Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T22:39:58.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Piecewise smooth and safe trajectory planning *

Published online by Cambridge University Press:  09 March 2009

Ashraf Elnagar  and
Anup Basu
Ashraf Elnagar
Affiliation:
Alberta Center for Machine Intelligence and Robotics, Department of Computing Science, University of Alberta, Edmonton, Alberta (Canada) T6G 2H1
Anup Basu
Affiliation:
Alberta Center for Machine Intelligence and Robotics, Department of Computing Science, University of Alberta, Edmonton, Alberta (Canada) T6G 2H1
Get access Rights & Permissions [Opens in a new window]

Summary

A new approach to generating smooth piecewise local trajectories for mobile robots is proposed in this paper. Given the configurations (position and direction) of two points, we search for the trajectory that minimizes the integral of acceleration (tangential and normal). The resulting trajectory should not only be smooth but also safe in order to be applicable in real-life situations. Therefore, we investigate two different obstacle-avoidance constraints that satisfy the minimization problem. Unfortunately, in this case the problem becomes more complex and not suitable for real time implementations. Therefore, we introduce two simple solutions, based on the idea of polynomial fitting, to generate safe trajectories once a collision is detected with the original smooth trajectory. Simulation results of the different algorithms are presented.

Keywords

TrajectoryPiecewise smooth planningMobile robotsObstacle avoidance.
Type
Article
Information
Robotica , Volume 12 , Issue 4 , July 1994 , pp. 299 - 307
Copyright
Copyright © Cambridge University Press 1994

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.Dubins, L., “On curves of minimal length with constraint on average curvature and with prescribed initial and terminal positions and tangents” Amer. J. Mathematics 79, 497–516 (1957).CrossRefGoogle Scholar
2.Laumond, J., “Finding collision-free smooth trajectories for a nen-holonomic mobile robot” Proceedings of the Tenth International Joint Conference on Artificial Intelligence (1987) pp. 1120–1123.Google Scholar
3.Jacobs, P. and Canny, C., “Robust motion planning for mobile robots” Proceedings of the IEEE International Conference on Robotics and Automation (1990) pp. 2–7.Google Scholar
4.Donald, D. and Xavier, P., “A provably good approximation algorithm for optimal time trajectory planning” Proceedings of the IEEE International Conference on Robotics and Automation (1989) pp. 958–963.Google Scholar
5.Horn, B., “The curve of least energy” ACM Transactions on Mathematical Software 9, 441–460 (1983).CrossRefGoogle Scholar
6.Kallay, M., “Plane curves of minimal energy” ACM Transactions on Mathematical Software, 12, 219–222 (1986).CrossRefGoogle Scholar
7.Bruckstein, A. and Netravali, A. “On minimal energy trajectories” Computer Vision, Graphics and Image Processing 49, 283–296 (1990).CrossRefGoogle Scholar
8.Kanayama, Y. and Hartman, B. “Smooth local path planning for autonomous vehicles” Proceedings of the IEEE International Conference on Robotics and Automation (1980) pp. 1265–1270.Google Scholar
9.Elnagar, A. and Basu, A., “Heuristics for local path planning” Proceedings of the IEEE International Conference of Robotics and Automation (05, 1992) pp. 2481–2486.Google Scholar
10.Elsgolc, L., Calculus of Variation (Addison-Wesley, Massachusetts, USA, 1961).Google Scholar
11.Keller, H., Numerical Methods for Two-point Boundary-Value Problems (Blaisdell Publishing Co., Massachusetts, USA, 1968).Google Scholar
12.Roberts, S. and Shipman, J., Two-point Boundary Value Problems: Shooting Methods (American Elsevier Publishing Co., New York, USA, 1972).Google Scholar
13.DeBoor, C., A Practical Guide to Splines (springer Verlag, New York, USA, 1978).CrossRefGoogle Scholar
14.Chasen, S., Geometric Principles and Procedures for Computing Graphic Applications (Prentice-Hall, New Jersey, USA, 1978).Google Scholar