Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T11:40:54.398Z Has data issue: false hasContentIssue false
  • English
  • Français

Collision course by transformation of coordinates and plane decomposition

Published online by Cambridge University Press:  01 July 2009

K. Bendjilali  and
F. Belkhouche
K. Bendjilali
Affiliation:
Department of ECE, Lehigh University, PA
F. Belkhouche*
Affiliation:
Texas A&M International University, TX
*
*Corresponding author. E-mail: fbelkhouche@tamiu.edu
Get access Rights & Permissions [Opens in a new window]

Summary

This paper deals with the problem of collision course checking in a dynamic environment for mobile robotics applications. Our method is based on the relative kinematic equations between moving objects. These kinematic equations are written under polar form. A transformation of coordinates is derived. Under this transformation, collision between two moving objects is reduced to collision between a stationary object and a virtual moving object. In addition to the direct collision course, we define the indirect collision course, which is more critical and difficult to detect. Under this formulation, the collision course problem is simplified, and complex scenarios are reduced to simple scenarios. In three-dimensional (3D) settings, the working space is decomposed into two planes: the horizontal plane and the vertical plane. The collision course detection in 3D is studied in the vertical and horizontal planes using 2D techniques. This formulation brings important simplifications to the collision course detection problem even in the most critical and difficult scenarios. An extensive simulation is used to illustrate the method in 2D and 3D working spaces.

Keywords

Collision course in 3DTransformation of coordinatesHorizontal and vertical planesVirtual planes
Type
Article
Information
Robotica , Volume 27 , Issue 4 , July 2009 , pp. 499 - 509
Copyright
Copyright © Cambridge University Press 2008

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.Akella, M. and Alfriend, K., “Probability of collision between space objects,” J. Guidance, Control, Dyn. 23 (5), 769–772 (2000).CrossRefGoogle Scholar
2.Patera, R., “Satellite collision probability for nonlinear relative motion,” J. Guidance, Control, Dyn. 26 (5), 728–731 (2003).CrossRefGoogle Scholar
3.Carlson, R. and Lee, J., “Detecting near collisions for satellites,” IEEE Trans. Aerospace Electron. Syst. 33 (3), 921–929 (1997).CrossRefGoogle Scholar
4.Latombe, J., Robot Motion Planning (Kluwer Academic Press, The Netherlands) (1991).CrossRefGoogle Scholar
5.Foisy, A. and Hayward, V., “A Safe Swept Volume Method for Collision Detection,” The Sixth International Symposium of Robotics Research, Pittsburgh (Oct. 1993) pp. 61–68.Google Scholar
6.Cameron, S., “Collision detection by four-dimensional intersection testing,” IEEE Trans. Rob. Automat. 6 (3), 291–302 (1990).CrossRefGoogle Scholar
7.Choi, Y. K., Wang, W., Liu, Y. and Kim, M., “Continuous collision detection for two moving elliptic disks,” IEEE Trans. Rob. 22 (2), 213–224 (2006).CrossRefGoogle Scholar
8.Choi, Y.-K., Wang, W. and Kim, M.-S., “Exact Collision Detection of Two Moving Ellipsoids Under Rational Motions,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sep. 2003) pp. 349–354.Google Scholar
9.Ming-Yi, J., Liu, J.-S., Shiang, S.-P., Hwang, Y.-R. C. K.-S. and Lee, W.-C., “A Novel Collision Detection Method Based on Enclosed Ellipsoid,” Proceedings of IEEE International Conference on Robotics and Automation, Seoul, S. Korea (Apr. 2001) pp. 2897–2902.Google Scholar
10.Canny, J., “Collision detection for moving polyhedra,” IEEE Trans. Pattern Anal. Mach. Intell. 8 (2), 200–209 (1986).CrossRefGoogle ScholarPubMed
11.Mirolo, C. and Pagello, E., “Fast Convex Minimization to Detect Collisions Between Polyhedra,” Proceedings of IEEE International Conference on Intelligent Robots and Systems, Takamatsu, Japan (Nov. 2000) pp. 1605–1610.Google Scholar
12.Ponamgi, M., Manocha, D. and Lin, M., “Incremental algorithms for collision detection between polygonal models,” IEEE Trans. Visual. Comput. Graph. 3 (1), 51–64 (1997).CrossRefGoogle Scholar
13.Hubbard, P., “Collision detection for interactive graphics applications,” IEEE Trans. Visual. Comput. Graph. 1 (3), 218–230 (1995).CrossRefGoogle Scholar
14.Hayward, V., Auby, S., Foisy, A. and Ghallab, Y., “Effecient collision prediction among many moving objects,” Int. J. Rob. Res. 14 (2), 129–143 (1995).CrossRefGoogle Scholar
15.Kim, H., Guidas, L. and Shin, S., “Effecient collision detection among moving spheres with unknown trajectories,” Algorithmica 43, 195–210 (2005).CrossRefGoogle Scholar
16.Baciu, G. and Wong, W., “Image-based techniques in a hybrid collision detector,” IEEE Trans. Visual. Comput. Graph. 9 (2), 254–271 (2003).CrossRefGoogle Scholar
17.Ebert, M. and Henrich, D., “Safe Human–Robot-Cooperation: Image-Based Collision Detection for Industrial Robots,” Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Lausanne, Switzerland (Sep. 2002) pp. 1826–1831.Google Scholar
18.Woelk, F., Gehrig, S. and Koch, R., “A Monocular Collision Warning System,” Proceedings of the 2nd Canadian Conference on Computer and Robot Vision, Victoria, BC, Canada (May 2005) pp. 220–227.Google Scholar
19.Guibas, L., Xie, F. and Zhang, L., “Kinetic Collision Detection: Algorithms and Experiments,” Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, S. Korea (Apr. 2001) pp. 2903–2910.Google Scholar
20.Hwang, K. and Ju, M., “3D collision-free motion based on collision index,” J. Intell. Rob. Syst. 33, 45–60 (2002).CrossRefGoogle Scholar
21.Jiménez, P., Thomas, F. and Torras, C., “3D collision detection: A survey,” Comput. Graph. 25 (2), 269–285 (2001).CrossRefGoogle Scholar
22.Fujimura, K. and Samet, H., “Planning a time minimal motion among moving obstacles,” Algorithmica 10, 41–63 (1993).CrossRefGoogle Scholar
23.Petti, S. and Fraichard, T., “Safe Motion Planning in Dynamic Environments,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Alberta, Canada (Aug. 2005) pp. 2210–2215.CrossRefGoogle Scholar
24.Berg, J. van den and Overmars, M., “Roadmap-based motion planning in dynamic environments,” IEEE Trans. Rob. 21 (5), 885–897 (2005).CrossRefGoogle Scholar
25.Owen, E. and Montano, L., “Motion Planning in Dynamic Environments Using the Velocity Space,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Alberta, Canada (Aug. 2005) pp. 2833– 2838.CrossRefGoogle Scholar
26.Zhang, F. and Tan, D., “Motion Planning Based on Relative Coordinates in Dynamic Environments for Mobile Robot,” Control, Automation, Robotics and Vision Conference, Nanyang, China (Dec. 2004) pp. 1564–1568.Google Scholar
27.Jing, X.-J., Tan, D.-L. and Wang, Y.-C., “Behavior Dynamics of Collision-Avoidance in Motion Planning of Mobile Robots,” IEEE/RJS International Conference on Intelligent Robots and Systems, Alberta, Canada (Sep. 2004) pp. 1624–1629.Google Scholar
28.Loizou, S. G., Tanner, H., Kumar, V. and Kyriakopoulos, K., “Closed Loop Navigation for Mobile Agents in Dynamic Environments,” IEEE/RJS International Conference on Intelligent Robots and Systems, Las Vegas, NV (Oct. 2003) pp. 3769–3774.Google Scholar
29.Spence, R. and Hutchinson, S., “An integrated architecture for robot motion planning and control in the presence of obstacles with unknown trajectories,” IEEE Trans. Syst., Man Cybernet. 25 (1), 100–110 (1995).CrossRefGoogle Scholar
30.Zhang, X., Lee, M. and Kim, Y., “Interactive continuous collision detection for non-convex polyhedra,” Visual Comput. 22, 749–760 (2006).CrossRefGoogle Scholar
31.Kant, K. and Zucker, S., “Toward efficient trajectory planning: The path-velocity decomposition,” Int. J. Rob. Res. 5 (3), 72–89 (1986).CrossRefGoogle Scholar
32.Fraichart, T., “Trajectory planning amidst moving obstacles: Path–velocity decomposition revisited,” J. Braz. Comput. Sci. Soc. 4 (3), 1–8 (1998).Google Scholar
33.Chakravarthy, A. and Ghose, D., “Obstacle avoidance in dynamic environment: A collision cone approach,” IEEE Trans. Syst., Man Cybernet. Part A 28 (5), 562–574 (1998).CrossRefGoogle Scholar
34.Bernabeu, E. and Tornero, J., “Hough transform for distance computation and collision avoidance,” IEEE Trans. Rob. Automat. 18 (3), 393–398 (2002).CrossRefGoogle Scholar
35.Gilbert, E., Johnson, D. and Keerthi, S., “A fast procedure for computing the distance between complex objects in three-dimensional,” IEEE J. Rob. Automat. 4 (2), 193–203 (1988).CrossRefGoogle Scholar
36.Krishna, K. M. and Karla, P., “Detection, tracking and avoidance of multiple dynamic objects,” J. Intell. Rob. Syst. 33, 371–408 (2002).CrossRefGoogle Scholar
37.Lin, M. and Canny, J., “A Fast Algorithm for Incremental Distance Calculation,” IEEE International Conference on Robotics and Automation, Sacramento, CA (Apr. 1991) pp. 1008– 1014.Google Scholar
38.Gilbert, E. and Johnson, D., “Distance functions and their application to robot path planning in the presence of obstacles,” IEEE J. Rob. Automat. 1 (1), 21–30 (1985).CrossRefGoogle Scholar
39.Kyriakopoulos, K. and Saridis, G., “Distance estimation and collision prediction for online robotic motion planning,” Automatica 28 (2), 389–394 (1992).CrossRefGoogle Scholar
40.Nearchou1, A., Aspragathos, N. and Sofotassios, D., “Reducing the complexity of robot's scene for faster collision detection,” J. Intell. Rob. Syst. 26, 79–89 (1999).CrossRefGoogle Scholar
41.Yeo, T. S., Du, G. and Zhang, S., “Estimation of three-dimensional motion parameters in interferometric isar imaging,” IEEE Trans. Geosci. Remote Sensing 42 (2), 292–300 (2004).Google Scholar