PROJECTED GAUSS–SEIDEL SUBSPACE MINIMIZATION METHOD FOR INTERACTIVE RIGID BODY DYNAMICS - Improving Animation Quality using a Projected Gauss–Seidel Subspace Minimization Method

Morten Silcowitz, Sarah Niebe, Kenny Erleben

2010

Abstract

In interactive physical simulation, contact forces are applied to prevent rigid bodies from penetrating and to control slipping between bodies. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. This results in visual artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We formulate the contact force problem as a nonlinear complementarity problem, and discretize the problem to derive the Projected Gauss–Seidel method. We combine the Projected Gauss–Seidel method with a subspace minimization method. Our new method shows improved qualities and superior convergence properties for specific configurations.

References

  1. Anitescu, M. and Potra, F. A. (1997). Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems.
  2. Arechavaleta, G., E.Lopez-Damian, and Morales, J. (2009). On the use of iterative lcp solvers for dry frictional contacts in grasping. In International Conference on Advanced Robotics 2009, ICAR 2009.
  3. Billups, S. C. (1995). Algorithms for complementarity problems and generalized equations. PhD thesis, University of Wisconsin at Madison.
  4. Cottle, R., Pang, J.-S., and Stone, R. E. (1992). The Linear Complementarity Problem. Academic Press.
  5. Erleben, K. (2007). Velocity-based shock propagation for multibody dynamics animation. ACM Trans. Graph., 26(2).
  6. Erleben, K. and Ortiz, R. (2008). A Non-smooth Newton Method for Multibody Dynamics. In American Institute of Physics Conference Series.
  7. Featherstone, R. (1998). Robot Dynamics Algorithms. Kluwer Academic Publishers, second printing edition.
  8. Guendelman, E., Bridson, R., and Fedkiw, R. (2003). Nonconvex rigid bodies with stacking. ACM Trans. Graph.
  9. Hahn, J. K. (1988). Realistic animation of rigid bodies. In SIGGRAPH 7888: Proceedings of the 15th annual conference on Computer graphics and interactive techniques.
  10. Kaufman, D. M., Sueda, S., James, D. L., and Pai, D. K. (2008). Staggered projections for frictional contact in multibody systems. ACM Trans. Graph., 27(5).
  11. Milenkovic, V. J. and Schmidl, H. (2004). A fast impulsive contact suite for rigid body simulation. IEEE Transactions on Visualization and Computer Graphics, 10(2).
  12. Mirtich, B. V. (1996). Impulse-based dynamic simulation of rigid body systems. PhD thesis, University of California, Berkeley.
  13. Morales, J. L., Nocedal, J., and Smelyanskiy, M. (2008). An algorithm for the fast solution of symmetric linear complementarity problems. Numer. Math., 111(2).
  14. O'Sullivan, C., Dingliana, J., Giang, T., and Kaiser, M. K. (2003). Evaluating the visual fidelity of physically based animations. ACM Trans. Graph., 22(3).
  15. Redon, S., Kheddar, A., and Coquillart, S. (2003). Gauss least constraints principle and rigid body simulations. In In proceedings of IEEE International Conference on Robotics and Automation.
  16. Silcowitz, M., Niebe, S., and Erleben, K. (2009). Nonsmooth Newton Method for Fischer Function Reformulation of Contact Force Problems for Interactive Rigid Body Simulation. In VRIPHYS 09: Sixth Workshop in Virtual Reality Interactions and Physical Simulations, pages 105-114. Eurographics Association.
  17. Stewart, D. E. (2000). Rigid-body dynamics with friction and impact. SIAM Review.
  18. Stewart, D. E. and Trinkle, J. C. (1996). An implicit timestepping scheme for rigid body dynamics with inelastic collisions and coulomb friction. International Journal of Numerical Methods in Engineering.
  19. Trinkle, J. C., Tzitzoutis, J., and Pang, J.-S. (2001). Dynamic multi-rigid-body systems with concurrent distributed contacts: Theory and examples. Philosophical Trans. on Mathematical, Physical, and Engineering Sciences.
Download


Paper Citation


in Harvard Style

Silcowitz M., Niebe S. and Erleben K. (2010). PROJECTED GAUSS–SEIDEL SUBSPACE MINIMIZATION METHOD FOR INTERACTIVE RIGID BODY DYNAMICS - Improving Animation Quality using a Projected Gauss–Seidel Subspace Minimization Method . In Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010) ISBN 978-989-674-026-9, pages 38-45. DOI: 10.5220/0002830700380045


in Bibtex Style

@conference{grapp10,
author={Morten Silcowitz and Sarah Niebe and Kenny Erleben},
title={PROJECTED GAUSS–SEIDEL SUBSPACE MINIMIZATION METHOD FOR INTERACTIVE RIGID BODY DYNAMICS - Improving Animation Quality using a Projected Gauss–Seidel Subspace Minimization Method},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)},
year={2010},
pages={38-45},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002830700380045},
isbn={978-989-674-026-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)
TI - PROJECTED GAUSS–SEIDEL SUBSPACE MINIMIZATION METHOD FOR INTERACTIVE RIGID BODY DYNAMICS - Improving Animation Quality using a Projected Gauss–Seidel Subspace Minimization Method
SN - 978-989-674-026-9
AU - Silcowitz M.
AU - Niebe S.
AU - Erleben K.
PY - 2010
SP - 38
EP - 45
DO - 10.5220/0002830700380045