Abstract
In this paper a local variation method is proposed to determine a cheap path for nonholonomic motion planning. It can be used as a preliminary step in motion planning to find the path to be followed with the minimal control effort. The algorithm based on the method is detailed and parameters that influence its work discussed. Simulations performed on the unicycle mobile robot confirm efficiency of the method.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
W.L. Chow. Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math. Ann., 117(1):98–105, 1939.
I. Duleba. Checking controllability of nonholonomic systems via optimal Ph. Hall basis generation. In Proc. IFAC SyRoCo Conf., pages 485–490, 1997a.
I. Duleba. Locally optimal motion planning of nonholonomic systems. Journ. of Rob. Syst., 14(11):767–788, 1997b.
I. Duleba. Algorithms of motion planning for nonholonomic robots. Wroclaw Univ. of Technology Publ., 1999.
I. Duleba and W. Khefifi. Pre-control form of the generalized Campbell-Baker-Hausdorff-Dynkin formula for affine nonholonomic systems. Syst. Contr. Lett., 55:146–157, 2006.
G. Lafferriere and H. Sussmann. Motion planning for controllable systems without drift. In Proc. IEEE Conf. on Rob. and Autom., pages 1148–1153, 1991.
R. Montgomery. Abnormal minimizers. SI AM Jorn. Contr. and Optimization, 32(6): 1605–1620, 1994.
Y. Nakamura. Advanced Robotics: Redundancy and Optimization. Addison Wesley, 1991.
S. Sekhavat and M. Chyba. Nonholonomic deformation of a potential field for motion planning. In Proc. IEEE Conf. on Rob. and Autom., pages 817–822, 1999.
R.S. Strichartz. The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations. Journ. of Fund. Anal., 72:320–345, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 CISM, Udine
About this chapter
Cite this chapter
Duleba, I., Ludwików, P. (2006). Local Variation Method to Determine Cheap Path for Nonholonomic Systems. In: Zielińska, T., Zieliński, C. (eds) Romansy 16. CISM Courses and Lectures, vol 487. Springer, Vienna. https://doi.org/10.1007/3-211-38927-X_19
Download citation
DOI: https://doi.org/10.1007/3-211-38927-X_19
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-36064-4
Online ISBN: 978-3-211-38927-0
eBook Packages: EngineeringEngineering (R0)