A robust and tractable contact model for dynamic robotic simulation

ABSTRACT

Existing contact modeling in rigid body simulation is inadequate for robotics: no algorithms guarantee both convergence and nonpenetration at multiple contact points in the presence of Coulomb friction. We present a convex optimization based algorithm that models simultaneous contact at multiple points, ensures nonpenetration, and yields Coulomb friction effects. An example of simulated robotic grasping shows that the proposed algorithm is robust where most other methods fail.

REFERENCES

• 1: M. Anitescu, F. Potra, and D. Stewart. Time-stepping for three dimensional rigid body dynamics. Computer Methods in Applied Mechanics and Engineering, 177: 183--197, 1999.
• 2: D. Baraff, Analytical methods for dynamic simulation of non-penetrating rigid bodies, ACM SIGGRAPH Computer Graphics, v.23 n.3, p.223-232, July 1989
• 3: David Baraff, Coping with friction for non-penetrating rigid body simulation, ACM SIGGRAPH Computer Graphics, v.25 n.4, p.31-41, July 1991
• 4: David Baraff, Fast contact force computation for nonpenetrating rigid bodies, Proceedings of the 21st annual conference on Computer graphics and interactive techniques, p.23-34, July 1994 [doi>10.1145/192161.192168]
• 5: V. Bhatt and J. Koechling. Three-dimensional frictional rigid-body impact. ASME J. Appl. Mech., 62: 893--896, 1995.
• 6: Stephen Boyd , Lieven Vandenberghe, Convex Optimization, Cambridge University Press, New York, NY, 2004
• 7: R. P. Brent. Algorithms for Minimization without Derivatives. Prentice-Hall, Engelwood Cliffs, NJ, 1973.
• 8: B. Brogliato, A. ten Dam, L. Paoli, F. Génot, and M. Abadie. Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. ASME Appl. Mech. Reviews, 55(2): 107--150, March 2002.
• 9: A. Chatterjee and A. Ruina. A new algebraic rigid body collision law based on impulse space considerations. ASME J. Appl. Mech., 65(4): 939--951, Dec 1998.
• 10: R. W. Cottle, J.-S. Pang, and R. Stone. The Linear Complementarity Problem. Academic Press, Boston, 1992.
• 11: Evan Drumwright, A Fast and Stable Penalty Method for Rigid Body Simulation, IEEE Transactions on Visualization and Computer Graphics, v.14 n.1, p.231-240, January 2008 [doi>10.1109/TVCG.2007.70416]
• 12: Roy Featherstone , Kluwer Academic Publishers, Robot Dynamics Algorithm, Kluwer Academic Publishers, Norwell, MA, 1987
• 13: Eran Guendelman , Robert Bridson , Ronald Fedkiw, Nonconvex rigid bodies with stacking, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 14: James K. Hahn, Realistic animation of rigid bodies, ACM SIGGRAPH Computer Graphics, v.22 n.4, p.299-308, Aug. 1988
• 15: L. Johansson. A newton method for rigid body frictional impact with multiple simultaneous impact points. Comput. Methods Appl. Mech. Engrg., 191: 239--254, 2001.
• 16: J. B. Keller. Impact with friction. ASME J. Appl. Mech., 53: 1--3, Mar 1986.
• 17: E. Kokkevis. Practical physics for articulated characters. In Proc. of Game Developers Conf., 2004.
• 18: Brian Vincent Mirtich, Impulse-based dynamic simulation of rigid body systems, University of California, Berkeley, 1996
• 19: Brian Mirtich, V-Clip: fast and robust polyhedral collision detection, ACM Transactions on Graphics (TOG), v.17 n.3, p.177-208, July 1998 [doi>10.1145/285857.285860]
• 20: Matthew Moore , Jane Wilhelms, Collision detection and response for computer animationr3, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, p.289-298, June 1988
• 21: P. Painlevé. Sur le lois du frottement de glissemment. C. R. Académie des Sciences Paris, 121: 112--115, 1895.
• 22: F. Pfeiffer and C. Glocker. Dynamics of rigid body systems with unilateral constraints. John Wiley and Sons, 1996.
• 23: E. J. Routh. Dynamics of a system of rigid bodies, 6th ed. Macmillan and Co., London, 1897.
• 24: C. E. Smith. Predicting rebounds using rigid-body dynamics. ASME J. Appl. Mech., 58: 754--758, 1991.
• 25: R. Smith. ODE: Open Dynamics Engine.
• 26: D. Stewart and J. Trinkle. An implicit time-stepping scheme for rigid body dynamics with coulomb friction. In Proc. of the IEEE Intl. Conf. on Robotics and Automation (ICRA), San Francisco, CA, April 2000.
• 27: David E. Stewart, Rigid-Body Dynamics with Friction and Impact, SIAM Review, v.42 n.1, p.3-39, March 2000 [doi>10.1137/S0036144599360110]
• 28: W. J. Stronge. Rigid body collisions with friction. Proc. of the Royal Society of London A, 431(169--181), 1990.
• 29: E. T. Whittaker. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th ed. Dover, 1944.