Dynamic Modeling of Constrained Flexible Robot Arms for Controller Design

Abstract

The modeling for controller design of a constrained rigid-flexible robot arm is considered. The mathematical model is obtained as a set of nonlinear hybrid ordinary-partial differential equations and an algebraic constraint equation. Galerkin’s method is employed to discretize the partial differential equations. Because of the constrained environment of the robot arm, the choice of approximating functions in the spatial discretization is crucial for obtaining accurate simulation results from a low order model. Several candidate approximating functions are evaluated through convergence and accuracy studies. This work also investigates the effects of coupling between rigid- and flexible-body motion, and the effects of axial force (due to the contact force) on bending vibrations through axial shortening. It is shown that the use of inappropriate spatial approximating functions with a low order model can result in faulty predictions of the dynamic response, especially, the axial force effects due to the contact force.