A bound for the degree of nonholonomy in the plane

Theoretical Computer Science

Volumn 157, Issue 1, 1996, Pages 129-136

  Risler, Jean Jacques ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS; CONTROL THEORY; FUNCTIONS; POLYNOMIALS; VECTORS;

COORDINATES; NONHOLONOMY;

COMPUTATION THEORY;

EID: 0030576165     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00180-8     Document Type: Article

References (10)

1. W.L. Chow, Uber Systeme von linearen partiellen Differentialgleichungen erster Ordnung., Math. Ann. 117 (1940) 98-115.
2. A. Gabrielov, Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy, preprint, Cornell University, January 1995, to appear.
3. A. Gabrielov, J-M. Lion and R. Moussu, Ordre de contact de courbes intégrales du plan, CRAS Paris 319 (1994) 219-221.
4. Cl. Godbillon, Géométrie différentielle et Mécanique analytique (Hermann, Paris, 1969).
5. J-P. Laumond, Singularities and topological aspects in nonholonomic motion planning, in: Z. Li and J. Canny, eds., Nonholonomic Motion Planning (Kluwer. Dordrecht, 1993) 149-199.
6. F. Luca and J-J. Risler, The maximum of the degree of nonholonomy for the car with n trailers, preprint LMENS-93-14, Ecole Normale Supérieure, Paris, 1993.
7. Nagel, Stein and Wainger, Metrics defined by vector fields, Acta Math. 155 (1985) 103-147.
8. A. Seidenberg, On the length of Hubert ascending chain. Proc. Amer. Math. Soc. 29 (1971) 443-450.
9. E. Sontag, Some complexity questions regarding controllability, in: Proc. 27th IEEE Conf. on Decision and Control (Austin, 1988) 1326-1329.
10. H.J. Sussmann, Lie brackets, real analyticity and geometric control, in: Brockett, Millman, Sussmann, eds., Differential Geometric Control Theory (Birkäuser, Basel, 1982) 1-116.