Constrained dynamics with frictional contact on smooth surfaces

Friction and contact pose a great challenge to efficient and accurate simulation of deformable objects for computer graphics and engineering applications. In contrast to many engineering applications, simulation software for graphics often permits larger approximation errors in favour of better predictability, controllability and efficiency. This dissertation explores modern methods for frictional contact resolution in computer graphics. In particular, the focus is on offline simulation of smooth elastic objects subject to contact with other elastic solids and cloth. We explore traditional non-smooth friction formulations as well as smoothed frictional contact, which lends itself well to differentiable simulation and analysis. We then explore a particular application of differentiable simulation to motivate the direction of research.

In graphics, even smooth objects are typically approximated using piecewise linear polyhedra, which exhibit sliding artifacts that can be interpreted as artificial friction making simulations less predictable. We develop a technique for improving fidelity of sliding contact between smooth objects.

Frictional contacts are traditionally resolved using non-smooth models, which are complex to analyse and difficult to compute to a desirable error estimate. We propose a unified description of the equations of motion subject to frictional contacts using a smooth model that converges to an accurate friction response. We further analyse the implications of this formulation and compare our results to state-of-the-art methods.

The smooth model uniquely resolves frictional contacts, while also being fully differentiable. This allows inverse problems using our formulation to be solved by gradient-based methods. We begin our exploration of differentiable simulation applications with a parameter estimation task. Elastic parameters are estimated for a three distinct cloth materials using a novel capture, registration and estimation pipeline. Static equilibrium cloth configurations are efficiently estimated using a popular compliant constraint dynamics. In this work we address a common issue of bifurcation in cloth, which causes final configuration mismatches during estimation. Finally, we postulate an extension to compliant constraint dynamics using our friction model, to show how our previous work can be used in parameter estimation tasks involving contact and friction.
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BibTeX

@phdthesis{larionov22phd,
  series = {Electronic Theses and Dissertations (ETDs) 2008+},
  title = {Constrained dynamics with frictional contact on smooth surfaces},
  url = {https://open.library.ubc.ca/collections/ubctheses/24/items/1.0422992},
  DOI = {http://dx.doi.org/10.14288/1.0422992}, school={University of British Columbia},
  author = {Larionov, Egor},
  year = {2022},
  collection = {Electronic Theses and Dissertations (ETDs) 2008+}
}