Linear viscoelastic rheological FrBD models
This work provides incremental improvements to friction modeling for control systems in robotics and related fields.
The paper tackled the problem of developing rate-and-state-dependent friction models by introducing two novel formulations based on Generalized Maxwell and Generalized Kelvin-Voigt linear viscoelastic elements within the FrBD framework, resulting in models that satisfy boundedness and passivity for any physically meaningful parametrization and demonstrating an application in robotics control design.
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.