Bulletin of the American Mathematical Society

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Book Information:

Author: Frédéric Jean
Title: Control of nonholonomic systems: from sub-Riemannian geometry to motion planning
Additional book information: Springer Briefs in Mathematics, Springer, New York, 2014, x+104 pp., ISBN 978-3-319-08690-3, US $39.99

A. Agrachev and A. Marigo, Nonholonomic tangent spaces: intrinsic construction and rigid dimensions, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 111–120. MR 2029472, DOI 10.1090/S1079-6762-03-00118-5

Andrei A. Agrachev and Yuri L. Sachkov, Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences, vol. 87, Springer-Verlag, Berlin, 2004. Control Theory and Optimization, II. MR 2062547, DOI 10.1007/978-3-662-06404-7

André Bellaïche, The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry, Progr. Math., vol. 144, Birkhäuser, Basel, 1996, pp. 1–78. MR 1421822, DOI 10.1007/978-3-0348-9210-0_{1}

Yacine Chitour, Frédéric Jean, and Ruixing Long, A global steering method for nonholonomic systems, J. Differential Equations 254 (2013), no. 4, 1903–1956. MR 3003297, DOI 10.1016/j.jde.2012.11.012

W.L. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann. 117 (1940) 98-115.

Mikhael Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P. Pansu. MR 682063

Matthew Grayson and Robert Grossman, Models for free nilpotent Lie algebras, J. Algebra 135 (1990), no. 1, 177–191. MR 1076084, DOI 10.1016/0021-8693(90)90156-I

Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081

S. Yu. Ignatovich, Realizable growth vectors of affine control systems, J. Dyn. Control Syst. 15 (2009), no. 4, 557–585. MR 2558570, DOI 10.1007/s10883-009-9075-y

Claude Lobry, Contrôlabilité des systèmes non linéaires, SIAM J. Control 8 (1970), 573–605 (French). MR 0271979

Richard M. Murray and S. Shankar Sastry, Nonholonomic motion planning: steering using sinusoids, IEEE Trans. Automat. Control 38 (1993), no. 5, 700–716. MR 1224308, DOI 10.1109/9.277235

Yu. Nejmark, N. Fufaev, Dynamics of nonholomic systems, Moscow, Nauka, 1967, English translation in Transl.Math. Monogr. AMS, 33.IX, 1972.

P.K. Rashevsky, Any two points of a totally nonholonomic space may be connected by an admissible line, Uch. Zap. Ped. Inst. im. Liebknechta, Ser. Phys. Math. 2 (1938) (in Russian).

P. Stefan, Accessible sets, orbits, and foliations with singularities, Proc. London Math. Soc. (3) 29 (1974), 699–713. MR 362395, DOI 10.1112/plms/s3-29.4.699

Héctor J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171–188. MR 321133, DOI 10.1090/S0002-9947-1973-0321133-2

Noboru Tanaka, On differential systems, graded Lie algebras and pseudogroups, J. Math. Kyoto Univ. 10 (1970), 1–82. MR 266258, DOI 10.1215/kjm/1250523814

• A. Agrachev and A. Marigo, Nonholonomic tangent spaces: intrinsic construction and rigid dimensions, Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 111–120 (electronic). MR 2029472 (2005i:58003), DOI 10.1090/S1079-6762-03-00118-5
• Andrei A. Agrachev and Yuri L. Sachkov, Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences, vol. 87, Springer-Verlag, Berlin, 2004. Control Theory and Optimization, II. MR 2062547 (2005b:93002), DOI 10.1007/978-3-662-06404-7
• André Bellaïche, The tangent space in sub-Riemannian geometry, Sub-Riemannian geometry, Progr. Math., vol. 144, Birkhäuser, Basel, 1996, pp. 1–78. MR 1421822 (98a:53108), DOI 10.1007/978-3-0348-9210-0_1
• Yacine Chitour, Frédéric Jean, and Ruixing Long, A global steering method for nonholonomic systems, J. Differential Equations 254 (2013), no. 4, 1903–1956. MR 3003297, DOI 10.1016/j.jde.2012.11.012
• W.L. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann. 117 (1940) 98-115.
• Mikhael Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P. Pansu. MR 682063 (85e:53051)
• Matthew Grayson and Robert Grossman, Models for free nilpotent Lie algebras, J. Algebra 135 (1990), no. 1, 177–191. MR 1076084 (91g:17015), DOI 10.1016/0021-8693(90)90156-I
• Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 0222474 (36 \#5526)
• S. Yu. Ignatovich, Realizable growth vectors of affine control systems, J. Dyn. Control Syst. 15 (2009), no. 4, 557–585. MR 2558570 (2011a:93050), DOI 10.1007/s10883-009-9075-y
• Claude Lobry, Contrôlabilité des systèmes non linéaires, SIAM J. Control 8 (1970), 573–605 (French). MR 0271979 (42 \#6860)
• Richard M. Murray and S. Shankar Sastry, Nonholonomic motion planning: steering using sinusoids, IEEE Trans. Automat. Control 38 (1993), no. 5, 700–716. MR 1224308 (94a:93035), DOI 10.1109/9.277235
• Yu. Nejmark, N. Fufaev, Dynamics of nonholomic systems, Moscow, Nauka, 1967, English translation in Transl.Math. Monogr. AMS, 33.IX, 1972.
• P.K. Rashevsky, Any two points of a totally nonholonomic space may be connected by an admissible line, Uch. Zap. Ped. Inst. im. Liebknechta, Ser. Phys. Math. 2 (1938) (in Russian).
• P. Stefan, Accessible sets, orbits, and foliations with singularities, Proc. London Math. Soc. (3) 29 (1974), 699–713. MR 0362395 (50 \#14837)
• Héctor J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171–188. MR 0321133 (47 \#9666)
• Noboru Tanaka, On differential systems, graded Lie algebras and pseudogroups, J. Math. Kyoto Univ. 10 (1970), 1–82. MR 0266258 (42 \#1165)