First-order friction models with bristle dynamics: lumped and distributed formulations

Researchers have introduced a novel class of first-order dynamic friction models derived from fundamental physical principles, offering greater interpretability than empirical models. A key formulation closely resembles the widely-used LuGre model but is built from a simple rheological equation for a bristle element. The model is rigorously analyzed for stability and passivity—crucial for designing observers and controllers—and includes a distributed version using a hyperbolic PDE to model rolling contact friction. Validation against LuGre shows both similarities and key differences.