# The car with $N$ trailers : characterisation of the singular configurations

ESAIM: Control, Optimisation and Calculus of Variations (1996)

- Volume: 1, page 241-266
- ISSN: 1292-8119

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topJean, Frédéric. "The car with $N$ trailers : characterisation of the singular configurations." ESAIM: Control, Optimisation and Calculus of Variations 1 (1996): 241-266. <http://eudml.org/doc/90498>.

@article{Jean1996,

author = {Jean, Frédéric},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Control Lie Algebra; Multibody mobile robot; Nonholonomic systems; car pulling trailers; degree of nonholonomy; vector fields; Lie algebra},

language = {eng},

pages = {241-266},

publisher = {EDP Sciences},

title = {The car with $N$ trailers : characterisation of the singular configurations},

url = {http://eudml.org/doc/90498},

volume = {1},

year = {1996},

}

TY - JOUR

AU - Jean, Frédéric

TI - The car with $N$ trailers : characterisation of the singular configurations

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 1996

PB - EDP Sciences

VL - 1

SP - 241

EP - 266

LA - eng

KW - Control Lie Algebra; Multibody mobile robot; Nonholonomic systems; car pulling trailers; degree of nonholonomy; vector fields; Lie algebra

UR - http://eudml.org/doc/90498

ER -

## References

top- [1] A. Bellaïche, J.-P. Laumond et J.-J. Risler: Nilpotent infinitesimal approximations to a control Lie algebra, in Proceedings of the IFAC Non linear Control Systems Design Symposium, pp. 174-181, Bordeaux, France, 1992.
- [2] A. Bellaïche, J.-P. Laumond et J. Jacobs: Controllability of car-like robots and complexity of the motion planning problem, in International Symposium on Intelligent Robotics, pp. 322-337, Bangladore, India, 1991.
- [3] M. Fliess, J. Levine, P. Martin, P. Rouchon: On differential flat nonlinear Systems, in Proceedings of the IFAC Non linear Control Systems Design Symposium, pp. 408-412, Bordeaux, France, 1992. MR1181303
- [4] B. Jacquard: Le problème de la voiture à 2, 3 et 4 remorques, Preprint, DMI, ENS Paris, 1993.
- [5] F. Jean: The singular locus for the n-trailers car control System, in Proceedings of the 34 th IEEE International Conference on Decision end Control, New-Orleans, 1995.
- [6] J.-P. Laumond: Controllability of a multibody mobile robot, in Proceedings of the International Conference on Advanced robotics and Automation, pp. 1033-1038, Pisa, Italy, 1991.
- [7] J.-P. Laumond, P.E. Jacobs, M. Taix, R.M. Murray: A motion planner for nonholonomic mobile robot, in LAAS-CNRS Report, Oct. 1992.
- [8] J.-P. Laumond: Singularities and Topological Aspects in Nonholonomic Motion Planning, in Nonholonomic Motion Planning, Z. Li and J. Canny Ed., Kluver Academic Publishers ( 1993), 149-199. Zbl0787.70019
- [9] F. Luca, J.-J. Risler: The maximum of the degree of non holonomy for the car with n trailers, in Proceedings of the 4th IFAC Symposium on Robot Control, Capri, 1994.
- [10] F. Luca, 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.
- [11] R. Murray, S. Sastry: Nonholonomic Motion Planning: Steering Using Sinusoids, IEEE Transactions on Automatic Control, Vol 38, May 1993. Zbl0800.93840MR1224308
- [12] O.J. Sørdalen: Conversion of the kinematics of a car with n trailers into a chain form, IEEE International Conference on Robotics and Automation, 1993.
- [13] O.J. Sørdalen: On the global degree of non holonomy of a car with n trailers, Memorandum of Electronic Research Laboratory, Berkeley, 1993.
- [14] H. J. Sussmann: Lie brackets, real analyticity and geometric control, Differential Geometric Control Theory, Brockett, Millman, Sussmann Eds, Birkhäuser, 1982. Zbl0545.93002MR708500
- [15] D. Tilbury, J.-P. Laumond, R. Murray, S. Sastry, G. Walsh: Steering Car-like System with Trailers Using Sinusoids, in Procedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, France.

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