Shear force feedback control of a single-link flexible robot with a revolute joint

In this paper we present a shear force feedback control method for a single-link flexible robot arm with a revolute joint for which it has been shown that direct bending strain feedback can suppress its vibration. Our primary concern is the stability analysis of the closed-loop equation which has not appeared in the literature. We show the existence of a unique solution and the exponential stability of this solution by doing spectral analysis and estimating the norm of the resolvent operator associated with this equation. Some experiments are also conducted to verify these theoretical developments.

[1]  Bao-Zhu Guo,et al.  Stability analysis of a hybrid system arising from feedback control of flexible robots , 1996 .

[2]  Bruno Siciliano,et al.  Trajectory control of a non-linear one-link flexible arm , 1989 .

[3]  F.-Y. Wang,et al.  Influences of Rotatory Inertia, Shear and Loading on Vibrations of Flexible Manipulators , 1994 .

[4]  Z. Luo,et al.  Further theoretical results on direct strain feedback control of flexible robot arms , 1995, IEEE Trans. Autom. Control..

[5]  Z. Luo.  Direct strain feedback control of flexible robot arms: new theoretical and experimental results , 1993, IEEE Trans. Autom. Control..

[6]  Steven G. Krantz,et al.  The Euler-Bernoulli beam equation with boundary energy dissipation , 1988 .

[7]  Bruno Siciliano,et al.  A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators , 1988, Int. J. Robotics Res..

[8]  A. Krall,et al.  Modeling stabilization and control of serially connected beams , 1987 .

[9]  Ö. Morgül.  Orientation and stabilization of a flexible beam attached to a rigid body: planar motion , 1991 .

[10]  Alessandro De Luca,et al.  Closed-form dynamic model of planar multilink lightweight robots , 1991, IEEE Trans. Syst. Man Cybern..

[11]  R. H. Cannon,et al.  Initial Experiments on the End-Point Control of a Flexible One-Link Robot , 1984 .

[12]  Fumitoshi Matsuno,et al.  Modeling and feedback control of a flexible arm , 1985, J. Field Robotics.

[13]  Wayne J. Book,et al.  Feedback control of two beam, two joint systems with distributed flexibility , 1975 .

[14]  Zheng-Hua Luo,et al.  Shear force feedback control of flexible robot arms , 1995, IEEE Trans. Robotics Autom..

[15]  J. Yuh,et al.  Dynamic Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment , 1991 .

[16]  B. S. Yuan,et al.  Small Motion Experiments on a Large Flexible Arm with Strain Feedback , 1989, 1989 American Control Conference.

[17]  Frank Neubrander,et al.  INTEGRATED SEMIGROUPS AND THEIR APPLICATIONS TO THE ABSTRACT CAUCHY PROBLEM , 1988 .

[18]  Omer Morgiil.  Dynamic Boundary Control of a Euler-Bernoulli Beam , 1992 .

[19]  Richard Beals,et al.  On the abstract Cauchy problem , 1972 .

[20]  Hideaki Kanoh,et al.  Vibration control of one-link flexible arm , 1985, 1985 24th IEEE Conference on Decision and Control.