Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T11:47:53.624Z Has data issue: false hasContentIssue false
  • English
  • Français

Modified Newton's method applied to potential field based navigation for nonholonomic robots in dynamic environments

Published online by Cambridge University Press:  01 May 2008

Jing Ren ,
Kenneth A. McIsaac  and
Rajni V. Patel
Jing Ren
Affiliation:
Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, Ontario, Canada1 LH 7K4
Kenneth A. McIsaac*
Affiliation:
Department of Electrical and Computer Engineering, University of western Ontario, London, Ontario, CanadaN 6 G 1 H 1
Rajni V. Patel
Affiliation:
Department of Electrical and Computer Engineering, University of western Ontario, London, Ontario, CanadaN 6 G 1 H 1
*
*Corresponding author. E-mail: kmcisaac@engga.uwo.ca
Get access Rights & Permissions [Opens in a new window]

Summary

This paper is to investigate inherent oscillations problems of Potential Field Methods (PFMs) for nonholonomic robots in dynamic environments. In prior work, we proposed a modification of Newton's method to eliminate oscillations for omnidirectional robots in static environment. In this paper, we develop control laws for nonholonomic robots in dynamic environment using modifications of Newton's method. We have validated this technique in a multirobot search-and-forage task. We found that the use of the modifications of Newton's method, which applies anywhere C2 continuous navigation functions are defined, can greatly reduce oscillations and speed up robot's movement, when compared to the standard gradient approaches.

Keywords

Potential field methodsnonholonomic constraintsmobile robotics
Type
Article
Information
Robotica , Volume 26 , Issue 3 , May 2008 , pp. 285 - 294
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.Khatib, O., “Real-time obstacle avoidance for manipulators and mobile robots,” Int. J. Robot. Res. 5 (1), 90–98 (1986).Google Scholar
2.Ge, S. S. and Cui, Y. J., “New potential functions for mobile robot path planning,” IEEE Trans. Robot. Automat. 16 (5), 609–615 (2000).Google Scholar
3.Latombe, J. C, Robot Motion Planning (Kluwer Academic Publishers, Boston, Massachusetts, 1991).CrossRefGoogle Scholar
4.Koren, Y., et al. , “Potential Field Methods and Their Inherent Limitations for Mobile Robot Navigation,” IEEE International Conference on Robotics and Automation, Sacramento (April, 1991) pp. 1398–1404.Google Scholar
5.Ren, J., McIsaac, K. A. and Patel, R. V., “Modified Newton's method applied to potential field based navigation for omnidirectional mobile robots,” IEEE Trans. Robot. 22 (2), 384–391 (2006).Google Scholar
6.Bazaraa, M., Sherali, H., and Shetty, C.. Nonlinear Programming Theory and Algorithms (John Wiley and Sons, Inc., New York, 1995).Google Scholar
7.Fukao, T., Nakagawa, H. and Adachi, N, “Adaptive tracking control of a nonholonomic mobile robot,” IEEE Trans. Robot. Automat. 16 (5), 609–615 (2000).CrossRefGoogle Scholar
8.Shim, H. S. and Sung, Y. G., “Stability and four-posture control for nonholonomic mobile robots,” IEEE Trans. Robot. Automat. 20 (1), 148–154 (2004).CrossRefGoogle Scholar
9. “Hilare 2 Robot Specifications,” Available at: http://www.laas.fr/matthieu/robots/h2+.Google Scholar
10.Tanner, H. G. and Kyriakopoulos, K. J., “Nonholonomic Motion Planning for Mobile Manipulators,” IEEE International. Conference on Robotics and Automation, San Franscisco (April, 2000) pp. 1233–1238.Google Scholar
11.Esposito, J. and Kumar, V., “A Method for Modifying Closed-Loop Motion Plans to Satisfy Unpredictable Dynamic Constraints at Run-Time,” IEEE International Conference on Robotics and Automation, Washington, DC, (May, 2002), pp. 1691–1696.Google Scholar
12.Tanner, H. G., Loizon, S. and Kyriakopoulos, K. J., “Nonholonomic Stabilization with Collision Avoidance for Mobile Robots,” IEEE International Conference on Intelligent Robots and Systems, Hawaii (October/November, 2001) pp. 1220–1225.Google Scholar
13.Tanner, H. G., Loizou, S. G. and Kyriakopoulos, K. J., “Nonholonomic navigation and control of cooperating mobile manipulators,” IEEE Trans. Robot. Automat. 19 (1), 53–64 (2003).Google Scholar
14.Ren, J., McIsaac, K. A. and Patel, R. V., “A Fast Algorithm for Moving Obstacle Avoidance for Mobile Robots,” Proceedings of the IEEE Conference on Control Applications, Canada (August, 2005) pp. 209–214.Google Scholar
15.Ren, J. and McIsaac, K. A., “A Hybrid-Systems Approach to Potential Field Navigation for a Multi-Robot Team,” IEEE International Conference on Robotics and Automation, Taiwan (September, 2003) pp. 3875–3880.Google Scholar
16.Lafferriere, G. A. and Sontag, E. D., “Remarks on Control Lyapunov Functions for Discontinuously Stabilizing Feedback,” IEEE International Conference Decision and Control, San Antonio, TX (December, 1993) pp. 2398–2403.Google Scholar