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

Ignacy Dulęba; Jacek Jagodziński

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 3, page 525-534
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Ignacy Dulęba, and Jacek Jagodziński. "Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems." International Journal of Applied Mathematics and Computer Science 21.3 (2011): 525-534. <http://eudml.org/doc/208067>.

@article{IgnacyDulęba2011,
abstract = {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.},
author = {Ignacy Dulęba, Jacek Jagodziński},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {control; nilpotent system; algorithm; motion representation; nilpotent control system; Lafferriere-Sussmann algorithm; robotics},
language = {eng},
number = {3},
pages = {525-534},
title = {Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems},
url = {http://eudml.org/doc/208067},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Ignacy Dulęba
AU - Jacek Jagodziński
TI - Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 3
SP - 525
EP - 534
AB - 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.
LA - eng
KW - control; nilpotent system; algorithm; motion representation; nilpotent control system; Lafferriere-Sussmann algorithm; robotics
UR - http://eudml.org/doc/208067
ER -

References

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  4. 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. 
  5. 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). 
  6. 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. 
  7. 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. 
  8. 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. Zbl1129.93353
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  14. Lafferriere, G. and Sussmann, H. (1991). Motion planning for controllable systems without drift, IEEE Conference on Robotics and Automation, Brighton, UK, pp. 1148-1153. 
  15. LaValle, S. (2006). Planning Algorithms, Cambridge University Press, Cambrigde, MA. Zbl1100.68108
  16. Reutenauer, C. (1993). Free Lie Algebras, Clarendon Press, Oxford. Zbl0798.17001
  17. Rouchon, P. (2001). Motion planning, equivalence, infinite dimensional systems, International Journal of Applied Mathematics and Computer Science 11(1): 165-188. Zbl0972.93048
  18. Strichartz, R.S. (1987). The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, Journal of Functional Analysis 72(2): 320-345. Zbl0623.34058
  19. 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. 
  20. Sussmann, H. (1991). Two new methods for motion planning for controllable systems without drift, European Control Conference, Grenoble, France, pp. 1501-1506. 
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