Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems

• Autorzy: Ignacy Dulęba , Jacek Jagodziński
• Języki publikacji: EN

Abstrakty

EN

In this paper, an extension of the Lafferriere-Sussmann algorithm of motion planning for driftless nilpotent control systems is analyzed. It is aimed at making more numerous admissible representations of motion in the algorithm. The representations allow designing a shape of trajectories joining the initial and final configuration of the motion planning task. This feature is especially important in motion planning in a cluttered environment. Some natural functions are introduced to measure the shape of a trajectory in the configuration space and to evaluate trajectories corresponding to different representations of motion.

Słowa kluczowe

EN

control; nilpotent system; algorithm; motion representation

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2011
• Tom: 21
• Numer: 3
• Strony: 525-534

Daty

wydano

2011

otrzymano

2010-05-31

poprawiono

2010-09-28

Twórcy

autor

Ignacy Dulęba

• Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland

autor

Jacek Jagodziński

• Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland

Bibliografia

• 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 Jagodziński, J. (2008a). On impact of reference trajectory on Lafferierre-Sussmann algorithm applied to the Brockett integrator system, in K. Tchoń and C. Zieliński (Eds.), Problems of Robotics, Science Works: Electronics, Vol. 166, Warsaw University of Technology Publishing House, Warsaw, pp. 515-524, (in Polish).
• Dulęba, I. and Jagodziński, J. (2008b). On the structure of Chen-Fliess-Sussmann equation for Ph. Hall motion representation, in K. Tchoń (Ed.), Progress in Robotics, Wydawnictwa Komunikacji i Łączności, Warsaw, pp. 9-20.
• Dulęba, I. and Jagodziński, J. (2009). Computational algebra support for the Chen-Fliess-Sussmann differential equation, in 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.

Identyfikatory

DOI

10.2478/v10006-011-0041-y