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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| Vydáno v: | Computer graphics forum Ročník 39; číslo 8; s. 89 - 100 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Blackwell Publishing Ltd
01.12.2020
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Erleben, K. Macklin, M. Müller, M. Chentanez, N. Kim, T.Y. Jeschke, S. |
| Author_xml | – sequence: 1 givenname: M. surname: Macklin fullname: Macklin, M. organization: University of Copenhagen – sequence: 2 givenname: K. surname: Erleben fullname: Erleben, K. organization: University of Copenhagen – sequence: 3 givenname: M. surname: Müller fullname: Müller, M. organization: NVIDIA – sequence: 4 givenname: N. surname: Chentanez fullname: Chentanez, N. organization: NVIDIA – sequence: 5 givenname: S. surname: Jeschke fullname: Jeschke, S. organization: NVIDIA – sequence: 6 givenname: T.Y. surname: Kim fullname: Kim, T.Y. organization: NVIDIA |
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| SubjectTerms | 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 |
| Title | Primal/Dual Descent Methods for Dynamics |
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