A fractional order viscous friction model in robotic joints

Abstract

The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this paper, dynamic model of robot manipulator is introduced using the Rodriquez approach. Then, a viscous friction term is extended to be proportional to the fractional derivative of the angular displacement. This model is introduced into dynamic equations via generalized forces which are derived by using the principle of virtual work. Numerical example for the robotic system with three degrees of freedom is presented. The results obtained for generalized forces are compared for different values of parameters in the fractional order derivative model