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Inverse kinematics of planar redundant manipulators via virtual links with configuration index. (English) Zbl 0805.70006

The paper presents a method which handles the inverse kinematic problem of a discrete planar hyper-redundant manipulator with large redundancy at joint position level. Instead of manipulator modeling as a continuous curve, the method uses the so-called “virtual link” concept which is divided into singular and non-singular cases. A dexterity index is used to provide a switching criterion between the both cases. The proposed method simplifies the inverse kinematic problem of a general planar \(n\)- dof manipulator to that of a 2-link, 3-link module, which greatly reduces the computational burden.

MSC:

70B15 Kinematics of mechanisms and robots
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[1] T. Yoshikawa, ”Analysis and control of robot manipulators with redundancy,” in Robotics Research: The First International Symposium, M. Brady and R. Paul, Eds., MIT Press, Cambridge, MA, 1984, pp. 439-446.
[2] Maciejewski, Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments,, The International Journal of Robotics Research 1 (3) pp 109– (1985)
[3] J. Baillieul, ”Avoiding obstacles and resolving kinematic redundancy,” Proc. IEEE Int. Conf. on Robotics and Automation, San Francisco, CA, April 1986, pp. 1698-1704.
[4] Liègeois, Automatic supervisory control of configuration and behavior of multibody mechanism,, IEEE Trans. Systems, Man and Cybernetics SMC-7 (2) pp 868– (1977)
[5] Klein, Review of pseudoinverse control for use with kinematically redundant manipulators,, IEEE Trans. Systems, Man and Cybernetics SMC-13 (2) pp 245– (1983) · doi:10.1109/TSMC.1983.6313123
[6] Klein, Dexterity measures for the design and control of kinematically redundant manipulators,, The International Journal of Robotics Research 6 (2) pp 72– (1987)
[7] R. Dubey and J. Y. S. Luh, ”Redundant robot control for higher flexibility,” Proc. IEEE Int. Conf. on Robotics and Automation, Raleigh, NC, April 1987, pp. 1066-1072.
[8] Chiu, Task compatibility of manipulators posture,, The International Journal of Robotics Research 7 (5) pp 13– (1988)
[9] O. Khatib and J.-F. Le Maitre, ”Dynamic control of manipulators operating in a complex environment,” Proc. 3rd Int. CISM-IFToMM Symp., Udine, Italy, 1978, pp. 267-282.
[10] J. Angeles, F. Ranjbaran, and R. V. Patel, ”On the design of the kinematic structure of seven-axes redundant manipulators for maximum conditioning,” Proc. IEEE Int. Conf. on Robotics and Automation, Nice, France, May 1992, pp. 494-499.
[11] Ben-israel, Generalized Inverse: Theory and Applications (1980)
[12] G. S. Chirikijan and J. W. Burdick, ”An obstacle avoidance algorithm for hyper-redundant manipulators,” Proc. IEEE Int. Conf. on Robotics and Automation, Cincinnati, OH, May 1990, pp. 625-631.
[13] Naccarato, An Inverse Kinematics Algorithm for a Highly Redundant Variable-geometry-truss Manipulator pp 89– (1989)
[14] T. Fukuda, H. Hosokai, and M. Uemura, ”Rubber gas actuator driven by hydrogen storage alloy for in-pipe inspection mobile robot with flexible structure,” Proc. IEEE Int. Conf. on Robotics and Automation, Scottsdale, AZ, May 1989. pp. 1847-1852.
[15] H. Kobayashi, E. Shimemura, and K. Suzuki, ”A distributed control for hyper redundant manipulator,” Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Raleigh, NC, July 1992, pp. 1958-1963.
[16] A. Hayashi and B. Kuipers, ”A continuous approach to robot motion planning with many degrees of freedom,” Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Raleigh, NC, July 1992, pp. 1935-1942.
[17] G. S. Chirikijan and J. W. Burdick, ”Kinematics of hyper-redundant robot locomotion with applications to grasping,” Proc. IEEE Int. Conf. on Robotics and Automation, Sacramento, CA, April 1991, pp. 720-725.
[18] J. Baillieul, ”Kinematic programming alternatives for redundant manipulators,” Proc. IEEE Int. Conf. on Robotics and Automation, St. Louis, MO, March 1985, pp. 722-728.
[19] Chang, A closed-form solution for inverse kinematics of robot manipulators with redundancy,, IEEE Journal of Robotics and Automation RA-3 (5) pp 393– (1987)
[20] K. Kreutz-delgado, M. Long, and H. Seraji, ”Kinematic analysis of 7 DOF anthropomorphic arms,” Proc. IEEE Int. Conf. on Robotics and Automation, Cincinnati, OH, May 1990, pp. 824-830.
[21] J. M. Hollerbach, ”Optimum kinematic design for a seven degree of freedom manipulator,” 2nd Int. Symposium on Robotics Research, Kyoto, Japan, August 1984, pp. 215-222.
[22] W. J. Chung, W. K. Chung, and Y. Youm, ”Inverse kinematics of planar redundant manipulators using virtual link and displacement distribution schemes,” Proc. IEEE Int. Conf. on Robotics and Automation, Sacramento, CA, April 1991, pp. 926-932.
[23] Jeong, Robotics and Manufacturing 3 pp 577– (1990)
[24] Chung, Kinematic control of planar redundant manipulators by extended motion distribution scheme,, Robotica 10 pp 255– (1992)
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