A Continuous Velocity-Based Friction Model for Dynamics and Control With Physically Meaningful Parameters

Friction is an important part of many dynamic systems, and, as a result, a good model of friction is necessary for simulating and controlling these systems. A new friction model, designed primarily for optimal control and real-time dynamic applications, is presented in this paper. This new model defines friction as a continuous function of velocity and captures the main velocity-dependent characteristics of friction: the Stribeck effect and viscous friction. Additional phenomena of friction such as micro-displacement and the time dependence of friction were not modeled due to the increased complexity of the model, leading to reduced performance of real-time simulations or optimizations. Unlike several current friction models, this model is C-1 continuous and differentiable, which is desirable for optimal control applications, sensitivity analysis, and multibody dynamic analysis and simulation. To simplify parameter identification, the proposed model was designed to use a minimum number of parameters, all with physical meaning and readily visible on a force-velocity curve, rather than generic shape parameters. A simulation using the proposed model demonstrates that the model avoids any discontinuities in force at initial impact and the transition from slipping to sticking.