Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T18:40:04.323Z Has data issue: false hasContentIssue false
  • English
  • Français

Velocity space approach to motion planning of nonholonomic systems

Published online by Cambridge University Press:  01 May 2007

Ignacy Duleba  and
Wissem Khefifi
Ignacy Duleba*
Affiliation:
Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Janiszewski St. 11/17, 50-372 Wroclaw, Poland
Wissem Khefifi
Affiliation:
Institute of Computer Engineering, Control and Robotics, Wroclaw University of Technology, Janiszewski St. 11/17, 50-372 Wroclaw, Poland
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, a velocity space method of motion planning for nonholonomic systems is presented. This method, based on Lie algebraic principles and locally around consecutive current states, plans a motion towards a goal. It is effective as most of the computations can be carried out analytically. This method is illustrated on the unicycle robot and the inverted pendulum.

Keywords

Nonholonomic systemsMotion planningLie algebraic method
Type
Article
Information
Robotica , Volume 25 , Issue 3 , May 2006 , pp. 359 - 366
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bloch, A. M., Nonholonomic Mechanics and Control (Springer-Verlag, Berlin, 2003).CrossRefGoogle Scholar
2.Dubins, L. E., “On curves of minimal length with a constrained on average curvature and with prescribed initial and terminal positions and tangents,” Am. J. Math. 497–516 1957.Google Scholar
3.Reeds, J. A. and Shepp, R. A., “Optimal paths for a car that goes both forward and backwards,” Pacific J. Math. 145 (2), 367–393 1990.CrossRefGoogle Scholar
4.Fraichard, T. and Scheuer, A., “From Reed and Shepps’ to continuous-curvature paths,” IEEE Trans. Robot. 20 (6), 1025–1035 2004.CrossRefGoogle Scholar
5.Balcom, D. J. and Mason, M. T., “Time optimal trajectories for bounded velocity differential drive vehicles,” Int. J. Robot. Res. 21 (3), 199–217 2002.CrossRefGoogle Scholar
6.Brockett, R. W., “Control Theory and Riemannian Geometry,” In: New Directions in Applied Mathematics (Springer-Verlag, New York, 1981) pp. 11–27.Google Scholar
7.Murray, R. M. and Sastry, S., “Nonholonomic motion planning: Steering using sinusoids,” IEEE Trans. Autom. Control 38 (5), 700–716 1993.CrossRefGoogle Scholar
8.Fliess, M., Rouchon, P., Lévine, J. and Martin, P., “Flatness, Motion Planning and Trailer Systems,” Proceedings of the Conference on Decision and Control, San Antonio, Texas 1993 pp. 2700–2705.Google Scholar
9.Lafferriere, G. and Sussmann, H., “Motion Planning for Controllable Systems Without Drift,” Proceedings of IEEE Conference on Robotics and Automation, Sacramento, California 1991, pp. 1148–1153.Google Scholar
10.Fernandes, C., Gurvits, L. and Li, Z., “Optimal Nonholonomic Motion Planning for Falling Cat,” In: Nonholonomic Motion Planning (Kluwer Academic, Massachussets, 1993 pp. 379–421.CrossRefGoogle Scholar
11.Sussmann, H., “A Continuation Method for Nonholonomic Path Finding Problem,” Proceedings of the Conference on Decision and Control, San Antario, Texas 1993 pp. 2718–2723.CrossRefGoogle Scholar
12.Divelbiss, A. W. and Wen, J. T., “Nonholonomic Path Planning With Inequality Contraints,” IEEE Conference on Robotics and Automation, San Diego, California 1994 pp. 52–57.Google Scholar
13.Tchon, K. and Jakubiak, J., “Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms,” Int. J. Control 26 (14), 1387–1419 2003.CrossRefGoogle Scholar
14.Duleba, I. and Sasiadek, J., “Nonholonomic motion planning based on Newton Algorithm with energy optimization,” IEEE Trans. Control Syst. Technol. 11 (3), 355–365 2003.CrossRefGoogle Scholar
15.Laumond, J. P., Robot Motion Planning and Control (Springer-Verlag, Berlin, 1998).CrossRefGoogle Scholar
16.Li, Z. and Canny, J. F., Nonholonomic Motion Planning (Kluwer Academic, Massachussets, 1993).CrossRefGoogle Scholar
17.LaValle, S., Planning Algorithms (Cambridge Univ. Press, UK, 2006).CrossRefGoogle Scholar
18.Duleba, I., “Checking controllability of nonholonomic systems via optimal Ph. Hall basis generation,” Proceedings of the IFAC Symposium on Robot Control, Nantes, France 1997 pp. 485–490.Google Scholar
19.Chow, W. L., “Über systeme von linearen partiellen differentialgleichungen erster ordnung,” Math. Ann. 117 (1), 98–105 1939.CrossRefGoogle Scholar
20.Strichartz, R. S., “The Campbell–Baker–Hausdorff–Dynkin formula and solutions of differential equations,” J. Funct. Anal. 72, 320–345 1987.CrossRefGoogle Scholar
21.Duleba, I., “On a computationally simple form of the generalizad Campbell–Baker–Hausdorff-Dynkin formula,” Syst., Control Lett. 34, 191–202 1998.CrossRefGoogle Scholar
22.Duleba, I. and Khefifi, W., “Pre-control form of the gCBHD formula for affine nonholonomic systems,” Syst., Control Lett. 55 (2), 146–157 2006.CrossRefGoogle Scholar
23.Nakamura, Y., Advanced Robotics: Redundancy and Optimization (Addison Wesley, New York, 1991).Google Scholar
24.Spong, M. and Vidyasagar, M., Robot Dynamics and Control (MIT Press, Cambridge, 1989).Google Scholar
25.Hermann, R. and Krener, A., “Nonlinear controllability and observability,” IEEE Trans. Autom. Control 22, 728–740 1977.CrossRefGoogle Scholar
26.Sussmann, H. J. and Jurdjevic, V., Controllability of Nonlinear System (Springer-Verlag, New York, 1977).Google Scholar
27.Lian, K., Wang, L. and Fu, L., “Controllability of spacecraft systems in a central gravitational field,” IEEE Trans. Autom. Control 39 (12), 2426–2440 1994.CrossRefGoogle Scholar
28.Lynch, K. and Black, C. K., “Recurrence, controllability, and stabilization of juggling,” IEEE Trans. Robot. Autom. 17 (2), 113–124 2001.CrossRefGoogle Scholar