Primal/Dual Descent Methods for Dynamics

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 simul...

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Bibliographic Details
Published in:Computer graphics forum Vol. 39; no. 8; pp. 89 - 100
Main Authors: Macklin, M., Erleben, K., Müller, M., Chentanez, N., Jeschke, S., Kim, T.Y.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.12.2020
Subjects:
CCS Concepts
Computer systems organization → Robotics
Computing methodologies → Simulation by animation
contact
Contact force
Deformation
Formability
friction
Interactive simulation
Mathematical analysis
Numerical analysis
numerical optimization
Rigid structures
robotics
Simulation
Trajectory optimization
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.14104