Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems
By: Ignacy Dulęba and Jacek Jagodziñski
Open Access
|Sep 2011References
- Bellaiche, A., Laumond, J.-P. and Chyba, M. (1993). Canonical nilpotent approximation of control systems: Application to nonholonomic motion planning, IEEE Conference on Decision and Control, San Antonio, TX, USA, pp. 2694-2699.
- Chow, W.L. (1939). On system of linear partial differential equations of the first order, Mathematische Annalen 117(1): 98-105, (in German).
- Dulęba, I. (1998). Algorithms of Motion Planning for Nonholonomic Robots, Wrocław University of Technology Publishing House, Wrocław.
- Dulęba, I. (2009). How many P. Hall representations there are for motion planning of nilpotent nonholonomic systems?, IFAC International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland.
- Dulęba, I. and JagodziénAski, J. (2008a). On impact of reference trajectory on Lafferierre-Sussmann algorithm applied to the Brockett integrator system, in K. TchoénA and C. Zieli énAski (Eds.), Problems of Robotics, Science Works: Electronics, Vol. 166, Warsaw University of Technology Publishing House, Warsaw, pp. 515-524, (in Polish).
- Dulęba, I. and JagodziénAski, J. (2008b). On the structure of Chen-Fliess-Sussmann equation for Ph. Hall motion representation, in K. TchoénA (Ed.), Progress in Robotics, Wydawnictwa Komunikacji i ŁącznoésAci, Warsaw, pp. 9-20.
- Dulęba, I. and JagodziénAski, J. (2009). Computational algebra support for the Chen-Fliess-Sussmann differential equation, ins K. Kozłowski (Ed.), Robot Motion and Control, Lecture Notes in Control and Information Sciences, Vol. 396, Springer, Berlin/Heidelberg, pp. 133-142.
- Dulęba, I. and Khefifi, W. (2006). Pre-control form of the generalized Campbell-Baker-Hausdorff-Dynkin formula for affine nonholonomic systems, Systems and Control Letters 55(2): 146-157.
- Golub, G.H. and Loan, C.V. (1996). Matrix Computations, 3rd Edn., The Johns Hopkins University Press, London.
- Koussoulas, N. and Skiadas, P. (2001). Motion planning for drift-free nonholonomic system under a discrete levels control constraint, Journal of Intelligent and Robotic Systems 32(1): 55-74.
- Koussoulas, N. and Skiadas, P. (2004). Symbolic computation for mobile robot path planning, Journal of Symbolic Computation 37(6): 761-775.
- Lafferriere, G. (1991). A general strategy for computing steering controls of systems without drift, IEEE Conference on Decision and Control, Brighton, UK, pp. 1115-1120.
- Lafferriere, G. and Sussmann, H. (1990). Motion planning for controllable systems without drift: A preliminary report, Technical report, Rutgers Center for System and Control, Piscataway, NJ.
- Lafferriere, G. and Sussmann, H. (1991). Motion planning for controllable systems without drift, IEEE Conference on Robotics and Automation, Brighton, UK, pp. 1148-1153.
- LaValle, S. (2006). Planning Algorithms, Cambridge University Press, Cambrigde, MA.
- Reutenauer, C. (1993). Free Lie Algebras, Clarendon Press, Oxford.
- Rouchon, P. (2001). Motion planning, equivalence, infinite dimensional systems, International Journal of Applied Mathematics and Computer Science 11(1): 165-188.
- Strichartz, R.S. (1987). The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, Journal of Functional Analysis 72(2): 320-345.
- Struemper, H. (1998). Nilpotent approximation and nilpotentization for under-actuated systems on matrix Lie groups, IEEE Conference on Decision and Control, Tampa, FL, USA, pp. 4188-4193.
- Sussmann, H. (1991). Two new methods for motion planning for controllable systems without drift, European Control Conference, Grenoble, France, pp. 1501-1506.
- Vendittelli, M., Oriolo, G., Jean, F. and Laumond, J.-P. (2004). Nonhomogeneous nilpotent approximations for nonholonomic system with singularities, IEEE Transactions on Automatic Control 49(2): 261-266.
Language: English
Page range: 525 - 534
Published on: Sep 22, 2011
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
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© 2011 Ignacy Dulęba, Jacek Jagodziñski, published by University of Zielona Góra
This work is licensed under the Creative Commons License.