Algebra Rank Condition by Transverse Periodic Functions. SIAM J Control Optim 40(4): 1227\u20131249","journal-title":"SIAM J Control Optim"},{"issue":"9","key":"67_CR23","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1109\/TAC.2003.816963","volume":"48","author":"P Morin","year":"2003","unstructured":"Morin P, Samson C (2003) Practical stabilization of driftless systems on Lie groups: The transverse function approach. IEEE Trans Autom Control 48(9): 1496\u20131508","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"67_CR24","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1137\/S0363012903421868","volume":"43","author":"P Morin","year":"2004","unstructured":"Morin P, Samson C (2004) Practical and asymptotic stabilization of chained systems by the transverse function control approach. SIAM J Control Optim 43(1): 32\u201357","journal-title":"SIAM J Control Optim"},{"key":"67_CR25","doi-asserted-by":"crossref","unstructured":"Morin P, Samson C (2009) Transverse functions on special orthogonal groups for vector fields satisfying the LARC at the order one. In: IEEE Conference on Decision and Control (CDC), Shanghai, pp 7472\u20137477","DOI":"10.1109\/CDC.2009.5400526"},{"key":"67_CR26","unstructured":"Munkres JR (2000) Topology, 2nd edn. Prentice Hall Inc., Upper Saddle River"},{"key":"67_CR27","doi-asserted-by":"crossref","unstructured":"Murray RM, Walsh G, Sastry SS (1992) Stabilization and tracking for nonholonomic control systems using time-varying feedback. In: IFAC Nonlinear Control Systems Design Symposium (NOLCOS), pp 109\u2013114","DOI":"10.1016\/S1474-6670(17)52266-1"},{"key":"67_CR28","doi-asserted-by":"crossref","unstructured":"Panteley E, Lefeber E, Lor\u00eda A, Nijmeijer H (1998) Exponential tracking control of a mobile car using a cascaded approach. In: Proceedings of the \u201cIFAC Workshop on Motion Control\u201d, Grenoble, pp 221\u2013226","DOI":"10.1016\/S1474-6670(17)40028-0"},{"key":"67_CR29","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/0167-6911(92)90078-7","volume":"19","author":"L Rosier","year":"1992","unstructured":"Rosier L (1992) Homogeneous Lyapunov function for homogeneous continuous vector field. Syst Control Lett 19: 467\u2013473","journal-title":"Syst Control Lett"},{"key":"67_CR30","doi-asserted-by":"crossref","unstructured":"Samson C (1991) Velocity and torque feedback control of a nonholonomic cart. In: International Workshop in Adaptative and Nonlinear Control: Issues in Robotics. Grenoble 1990, vol 162. Springer, pp 125\u2013151","DOI":"10.1007\/BFb0039269"},{"key":"67_CR31","doi-asserted-by":"crossref","unstructured":"Samson C, Ait-Abderrahim K (1991) Feedback control of a nonholonomic wheeled cart in cartesian space. In: IEEE Conference on Robotics and Automation (ICRA), Sacramento, pp 1136\u20131141","DOI":"10.1109\/ROBOT.1991.131748"},{"key":"67_CR32","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511526411","volume-title":"The geometry of jet bundles. Number 142 in Lecture Note Series","author":"DJ Saunders","year":"1989","unstructured":"Saunders DJ (1989) The geometry of jet bundles. Number 142 in Lecture Note Series. Cambridge University Press, Cambridge"},{"key":"67_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0577-7","volume-title":"Mathematical control theory","author":"ED Sontag","year":"1998","unstructured":"Sontag ED (1998) Mathematical control theory. Springer, New York"},{"issue":"1","key":"67_CR34","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/9.273373","volume":"39","author":"G Walsh","year":"1994","unstructured":"Walsh G, Tilbury D, Sastry S, Murray R, Laumond J-P (1994) Stabilization of trajectories for systems with nonholonomic constraints. IEEE Trans Autom Control 39(1): 216\u2013222","journal-title":"IEEE Trans Autom Control"},{"key":"67_CR35","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1799-0","volume-title":"Foundations of differentiable manifolds and Lie groups. Graduate Texts in Mathematics, vol 94","author":"FW Warner","year":"1983","unstructured":"Warner FW (1983) Foundations of differentiable manifolds and Lie groups. Graduate Texts in Mathematics, vol 94. Springer, New York"}],"container-title":["Mathematics of Control, Signals, and Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-011-0067-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00498-011-0067-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00498-011-0067-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T20:19:21Z","timestamp":1593116361000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00498-011-0067-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,11]]},"references-count":35,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["67"],"URL":"https:\/\/doi.org\/10.1007\/s00498-011-0067-6","relation":{},"ISSN":["0932-4194","1435-568X"],"issn-type":[{"value":"0932-4194","type":"print"},{"value":"1435-568X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,11]]}}}