A REDUCED-ORDER DYNAMIC-MODEL FOR END-EFFECTOR POSITION CONTROL OF A FLEXIBLE ROBOT ARM

The dynamic model of a robot arm composed of flexible beams and revolu te joints is developed using a Rayleigh-Ritz based substructure synthe sis technique and the linear theory of elastodynamics. Low-degree powe r functions in space variables of each substructure (beam) are adopted as shape functions for the purpose of discretization. Boundary condit ions between substructures are then considered in the form of linear c onstraints of generalized (modal) coordinates and are enforced a poste riori, yielding the assembled dynamic system. This modified approach a llows a systematic formulation which is independent of the problem cha racteristics and analyst's initiative, and allows a simpler reduced-or der model with less degrees of freedom than those obtained by other di scretization schemes, e.g. the finite element method. Using a pole pla cement technique and such a model for a robot arm with a revolute join t and a single flexible link carrying a payload, a state feedback cont roller is designed for the purpose of vibration suppression as well as trajectory tracking. The output signals consist of ''modal'' measurem ents provided by accelerometers and ''rigid'' angular velocity and pos ition measurements provided by a tachometer and an optical shaft encod er on the motor shaft. Comparison of experimental and simulation resul ts confirms the simplicity and validity of the proposed method.