Implicit Multibody Penalty-based Distributed Contact

How to read this

Category

Method: stable penalty-based distributed contact for rigid/articulated bodies

Contributions

• A penalty-based frictional contact scheme that stays stable across large, time-varying contact areas among many rigid and articulated bodies, including conforming and self-contact
• Combines semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination, and an SVD solver to tame variable net stiffness
• Derivation of implicit proportional-derivative control forces for real-time control of articulated structures with loops

Context

Addresses long-standing penalty-contact instability and connects to robust simultaneous-collision handling (Harmon et al.'s 'Robust Treatment of Simultaneous Collisions'), here via an implicit, gradient-exact formulation.Builds on: Robust Treatment of Simultaneous Collisions

Correctness

The core claim is improved stability of penalty contact under distributed, geometrically complex contact; it targets rigid and articulated rigid bodies, so a reader should not assume the same guarantees for deformable contact, and stability still depends on the integration and solver choices described.

Clarity

Technical; a first pass conveys the problem and the ingredient list, but the formulation (analytical gradients, symbolic elimination, implicit PD) genuinely needs a second pass.

How to read it

Read for why naive penalty stiffness destabilizes and how each component (semi-implicit, exact gradients, SVD) addresses it; plan a second pass on the contact-gradient derivation and the implicit PD forces if implementing.