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 revolute joints is developed using a Rayleigh-Ritz based substructure synthesis technique and the linear theory of elastodynamics. Low-degree power functions in space variables of each substructure (beam) are adopted as shape functions for the purpose of discretization. Boundary conditions between substructures are then considered in the form of linear constraints of generalized (modal) coordinates and are enforced a posteriori, yielding the assembled dynamic system. This modified approach allows a systematic formulation which is independent of the problem characteristics and analyst's initiative, and allows a simpler reduced-order model with less degrees of freedom than those obtained by other discretization schemes, e.g. the finite element method. Using a pole placement technique and such a model for a robot arm with a revolute joint and a single flexible link carrying a payload, a state feedback controller is designed for the purpose of vibration suppression as well as trajectory tracking. The output signals consist of ''modal'' measurements provided by accelerometers and ''rigid'' angular velocity and position measurements provided by a tachometer and an optical shaft encoder on the motor shaft. Comparison of experimental and simulation results confirms the simplicity and validity of the proposed method