The Visual Computer

, Volume 24, Issue 4, pp 261–269 | Cite as

Continuous collision detection for adaptive simulation of articulated bodies

Original Article

Abstract

We perform continuous collision detection (CCD) for articulated bodies where motion is governed by an adaptive dynamics simulation. Our algorithm is based on a novel hierarchical set of transforms that represent the kinematics of an articulated body recursively, as described by an assembly tree. The performance of our CCD algorithm significantly improves as the number of active degrees of freedom in the simulation decreases.

Keywords

Continuous collision detection Articulated body dynamics Adaptive dynamics Interval arithmetic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdel-Malek, K., Blackmore, D., Joy, K.: Swept volumes: foundations, perspectives, and applications. Int. J. Shape Model. 12(1), 87–127 (2006)MATHCrossRefGoogle Scholar
  2. 2.
    Agarwal, P.K., Basch, J., Guibas, L.J., Hershberger, J., Zhang, L.: Deformable free space tiling for kinetic collision detection. In: Workshop on Algorithmic Foundations of Robotics, pp. 83–96 (2001)Google Scholar
  3. 3.
    Bae, D., Haug, E.: A recursive formulation for constrained mechanical systems dynamics: Part 1, Open-loop systems. Mech. Struct. Mach. 15(3), 359–382 (1987)CrossRefGoogle Scholar
  4. 4.
    Baraff, D.: Fast contact force computation for nonpenetrating rigid bodies. In: Glassner, A. (ed.) Proceedings of SIGGRAPH ’94, pp. 23–34 (1994)Google Scholar
  5. 5.
    Brandl, H., Johanni, R., Otter, M.: A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix. In: IFAC/IFIP/IMACS Symposium, pp. 95–100 (1986)Google Scholar
  6. 6.
    Canny, J.F.: Collision detection for moving polyhedra. IEEE Trans. Pattern Anal. Mach. Intell. 8, 200–209 (1986)Google Scholar
  7. 7.
    Chenney, S., Forsyth, D.: View-dependent culling of dynamic systems in virtual environments. In: Proceedings of the ACM Symposium on Interactive 3D Graphics, pp. 55–58 (1997)Google Scholar
  8. 8.
    Choi, Y.K., Wang, W., Liu, Y., Kim, M.S.: Continuous collision detection for two moving elliptic disks. IEEE Trans. Robot. 22(2), 213–224 (2006)CrossRefGoogle Scholar
  9. 9.
    Faure, F.: Fast iterative refinement of articulated solid dynamics. IEEE Trans. Vis. Comput. Graph. 5(3), 268–276 (1999)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Featherstone, R.: Robot Dynamics Algorithms. Kluwer, Boston, MA (1987)Google Scholar
  11. 11.
    Featherstone, R.: A divide-and-conquer articulated body algorithm for parallel o(log(n)) calculation of rigid body dynamics: Part 1, Basic algorithm. Int. J. Robot. Res. 18(9), 867–875 (1999)CrossRefGoogle Scholar
  12. 12.
    Featherstone, R.: A divide-and-conquer articulated body algorithm for parallel o(log(n)) calculation of rigid body dynamics: Part 2, Trees, loops, and accuracy. Int. J. Robot. Res. 18(9), 876–892 (1999)CrossRefGoogle Scholar
  13. 13.
    Featherstone, R., Orin, D.E.: Robot dynamics: equations and algorithms. In: IEEE International Conference on Robotics and Automation, pp. 826–834 (2000)Google Scholar
  14. 14.
    Hollerbach, J.: A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans. Syst. Man Cybern. 10(11), 730–736 (1980)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kim, B., Rossignac, J.: Collision prediction for polyhedra under screw motions. In: ACM Conference on Solid Modeling and Applications, pp. 4–10 (2003)Google Scholar
  16. 16.
    Kim, D., Guibas, L., Shin, S.: Fast collision detection among multiple moving spheres. IEEE Trans. Vis. Comput. Graph. 4(3), 230–242 (1998)CrossRefGoogle Scholar
  17. 17.
    Kirkpatrick, D., Snoeyink, J., Speckmann, B.: Kinetic collision detection for simple polygons. In: Proceedings of the ACM Symposium on Computational Geometry, pp. 322–330 (2000)Google Scholar
  18. 18.
    McMillan, S., Orin, D.E.: Efficient computation of articulated-body inertias using successive axial screws. IEEE Trans. Robot. Autom. 11, 606–611 (1995)CrossRefGoogle Scholar
  19. 19.
    Moore, R.E.: Interval Analysis. Prentice Hall, Englewood Cliffs, NJ (1966)MATHGoogle Scholar
  20. 20.
    Ortega, M., Redon, S., Coquillart, S.: A six degree-of-freedom god-object method for haptic display of rigid bodies. IEEE Trans. Vis. Comput. Graph. 13(3), 458–469 (2007)CrossRefGoogle Scholar
  21. 21.
    Redon, S., Galoppo, N., Lin, M.C.: Adaptive dynamics of articulated bodies. ACM Trans. Graph. (SIGGRAPH 2005) 24(3) (2005)Google Scholar
  22. 22.
    Redon, S., Kheddar, A., Coquillart, S.: An algebraic solution to the problem of collision detection for rigid polyhedral objects. In: Proceedings of the IEEE Conference on Robotics and Automation, vol. 4, pp. 3733–3738 (2000)Google Scholar
  23. 23.
    Redon, S., Kheddar, A., Coquillart, S.: Fast continuous collision detection between rigid bodies. Comput. Graph. Forum 21(3), 279–287 (2002)CrossRefGoogle Scholar
  24. 24.
    Redon, S., Kheddar, K., Coquillart, S.: Gauss’ least constraints principle and rigid body simulation. In: Proceedings of the International Conference on Robotics and Automation, vol. 1, pp. 517–522 (2002)Google Scholar
  25. 25.
    Redon, S., Kim, Y.J., Lin, M.C., Manocha, D.: Fast continuous collision detection for articulated models. In: Proceedings of the ACM Symposium on Solid Modeling and Applications, pp. 145–156 (2004)Google Scholar
  26. 26.
    Redon, S., Kim, Y.J., Lin, M.C., Manocha, D.: Interactive and continuous collision detection for avatars in virtual environments. In: Proceedings of the IEEE Conference on Virtual Reality, pp. 117–283 (2004)Google Scholar
  27. 27.
    Redon, S., Lin, M.C.: An efficient, error-bounded approximation algorithm for simulating quasi-statics of complex linkages. In: Proceedings of the ACM Symposium on Solid and Physical Modeling, pp. 175–186 (2005)Google Scholar
  28. 28.
    Redon, S., Lin, M.C.: Practical local planning in the contact space. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 4200–4205 (2005)Google Scholar
  29. 29.
    Schwarzer, F., Saha, M., Latombe, J.C.: Exact collision checking of robot paths. In: Workshop on Algorithmic Foundations of Robotics (WAFR), pp. 25–42 (2002)Google Scholar
  30. 30.
    Zhang, X., Lee, M., Kim, Y.J.: Interactive continuous collision detection for non-convex polyhedra. Vis. Comput. 22, 9–11 (2006)Google Scholar
  31. 31.
    Zhang, X., Redon, S., Lee, M., Kim, Y.J.: Continuous collision detection for articulated models using Taylor models and temporal culling. ACM Trans. Graph. 26(3), 15 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringEwha Womans UniversitySeoulKorea
  2. 2.i3D, INRIA Grenoble – Rhône-AlpesMontbonnotFrance

Personalised recommendations