Modelling, control and validation of flexible robot manipulators

Abstract

The dynamics equations describing the motion of a flexible manipulator are developed. It is assumed that the manipulator supports the gravitational force, external punctual forces and torques applied at specific points along each link's neutral axis, a punctual force and torque at the end effector, and loads resulting from the application of piezoelectric patches that are bonded at specific points along the elastic links. A discrete model of the Newton-Euler type capturing the fundamental dynamics required for flexible manipulator analysis is deduced for a generic link. A Eulerian formulation is used for the rigid body motion and a total Lagrangian formulation is used for the elastic deformation. To this end, Jourdain's Principle or the Principle of Virtual Powers is adopted, assuming a Rayleigh-Ritz expansion of the elastic variables. The elastic variables, which are the links curvature and shear deformation, are assumed to be infinitesimal. However, nonlinear displacements are considered due to the large length/width aspect ratio of the links. The dynamics model of the manipulator is obtained from the assembling of the individual links. Both the Articulated Body (AB) method, and the Composite Inertia (CI) method are obtained. A validation and control exercise is performed on a single flexible link. Frequency domain and time domain validation is performed in regard to the order of the cross section rotation matrix. Linear and quadratic assumptions are compared against each other, and against the experimental apparatus. Curvature feedback control is compared against classical joint (collocated) feedback, and it's improved performance is shown through the measurement of tip acceleration.