Combining a Multirate Repetitive Learning Controller with Command Shaping for Improved Flexible Manipulator Control

Sungsoo Rhim School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 Email: [email protected] NaderSadegh School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 Email: [email protected] Command shaping, a feedforward approach used to control flexible manipulators, performs most effectively when applied to a linear system. In practice, various nonlinearities are present in a given system that will deteriorate the performance of command shaping. In this work, a multirate repetitive learning controller (MRLC) is used in conjunction with a command shaping method known as the optimal arbitrary time-delay filter (OATF) for discrete-time joint control of a single flexible link manipulator containing nonlinearities. With very little a priori knowledge of the given system, a MRLC is able to cancel the nonlinearities at select frequencies and achieve near-perfect tracking of a periodic desired trajectory. By doing this, a MRLC controls the joint to follow a given shaped command more closely, thus allowing the OATF to more effectively attenuate residual tip vibrations. It is shown both analytically and experimentally that this controller is more effective than a conventional PID and OATF controller at attenuating residual tip vibrations. INTRODUCTION Having flexibility in a mechanical manipulator will degrade trajectory tracking control and manipulator tip positioning. In practice, however, constraints imposed by manufacturing and operating costs, as well as by various operating environments, will render the presence of such flexibility unavoidable. Ai-Ping Hu School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 Email: [email protected] Wayne J. Book School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 Email: [email protected] Numerous researchers have proposed control schemes to attenuate tip vibration due to flexure during mechanical manipulator motion. These methods may be divided into two categories: feedback and feedforward. Feedback algorithms utilize measurement signals, whereas feedforward algorithms will only utilize desired reference signals. In this work, we will consider a particular feedforward method known as command shaping. Command shaping seeks to reduce tip vibrations by reshaping the desired trajectory to be tracked in order to produce a new trajectory that will not excite the resonances of the flexible manipulator. Command shaping is advantageous because it is able to accomplish this task without regard to the particular form of the desired trajectory. Since its introduction (Singer and Seering, 1990), the command shaping method has been applied successfully in several different applications ((Magee and Book, 1994), (Rhim and Book, 1997)). In our work, we have used a particular command shaping method known as the optimal arbitrary time-delay filter (OATF) (Magee, 1996). The effectiveness of command shaping relies on the linearity of the flexible manipulator system the (reshaped) desired trajectory is commanding. If this system is not linear, we will still observe excitation of the manipulator tip even when using a properly reshaped desired trajectory. The particular flexible mechanical manipulator we have used in our experiments is a gantry-type robot with a prismatic joint and a single flexible link. This is a configuration which is widely used in industry. It is often modFigure 1. CONCEPTUAL BLOCK DIAGRAM WITH COMMAND SHAP-