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Geometric Stiffness for Real‐time Constrained Multibody Dynamics
Author(s) -
Andrews Sheldon,
Teichmann Marek,
Kry Paul G.
Publication year - 2017
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13122
Subject(s) - stiffness , integrator , multibody system , stability (learning theory) , work (physics) , computer science , control theory (sociology) , focus (optics) , mathematical optimization , mathematics , classical mechanics , structural engineering , physics , engineering , artificial intelligence , computer network , control (management) , bandwidth (computing) , optics , machine learning , thermodynamics
Abstract This paper focuses on the stable and efficient simulation of articulated rigid body systems for real‐time applications. Specifically, we focus on the use of geometric stiffness which can dramatically increase simulation stability. We examine several numerical problems with the inclusion of geometric stiffness in the equations of motion, as proposed by previous work, and address these issues by introducing a novel method for efficiently building the linear system. This offers improved tractability and numerical efficiency. Furthermore, geometric stiffness tends to significantly dissipate kinetic energy. We propose an adaptive damping scheme, inspired by the geometric stiffness, that uses a stability criterion based on the numerical integrator to determine the amount of non‐constitutive damping required to stabilize the simulation. With this approach, not only is the dynamical behavior better preserved, but the simulation remains stable for mass ratios of 1,000,000‐to‐1 at time steps up to 0.1 s. We present a number of challenging scenarios to demonstrate that our method improves efficiency, and that it increases stability by orders of magnitude compared to previous work.