Linear viscoelastic rheological FrBD models

TL;DR

This paper introduces two new linear viscoelastic formulations within the FrBD framework, integrating rate-and-state friction models with linear viscoelasticity, and analyzes their properties for control applications.

Contribution

It presents novel formulations based on GM and GKV models within FrBD, analyzing their boundedness and passivity for control design.

Findings

Both models satisfy boundedness and passivity conditions.

Passivity analysis enables control design applications.

The models successfully integrate rate-and-state friction with viscoelasticity.

Abstract

In [1], a new modeling paradigm for developing rate-and-state-dependent, control-oriented friction models was introduced. The framework, termed Friction with Bristle Dynamics (FrBD), combines nonlinear analytical expressions for the friction coefficient with constitutive equations for bristle-like elements. Within the FrBD framework, this letter introduces two novel formulations based on the two most general linear viscoelastic models for solids: the Generalized Maxwell (GM) and Generalized Kelvin-Voigt (GKV) elements. Both are analyzed in terms of boundedness and passivity, revealing that these properties are satisfied for any physically meaningful parametrization. An application of passivity for control design is also illustrated, considering an example from robotics. The findings of this letter systematically integrate rate-and-state dynamic friction models with linear viscoelasticity.