Planar Friction Modelling with LuGre Dynamics and Limit Surfaces

TL;DR

The paper addresses the computationally challenging problem of accurately modeling planar friction with coupling between tangential and rotational forces. It combines LuGre dynamics with limit surface theory to produce a distributed planar friction model and an Elasto-Plastic extension that mitigates drift, then derives a computationally efficient reduced model by mapping to an ellipsoid limit surface and pre-computing a limit-surface representation. The reduced model, supported by bilinear interpolation and limit-surface scaling, achieves similar dynamics to the distributed model while offering up to roughly $\approx 80\times$ lower computational cost (and $\approx 63\times$ faster run-times in certain cases). These results enable fast, accurate friction handling for in-hand manipulation and contact-rich tasks, with potential for tactile-based perception and real-time control; future work includes generalizing pre-computation to arbitrary contact shapes and establishing benchmark datasets.

Abstract

During planar motion, contact surfaces exhibit a coupling between tangential and rotational friction forces. This paper proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended state models are proposed and the Elasto-Plastic model is extended for multi-dimensional friction. Subsequently, we derive a reduced planar friction model, coupled with a pre-calculated limit surface, that offers 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 ~80 times lower computational cost.

Figures (37)

• Figure 1: Planar friction in a parallel gripper, wherein the friction force is represented by a force wrench vector.
• Figure 2: The bristle analogy of the Dahl and LuGre friction model.
• Figure 3: The vector $\boldsymbol{\rho}(x,y)$ from CoP to the infinitesimal contact area $dA$ and the local velocity vector $\mathbf{v}_t(x,y)$, for a contact surface.
• Figure 4: Four illustrations of different contact surfaces.
• Figure 5: Simulation with predefined velocity profile for the distributed planar LuGre model. The simulation uses a circular contact surface with a radius of $10$ [mm] and a normal force of $1$ [N]. The velocity profile and friction force are at the CoP.