Fast Iterative Refinement of Articulated Solid Dynamics

A new dynamics algorithm for articulated solid animation is presented. It provides enhancements of computational efficiency and accuracy control with respect to previous solutions. Iterative refinement allows us to perform interactive animations which could be only computed off-line using previous methods. The efficiency results from managing two sets of constraints associated with the kinematic graph, and proceeding in two steps. First, the acyclic constraints are solved in linear time. An iterative process then reduces the closed-loop errors while maintaining the acyclic constraints. This allows the user to efficiently trade off accuracy for computation time. We analyze the complexity and investigate practical efficiency compared with other approaches. In contrast with previous research, we present a single method which is computationally efficient for acyclic bodies as well as for mesh-like bodies. The accuracy control is provided by the iterative improvement performed by the algorithm and also from the existence of two constraint priority levels induced by the method. Used in conjunction with a robust integration scheme, this new algorithm allows the interactive animation of scenes containing a few thousand geometric constraints, including closed loops. It has been successfully applied to real-time simulations.

[1]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[2]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[3]  R. Paul.  Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[4]  David E. Orin,et al.  Efficient Dynamic Computer Simulation of Robotic Mechanisms , 1982 .

[5]  Brian A. Barsky,et al.  Using dynamic analysis to animate articulated bodies such as humans and robots , 1985 .

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

[7]  Michael F. Cohen,et al.  Controlling dynamic simulation with kinematic constraints , 1987, SIGGRAPH.

[8]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[9]  Ronen Barzel,et al.  A modeling system based on dynamic constraints , 1988, SIGGRAPH.

[10]  Michael Gleicher,et al.  Interactive dynamics , 1990, I3D '90.

[11]  W. Press,et al.  Numerical Recipes - Example Book (FORTRAN) - Second Edition , 1992 .

[12]  J. Shewchuk.  An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

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

[14]  Michael Gleicher,et al.  A differential approach to graphical interaction , 1994 .

[15]  U. Ascher,et al.  Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds , 1995 .

[16]  Hong Sheng Chin,et al.  Stabilization methods for simulations of constrained multibody dynamics , 1995 .

[17]  K. Overveld,et al.  All You Need Is Force: a constraint-based approach for rigid body dynamics in computer animation , 1995 .

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