Planar Friction Modeling With LuGre Dynamics and Limit Surfaces

During planar motion, contact surfaces exhibit a coupling between tangential and rotational friction forces. This article proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended state models are proposed, and the elastoplastic model is extended for multidimensional friction. Subsequently, we derive a reduced planar friction model coupled with a precalculated limit surface, which offers the reduced computational cost. The limit surface approximation through an ellipsoid is discussed. The properties of the planar friction models are assessed in various simulations, demonstrating that the reduced planar friction model achieves comparable performance to the distributed model while exhibiting
$\sim\! 80$
times the lower computational cost.