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Authors
Mahmoud Tarokh; Xiaomang Zhang

Identifier
10.3182/20060906-3-IT-2910.00035

Index Terms
robot trajectory tracking,genetic algorithms

Abstract
The paper presents a genetic algorithm approach to real-time trajectory tracking of redundant and non-redundant manipulators. The joint angle trajectories are found by applying genetic operators to a set of suitably generated configurations so that the end-effector follows a desired workspace trajectory accurately. The probability of applying a particular genetic operator is adapted on-line to achieve fast convergence to the solution. The adaptation is based on two measures, namely, diversity and fitness of the generated configurations. In order to achieve fast tracking, special provisions are made so that only an appropriate small region in the joint space is searched. The tracking problem is solved at the position rather the then velocity level. As such the proposed method does not use the manipulator Jacobian inverse or pseudo-inverse matrix and is shown to be free from problems such as excessive joint velocities due to singularities. Simulation results are presented for the 6-DOF Puma and the 7-DOF Robotic that show good tracking accuracy and reasonable joint velocities.

References

[1] Whitney, D. E. (1972) The mathematics of coordinated
    control prosthetic arm and manipulators. Trans.
    ASME J. Dynamic Systems, Measurement and
    Control, pp. 303-309, vol. 94.
[2] Leigeois, A. (1977)Automatic supervisory control of
    configuration and behavior of multi-body
    mechanisms. IEEE Trans. Systems, Man, and
    Cybernetics, vol. SMC-7, no. 12, pp. 868-871.
[3] Nakamura, N. (1991) Advanced Robotics - Redundancy
    and Optimization, Addison-Wesley Publishers.
[4] Klein, C. A. (1983) and C. H. Huang. Review of pseudo-inverse
     control for use with kinematically redundant
    manipulators. IEEE Trans. Systems, Man, and
    Cybernetics, vol. SMC-13, no. 3, pp. 245-250.
[5] Bailieul, J. (1985) Kinematic programming alternatives for
    redundant manipulators. Proc. IEEE Int. Conf.
    Robotics & Automation, pp. 722-728, St. Louis, Mo.
[6] Seraji, H. (1989) Configuration control of redundant
    manipulators: theory and implementation. IEEE
    Trans. Robotics and Automation, vol. RA-5, pp. 472-
    490.
[7] Chiaverini, S., B. Sciliano and O. Egeland, (1994). Review
    of damped least squares inverse kinematics with
    experiments on an industrial robot manipulators.
    IEEE Trans. Control Systems Technology, vol. 2, no.
    2. pp. 123-134.
[8] Wolovich, W. A. and H. Elliot (1984). A computational
    technique for inverse kinematics. Proc. 23rd Conf.
    Decision and Control, pp. 1359-1363.
[9] Chevallereau, C. and B. Daya (1994). A new method for
    robot control in singular configurations with motion
    in any Cartesian direction. Proc. IEEE Int. Conf.
    Robotics and Automation, vol. 4, pp. 2692-2697.
[10] Lloyed, J. E. and V. Hayward (2001). Singularity robust
     trajectory generation. Int. J. Robotics Research, vol.
     20, no. 1, pp. 38-56.
[11] Dermatas E., A. Nearchou, and N. Aspragathos (1996).
     Error -Backpropagation Solution to the Inverse
     Kinematic Problem of Redundant Manipulators. J.
     Robotics and Computer Integrated Manufacturing,
     vol. 12, no. 4, pp. 303-310.
[12] Nearchou, A. C. (1998). Solving the inverse kinematics
     problem of redundant robots operationg in complex
     environments via a modified genetic algorithm. J.
     Mech. Mach. Theory, vol. 33, no. 3, pp. 273-292.
[13] Khwaja, A., M. O. Rahman and M. G. Wagner (1998).
     Inverse kinematics of arbitrary robotic manipulators
     using genetic algorithms. In J. Lenarcic and M. L.
     Justy (editors). Advances in Robot Kinematics:
     Analysis and Control. pp. 375-382, Kluwer
     Academic Publishers, 1998.