|
|
|
|
RI | Publications | Linear-Time Dynamics using Lagrange Multipliers
|
|
Text only version of this site
Linear-Time Dynamics using Lagrange Multipliers
D. Baraff
tech. report CMU-RI-TR-95-44, Robotics Institute, Carnegie Mellon University, January, 1996.
Jump to: Download | Abstract | Text Reference | BibTeX Reference
| Download [Help] |
Adobe portable document format (pdf) [113 KB] Compressed postscript (ps.gz) [128 KB] Compressed postscript (ps.z) [158 KB]
Copyright notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.
| Abstract |
Current linear-time simulation methods for articulated figures are based exclusively on reduced-coordinate formulations. This paper describes a general, non-iterative linear-time simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics applications because they bypass the difficult (and often intractable) problem of parameterizing a system's degrees of freedom. Given a loop-free set of n$ equality constraints acting between pairs of bodies, the method takes O(n) time to compute the system's dynamics. The method does not rely on matrix bandwidth, so no assumptions about the constraints' topology are needed. Bodies need not be rigid, constraints can be of various dimensions, and unlike reduced-coordinate approaches, nonholonomic (e.g. velocity-dependent) constraints are allowed. An additional set of k one-dimensional constraints which induce loops and/or handle inequalities can be accommodated with cost O(kn). This makes it practical to simulate complicated, closed-loop articulated figures with joint-limits and contact at interactive rates. A complete description of a sample implementation is provided in pseudocode.
| Text Reference |
D. Baraff, Linear-Time Dynamics using Lagrange Multipliers, tech. report CMU-RI-TR-95-44, Robotics Institute, Carnegie Mellon University, January, 1996.
| BibTeX Reference |
@techreport{Baraff_1996_3334,
author = "David Baraff",
title = "Linear-Time Dynamics using Lagrange Multipliers",
institution = "Robotics Institute, Carnegie Mellon University",
month = "January",
year = "1996",
number = "CMU-RI-TR-95-44",
address = "Pittsburgh, PA"
}