Hostname: page-component-89b8bd64d-b5k59 Total loading time: 0 Render date: 2026-05-08T07:20:02.550Z 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 January 2008

Jing Ren ,
Kenneth A. McIsaac  and
Rajni V. Patel
Jing Ren
Affiliation:
Faculty of Engineering and Applied Science, UOIT, Oshawa, ON, Canada1LH 7K4.
Kenneth A. McIsaac*
Affiliation:
Department of Electrical and Computer Engineering, University of Western Ontario, London, ON, CanadaN6G 1H1
Rajni V. Patel
Affiliation:
Department of Electrical and Computer Engineering, University of Western Ontario, London, ON, CanadaN6G 1H1
*
*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 multi-robot 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 the robot's movement, when compared to the standard gradient approaches.

Information

Type
Article
Information
Robotica , Volume 26 , Issue 1 , January 2008 , pp. 117 - 127
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.)

Article purchase

Temporarily unavailable

References

1.Bazaraa, M., Sherali, H. and Shetty, C., Nonlinear Programming Theory and Algorithms (Wiley, New York, 1995).Google Scholar
2.Esposito, J. and Kumar, V., “A Method for Modifying Closed-Loop Motion Plans to Satisfy Unpredictable Dynamic Constraints at Run-Time,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC (2002) pp. 1691–1696.Google Scholar
3.Fukao, T., Nakagawa, H. and Adachi, N, “Adaptive tracking control of a nonholonomic mobile robot,” IEEE Trans. Robot. Autom. 16 (5), 609–615 (2000).CrossRefGoogle Scholar
4.Ge, S. S. and Cui, Y. J., “New potential functions for mobile robot path planning,” IEEE Trans. Robot. Autom. 16 (5), 609–615 (2000).CrossRefGoogle Scholar
5.Khatib, O., “Real-time obstacle avoidance for manipulators and mobile robots,” Int. J. Robot. Res. 5 (1), 90–96, 1986.CrossRefGoogle Scholar
6.Koren, Y. et al. “Potential Field Methods and Their Inherent Limitations for Mobile Robot Navigation,” Proceeding of the IEEE International Conference on Robotics and Automation (1991) pp. 1398–1404.Google Scholar
7.C Latombe, J., Robot Motion Planning (Kluwer, Boston, MA, 1991).CrossRefGoogle Scholar
8.Lafferriere, G. A. and Sontag, E. D. “Remarks on Control Lyapunov Functions for Discontinuously Stabilizing Feedback,” Proceeding of the IEEE International Conference on Decision and Control, San Antonio, TX (1993) pp. 2398–2403.Google Scholar
9.Ren, J. and McIsaac, K. A., “A Hybrid-Systems Approach to Potential Field Navigation for a Multi-Robot Team,” Proceeding of the IEEE International Conference on Robotics and Automation, Taiwan 3 (2003) pp. 3875–3880.Google Scholar
10.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 (2005) pp. 209–214.Google Scholar
11.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
12.Shim, H. S. and Sung, Y. G., “Stability and four-posture control for nonholonomic mobile robots,” IEEE Trans. Robot. Autom. 20 (1), pp. 148–154 (2004).CrossRefGoogle Scholar
13.Tanner, H. G. and Kyriakopoulos, K. J., “Nonholonomic Motion Planning for Mobile Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation (2000) pp. 1233–1238.Google Scholar
14.Tanner, H. G., Loizon, S. and Kyriakopoulos, K. J., “Nonholonomic Stabilization with Collision Avoidance for Mobilr Robots,” Proceedings of the IEEE International Conference on Intelligent Robots and Systems (2001) pp. 1220–1225.Google Scholar
15.Tanner, H. G., Loizou, S. G. and Kyriakopoulos, K. J., “Nonholonomic navigation and control of cooperating mobile manipulators,” IEEE Trans. Robot. Autom. 19 (1), 53–64 (2003).CrossRefGoogle Scholar
16.Hilare 2 Robot Specifications. Available: http://www.laas.fr/~matthieu/robots/h2+Google Scholar