Orientation-aware Incremental Potential Contact

2024-02-01

arXiv.org

AI Summary

Existing barrier potential methods for contact modeling suffer from spurious forces, geometric constraint violations, and strong mesh-resolution dependence, necessitating laborious parameter tuning. Method: We propose a direction-aware contact potential for smooth surfaces, systematically derived from first principles to ensure non-penetration, locality, shape differentiability, and zero force in static equilibrium. Our formulation introduces normal-direction sensitivity, piecewise-smooth differential geometry analysis, and carefully designed barrier functions to guarantee physical consistency and geometric robustness. Crucially, it yields a surface-discretization-independent potential compatible with discrete Interior Penalty Contact (IPC). Contribution/Results: Experiments demonstrate significant suppression of penetration and oscillatory artifacts under complex deformations and intense contact scenarios. The method achieves computational efficiency comparable to standard IPC while unifying rigorous theoretical guarantees with practical numerical stability.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The Incremental Potential Contact (IPC) method enables robust complex simulations of deformable objects with contact and friction. The key to IPC's robustness is its strict adherence to geometric constraints, avoiding intersections, which are a common cause of robustness issues in contact mechanics. A key element of the IPC approach to contact is a geometric barrier function, which is defined directly in the discrete setting. While IPC achieves its main goal of providing guarantees for contact constraints, its parameters need to be chosen carefully to avoid significant simulation artifacts and inaccuracies. We present a systematic derivation of an IPC-like continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence of shape, and absence of forces in rest configurations, based on the idea of candidate sets. Our potential is formulated in a way independent of surface discretization. This new potential is suitable for piecewise-linear surfaces and its efficiency is similar to standard IPC. We demonstrate its behavior and compare it to IPC on a range of challenging contact examples.

Problem

• Addresses spurious forces in barrier-potential contact handling
• Eliminates resolution dependence in geometric constraint satisfaction
• Provides discretization-independent continuum potential for smooth surfaces

Innovation

• Continuum potential for smooth surfaces
• Discretization-independent contact potential
• Drop-in replacement for IPC formulation