A Fast and Stable Penalty Method for Rigid Body Simulation

Two methods have been used extensively to model resting contact for rigid-body simulation. The first approach, the penalty method, applies virtual springs to surfaces in contact to minimize interpenetration. This method, as typically implemented, results in oscillatory behavior and considerable penetration. The second approach, based on formulating resting contact as a linear complementarity problem, determines the resting contact forces analytically to prevent interpenetration. The analytical method exhibits an expected-case polynomial complexity in the number of contact points and may fail to find a solution in polynomial time when friction is modeled. We present a fast penalty method that minimizes oscillatory behavior and leads to little penetration during resting contact; our method compares favorably to the analytical method with regard to these two measures while exhibiting much faster performance both asymptotically and empirically.

[1]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[2]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[3]  David E. Muller,et al.  Finding the Intersection of two Convex Polyhedra , 1978, Theor. Comput. Sci..

[4]  Per Lötstedt.  Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints , 1982 .

[5]  Per Lötstedt.  Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics , 1984 .

[6]  J. Moreau.  Standard Inelastic Shocks and the Dynamics of Unilateral Constraints , 1985 .

[7]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[8]  Jane Wilhelms,et al.  Collision Detection and Response for Computer Animation , 1988, SIGGRAPH.

[9]  J. Moreau,et al.  Unilateral Contact and Dry Friction in Finite Freedom Dynamics , 1988 .

[10]  Katta G. Murty,et al.  Linear complementarity, linear and nonlinear programming , 1988 .

[11]  James K. Hahn,et al.  Realistic animation of rigid bodies , 1988, SIGGRAPH.

[12]  David Baraff,et al.  Analytical methods for dynamic simulation of non-penetrating rigid bodies , 1989, SIGGRAPH.

[13]  W. Stronge.  Rigid body collisions with friction , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[14]  Ming C. Lin,et al.  A fast algorithm for incremental distance calculation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[15]  David Baraff,et al.  Coping with friction for non-penetrating rigid body simulation , 1991, SIGGRAPH.

[16]  M. Marques,et al.  Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction , 1993 .

[17]  David Baraff,et al.  Fast contact force computation for nonpenetrating rigid bodies , 1994, SIGGRAPH.

[18]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[19]  Wayne J. Book,et al.  Contact Stability Analysis of Virtual Walls , 1995 .

[20]  Michael Kass,et al.  An introduction to continuum dynamics for computer graphics , 1995 .

[21]  J. Moreau.  Numerical Experiments in Granular Dynamics: Vibration-Induced Size Segregation , 1995 .

[22]  John F. Hughes,et al.  Plausible motion simulation for computer graphics animation , 1996 .

[23]  Brian Mirtich,et al.  Impulse-based dynamic simulation of rigid body systems , 1996 .

[24]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[25]  David Baraff,et al.  Linear-time dynamics using Lagrange multipliers , 1996, SIGGRAPH.

[26]  Norman I. Badler,et al.  User-controlled physics-based animation for articulated figures , 1996, Proceedings Computer Animation '96.

[27]  D. Baraff.  An Introduction to Physically Based Modeling: Rigid Body Simulation I—Unconstrained Rigid Body Dynamics , 1997 .

[28]  M. Anitescu,et al.  Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems , 1997 .

[29]  D. Baraff.  An Introduction to Physically Based Modeling : Rigid Body Simulation II — Nonpenetration Constraints , 1997 .

[30]  Brian Mirtich,et al.  V-Clip: fast and robust polyhedral collision detection , 1998, TOGS.

[31]  Joseph O'Rourke,et al.  Computational geometry in C (2nd ed.) , 1998 .

[32]  D. Stewart,et al.  Time-stepping for three-dimensional rigid body dynamics , 1999 .

[33]  Iain D. Craig,et al.  COMPUTATIONAL GEOMETRY IN C, SECOND EDITION, by Joseph O'Rourke, CUP, Cambridge, UK, 1998, 376 pages, inc. References and Index (Pb, £55) , 1999, Robotica.

[34]  Jeffrey C. Trinkle,et al.  An implicit time-stepping scheme for rigid body dynamics with Coulomb friction , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[35]  Oussama Khatib,et al.  A framework for multi-contact multi-body dynamic simulation and haptic display , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[36]  Ronald N. Perry,et al.  Adaptively sampled distance fields: a general representation of shape for computer graphics , 2000, SIGGRAPH.

[37]  Ming C. Lin,et al.  Deformed distance fields for simulation of non-penetrating flexible bodies , 2001 .

[38]  Dinesh Manocha,et al.  Fast penetration depth computation for physically-based animation , 2002, SCA '02.

[39]  M. Anitescu,et al.  A Time-stepping Method for Stii Multibody Dynamics with Contact and Friction ‡ , 2022 .

[40]  Atsushi Konno,et al.  An order n dynamic simulator for a humanoid robot with a virtual spring-damper contact model , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[41]  Ronald Fedkiw,et al.  Nonconvex rigid bodies with stacking , 2003, ACM Trans. Graph..

[42]  Evangelos Kokkevis,et al.  Practical Physics for Articulated Characters , 2004 .

[43]  Mihai Anitescu,et al.  A constraint‐stabilized time‐stepping approach for rigid multibody dynamics with joints, contact and friction , 2004 .

[44]  Victor J. Milenkovic,et al.  A fast impulsive contact suite for rigid body simulation , 2004, IEEE Transactions on Visualization and Computer Graphics.

[45]  Makoto Sato,et al.  Real‐time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects , 2004, Comput. Graph. Forum.

[46]  Ronald Fedkiw,et al.  Pre-stabilization for rigid body articulation with contact and collision , 2005, SIGGRAPH '05.

[47]  Ronald Fedkiw,et al.  Dynamic simulation of articulated rigid bodies with contact and collision , 2006, IEEE Transactions on Visualization and Computer Graphics.

[48]  Jakob Andreas Bærentzen,et al.  3D distance fields: a survey of techniques and applications , 2006, IEEE Transactions on Visualization and Computer Graphics.

[49]  Mihai Anitescu,et al.  A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contact, joints, and friction , 2006 .

[50]  Katsu Yamane,et al.  Stable penalty-based model of frictional contacts , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[51]  Richard W. Cottle,et al.  Linear Complementarity Problem , 2009, Encyclopedia of Optimization.