Kinematic Solutions for Redundant Robot Based on Paden-Kahan Subproblems
YANG Ming-ming1, CHEN Wei-hai2, YU Shou-qian1, WU Zhen2
1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics & Astronautics, Beijing 100083, China; 2. Robotics Institute, Beijing University of Aeronautics & Astronautics, Beijing 100083, China
Abstract：This paper deals with the inverse kinematic solutions of a 7-DOF redundant robot. A hybrid algorithm that can improve the control precision is proposed. This algorithm uses screw theory to describe the motion of the robot. Firstly it finds the joint rate solution through optimizing kinematic performance criterion. Then a special joint is fixed to transform the problem into kinematic control of a non-redundant robot, by using Paden-Kahan subproblems, other joint angles are solved. The effectiveness of the proposed algorithm has been verified by a simulation of a 7-DOF robot.
 Liegeois A. Automatic supervisory control of the configuration and behavior of multibody mechanisms[J]. IEEE Transations on Systems Man, and Cybernetics,1977,7(12):868-871.  Li L Y, Gruver W A, Zhang Q X, et al. Kinematic control of redundant robots and the motion optimizability measure[J]. IEEE Transations System Man,and Cybernetics. 2001,31(1):155-160.  Murray R, Li Z, Sastry S S. A Mathematical Introduction to Robotic Manipulation [M]. Boca Raton, FL, USA: CRC Press,1994.  Chen I M, Yang G L. Inverse kinematics for modular reconfigurable robots[A]. Proceedings of the IEEE International Conference on Robotics and Automation [C]. Leuven, Belgium: 1998.2.1647-1652.  Chen W H, Chen I M, Lim W K, et al. Cartesian coordinate control for redundant modular robots [A]. Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics [C]. Nashville,TN,USA:2000,5.3253-3258.  Park F C. Computational aspect of manipulators via product of exponential formula for robot kinematics[J]. IEEE Transations on Automatic Control,1994,39(3):643-647.  Chen W H, Yang G L, Ho E H L, et al. Interactive-motion control of modular reconfigurable manipulators [A]. Proceedings of the 2003IEEE/RSJ International Conference on Intelligent Robots and Systems [C]. Las Vegas, Nevada, USA: 2003,2.1620-1625.