Trajectory planning for residual vibration suppression of a two-link rigid-flexible manipulator considering large deformation

In this paper an optimal trajectory planning technique for suppressing residual vibrations in two-link rigid-flexible manipulators is proposed. In order to obtain an accurate mathematical model, the flexible link is modeled by taking the axial displacement and nonlinear curvature arising from large bending deformation into consideration. The equations of motion of the manipulator are derived using the Lagrangian approach and the assumed modes method. For the trajectory planning, the joint angle of the flexible link is expressed as a cubic spline function, and then the particle swarm optimization algorithm is used to determine the optimal trajectory. The optimal trajectory thus obtained satisfies the minimum vibration condition. By performing numerical simulations, the effectiveness of the proposed trajectory planning technique is verified.

[1]  Kyung-Jo Park,et al.  Flexible Robot Manipulator Path Design to Reduce the Endpoint Residual Vibration under Torque Constraints , 2004 .

[2]  M. K. Lim,et al.  A nonlinear finite element model for dynamics of flexible manipulators , 1996 .

[3]  Toshio Kobayashi,et al.  Residual vibration reduction control after catching a falling steel sphere by a two-link catching flexible robot arm , 2004 .

[4]  M. O. Tokhi,et al.  Command shaping techniques for vibration control of a flexible robot manipulator , 2004 .

[5]  Peter Eberhard,et al.  DYNAMIC ANALYSIS OF FLEXIBLE MANIPULATORS, A LITERATURE REVIEW , 2006 .

[6]  H. Saunders,et al.  Literature Review : SOLID MECHANICS: A VARIATIONAL APPROACH C. L. Dym and I.H. Shames McGraw-Hill Inc. , New York, N. Y. (1973) , 1974 .

[7]  I. Sharf,et al.  Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities , 1995 .

[8]  C. Lin,et al.  Formulation and optimization of cubic polynomial joint trajectories for industrial robots , 1983 .

[9]  Warren P. Seering,et al.  Preshaping Command Inputs to Reduce System Vibration , 1990 .

[10]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[11]  Ashitava Ghosal,et al.  Comparison of the Assumed Modes and Finite Element Models for Flexible Multilink Manipulators , 1995, Int. J. Robotics Res..

[12]  William E. Singhose,et al.  Effects of input shaping on two-dimensional trajectory following , 1996, IEEE Trans. Robotics Autom..

[13]  Ki-Seong Lee,et al.  Residual vibration reduction for a flexible structure using a modified input shaping technique , 2002, Robotica.

[14]  Lawrence S. Kroll.  Mathematica--A System for Doing Mathematics by Computer. , 1989 .

[15]  Leonardo Lanari,et al.  Rest-to-Rest Motion for Planar Multi-Link Flexible Manipulator Through Backward Recursion , 2004 .

[16]  Motoji Yamamoto,et al.  An efficient motion planning of flexible manipulator along specified path , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[17]  I. Sharf.  Geometric Stiffening in Multibody Dynamics Formulations , 1995 .

[18]  Paolo Pennacchi,et al.  Pre-shaping motion input for a rotating flexible link , 2001 .

[19]  Jorge Martins,et al.  Modeling of Flexible Beams for Robotic Manipulators , 2002 .

[20]  Kyung-Jo Park.  Path design of redundant flexible robot manipulators to reduce residual vibration in the presence of obstacles , 2003, Robotica.

[21]  Youn-Sik Park,et al.  Fourier-based optimal design of a flexible manipulator path to reduce residual vibration of the endpoint , 1993, Robotica.

[22]  Irving H. Shames,et al.  Solid mechanics: a variational approach , 1973 .

[23]  Jung-Keun Cho,et al.  Experimental evaluation of time-varying impulse shaping with a two-link flexible manipulator , 1996, Robotica.

[24]  Wayne J. Book,et al.  Eliminating multiple modes of vibration in a flexible manipulator , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[25]  B. O. Al-Bedoor,et al.  GEOMETRICALLY NON-LINEAR DYNAMIC MODEL OF A ROTATING FLEXIBLE ARM , 2001 .

[26]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.