Analysis and control of redundant parallel manipulators

As we all know, singularity is commonly encountered in parallel mechanisms. It is shown that the behavior of singularity of parallel mechanisms could be more complicated than that of serial ones. However, it is not very clear whether singularity will bring problems to kinematics, dynamics or other characteristics and what result will be caused when parallel mechanisms fall into the neighborhood of a singularity. We focus on the study of the undesired effects of singularity in parallel mechanisms and propose a method to solve them, namely the method of redundancy. Three kinds of redundant methods are developed and their advantages are discussed. In the experiments, we concentrate on the control of redundantly actuated parallel mechanisms. We control the parallel mechanisms tracking a given trajectory by kinematic control method and dynamic control method respectively. Experimental results verified the efficiency of the proposed algorithms.

[1]  W. Boothby An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[2]  Olivier Chételat,et al.  A Reduced Model for Constrained Rigid Bodies with application to Parallel Robots , 1994 .

[3]  Fathi H. Ghorbel,et al.  PD Control of Closed-Chain Mechanical Systems: An Experimental Study , 1997 .

[4]  Guanfeng Liu,et al.  On the dynamics of parallel manipulators , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[5]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[6]  Josip Loncaric,et al.  Normal forms of stiffness and compliance matrices , 1987, IEEE Journal on Robotics and Automation.

[7]  Vijay Kumar,et al.  Aane Connections for the Cartesian Stiiness Matrix , 1997 .

[8]  Jean-Pierre Merlet Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1989, Int. J. Robotics Res..

[9]  Jindong Tan,et al.  Hybrid system design for singularityless task level robot controllers , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[10]  Bahram Ravani,et al.  A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators , 2001 .

[11]  Yoshihiko Nakamura,et al.  Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators , 1989, IEEE Trans. Robotics Autom..

[12]  G. Hirzinger,et al.  Singularity Consistent Inverse Kinematics by Enhancing the Jacobian Transpose , 1998 .

[13]  Frank Chongwoo Park,et al.  Manipulability and singularity analysis of multiple robot systems: a geometric approach , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[14]  Fathi H. Ghorbel Modeling and PD control of closed-chain mechanical systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[15]  Vijay Kumar,et al.  Affine connections for the Cartesian stiffness matrix , 1997, Proceedings of International Conference on Robotics and Automation.

[16]  Yoshihiko Nakamura,et al.  Inverse kinematic solutions with singularity robustness for robot manipulator control , 1986 .

[17]  Bruno Siciliano,et al.  Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator , 1994, IEEE Trans. Control. Syst. Technol..