First-order friction models with bristle dynamics: lumped and distributed formulations
This work addresses the limitations of existing rate-dependent friction models, which are often empirical, lack physical interpretability, and fail to satisfy mathematical properties essential for control and estimation. By leveraging fundamental physical principles and inverting the dynamics of bristle elements, the authors propose a physically grounded first-order dynamic friction modeling framework that guarantees stability and passivity. The framework not only recovers lumped-parameter models akin to LuGre but also, for the first time, yields a distributed-parameter hyperbolic partial differential equation (PDE) model directly linked to bristle dynamics, suitable for rolling contact scenarios. Experimental validation demonstrates that the proposed model reproduces key behaviors of the LuGre model while revealing critical differences, thereby exhibiting superior physical consistency and modeling efficacy.