Primal/Dual Descent Methods for Dynamics

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.

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

“…This way, we achieve a strong coupling between contact forces and friction through one global monolithic system, which is crucial for simulation stability when considering rigid bodies [KSJP08]. While this is common practice in pure rigid body simulation frameworks [BET14, Erl17, PAK*19, MEM*19, MEM*20, FLS*21], we are not aware of an existing simulation method that strongly couples internal fluid pressure forces, fluid–rigid interface forces, rigid–rigid contact forces with dry friction forces. In Section 4, we provide an illustration of an efficient solver implementation that is able to compute $${{{ \mathbf {p}}}}$$ and $${{{ \bm {\lambda }}}}$$ satisfying the constraints given in Equations (9), (17) and (18).…”

A review for the noise source identification methods based microphone array

“…The expansion term of the basis function has a direct influence on the results of sound field reconstruction, so the reasonable selection of the number of measurement points and expansion terms is particularly critical. Dwarka [65] and Macklin [66] have combined geometric analysis from the perspective of scalability, analyzed the sound field in the smallest sphere covering irregular sound source with trigonometric function and spherical function as basis function, and obtained the scalable convergence of HELS.…”

Differentiable Depth for Real2Sim Calibration of Soft Body Simulations

“…Recently, many works have presented differentiable simulators for rigid bodies, articulated rigid bodies, cloth and fluids [dABPSA*18, SF18, LLK19, DHDw19, LL20, LLKL*20, KAMS20, SB20, HMZS20]. Recent work addressed multi‐body simulations of both rigid and soft bodies [MEM*20, GHZ*20]. In our work, we focus on hyper‐elastic soft materials that are connected to rigid fixed objects.…”