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Primal/Dual Descent Methods for Dynamics
Author(s) -
Macklin M.,
Erleben K.,
Müller M.,
Chentanez N.,
Jeschke S.,
Kim T.Y.
Publication year - 2020
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.14104
Subject(s) - solver , computer science , dual (grammatical number) , mathematical optimization , complementarity (molecular biology) , interior point method , constraint (computer aided design) , differentiable function , contact force , mathematics , geometry , art , physics , literature , mathematical analysis , quantum mechanics , biology , genetics
We examine the relationship between primal, or force‐based, and dual, or constraint‐based formulations of dynamics. Variational frameworks such as Projective Dynamics have proved popular for deformable simulation, however they have not been adopted for contact‐rich scenarios such as rigid body simulation. We propose a new preconditioned frictional contact solver that is compatible with existing primal optimization methods, and competitive with complementarity‐based approaches. Our relaxed primal model generates improved contact force distributions when compared to dual methods, and has the advantage of being differentiable, making it well‐suited for trajectory optimization. We derive both primal and dual methods from a common variational point of view, and present a comprehensive numerical analysis of both methods with respect to conditioning. We demonstrate our method on scenarios including rigid body contact, deformable simulation, and robotic manipulation.