A fast impulsive contact suite for rigid body simulation

A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) partial sequential collision resolution, 2) final resolution of collisions through the solution of a single convex QP (positive semidefinite quadratic program), 3) resolution of static contacts through the solution of a single convex QP, 4) freezing of "stationary" bodies. This suite can generate realistic-looking results for simple examples yet, for the first time, can also tractably resolve contacts for a simulation as large as 1,000 cubes in an "hourglass". Freezing speeds up this simulation by more than 25 times. Thanks to excellent commercial QP technology, the contact resolution suite is simple to implement and can be "plugged into" any simulation algorithm to provide fast and realistic-looking animations of rigid bodies.

[1]  J. Moreau.  Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints , 1966 .

[2]  I. Newton.  Philosophiæ naturalis principia mathematica , 1973 .

[3]  Per Lötstedt.  Coulomb Friction in Two-Dimensional Rigid Body Systems , 1981 .

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

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

[6]  J. Keller.  Impact With Friction , 1986 .

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

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

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

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

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

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

[13]  Charles E. Smith,et al.  Coefficients of Restitution , 1992 .

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

[15]  J. Trinkle,et al.  On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction , 1995 .

[16]  Y. Hurmuzlu,et al.  Three-dimensional rigid-body collisions with multiple contact points , 1995 .

[17]  V. Bhatt,et al.  Three-Dimensional Frictional Rigid-Body Impact , 1995 .

[18]  John F. Canny,et al.  Impulse-based simulation of rigid bodies , 1995, I3D '95.

[19]  Jeffrey C. Trinkle,et al.  Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction , 1996, Math. Program..

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

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

[22]  J. A. Batlle.  The sliding velocity flow of rough collisions in multibody systems , 1996 .

[23]  Victor J. Milenkovic.  Position-based physics: simulating the motion of many highly interacting spheres and polyhedra , 1996, SIGGRAPH.

[24]  A. Ruina,et al.  A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations , 1998 .

[25]  Zhi-Quan Luo,et al.  Approximation Algorithms for Quadratic Programming , 1998, J. Comb. Optim..

[26]  M. Rubin.  Physical Restrictions on the Impulse Acting During Three-Dimensional Impact of Two “Rigid” Bodies , 1998 .

[27]  Andrew P. Witkin,et al.  Large steps in cloth simulation , 1998, SIGGRAPH.

[28]  J. A. Batlle,et al.  The Jamb (Self-Locking) Process in Three-Dimensional Collisions , 1998 .

[29]  J. J.,et al.  Numerical aspects of the sweeping process , 1999 .

[30]  Brian Mirtich,et al.  Timewarp rigid body simulation , 2000, SIGGRAPH.

[31]  David E. Stewart,et al.  Rigid-Body Dynamics with Friction and Impact , 2000, SIAM Rev..

[32]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[33]  M. Ferris,et al.  Limit Analysis of Frictional Block Assemblies as a Mathematical Program With Complementarity Constraints , 2001 .

[34]  Pixar Animation Studios,et al.  Physically Based Modeling , 2001 .

[35]  Ronald Fedkiw,et al.  Practical animation of liquids , 2001, SIGGRAPH.

[36]  J. Trinkle,et al.  Dynamic multi-rigid-body systems with concurrent distributed contacts , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[37]  Victor J. Milenkovic,et al.  Optimization-based animation , 2001, SIGGRAPH.

[38]  J. Trinkle,et al.  Dynamic Multi-Rigid-Body Systems with Concurrent Distributed Contacts: Theory and Examples , 2001 .

[39]  Ronald Fedkiw,et al.  Robust treatment of collisions, contact and friction for cloth animation , 2002, SIGGRAPH Courses.