39-Issue 8

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Primal/Dual Descent Methods for Dynamics
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Macklin, Miles; Erleben, Kenny; Müller, Matthias; Chentanez, Nuttapong; Jeschke, Stefan; Kim, Tae-Yong; Bender, Jan and Popa, Tiberiu
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.