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Implementation of the velocities of the end-effector with the distributed arithmetic architecture

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Abstract

The fast implementation of the linear and of the angular velocities of the end-effector of robotic manipulators, using the distributed arithmetic technique is described. The linear and angular velocities of the end-effector as well as the positional and the orientational jacobian matrices is calculated by a cascade configuration of two pipelined arrays. The building blocks of the arrays are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculations. The digit-serial configuration of the proposed implementation of the linear and angular velocities of the end-effector is described, while the serial and the parallel configurations may result as special cases of the digit-serial configuration. The proposed distributed arithmetic computer architecture may be used in the real-time operation of the robot control system that requires the on-line computation of the position, of the linear and angular velocities of the end-effector and of the Jacobian matrix.

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References

  1. Ang, M. H. Jr. and Tourassis, V. D.: General-puprpose inverse kinematics transformations for robotic manipulators,J. Robotic Systems 4(4) (1987), 527–549.

    Google Scholar 

  2. Orin, D. E. and Schrader, W. W.: Efficient computation of the Jacobian for robot manipulators,Int. J. Robotics Res. 3(4) (Winter 1984), 66–75.

    Google Scholar 

  3. Li, C., Hemami, A. and Sankar, T. S.: An efficient computational method of the Jacobian for robot manipulators,Robotica 9 (1991), 231–234.

    Google Scholar 

  4. Paul, R., Shimano, B., and Mayer, G.: Kinematic control equations for simple manipulators,IEEE Trans. Syst., Man and Cybernetics SMC-11(6) (June 1981), 456–460.

    Google Scholar 

  5. Leung, S. S. and Shanblatt, M. A.: Real-time DKS on a single chip,IEEE J. Robotics and Autom. RA-3(4) (Aug. 1987), 281–290.

    Google Scholar 

  6. Turney, J. L. and Mudge, T. N.: VLSI implementation of a numerical processor for robotics, inProc. 27th IEEE Int. Instrumentation Symp., Indianapolis, April 1981, pp. 169–175.

  7. Lygouras, J. N., Mertzios, B. G. and Voulgaris, N. C.: Cartesian space sensor based on kinematics,J. Franklin Institute 327(3) (1990), 465–480.

    Google Scholar 

  8. Graham, J. H.: Special computer architectures for robotics: Turorial and survey,IEEE Trans. Robotics Automat. RA-5(5) (Oct. 1989), 543–554.

    Google Scholar 

  9. Mertzios, B. G.: Fast implementation of direct robot kinematics with CORDIC systolic arrays,Parallel Computing Journal. To appear.

  10. Walker, I. D. and Cavallaro, J. R.: Parallel VLSI architectures for real-time kinematics of redundant robots,J. Intelligent and Robotic Systems 9 (1994), 25–43.

    Google Scholar 

  11. Maciejewski, A. A. and Reagin, J. M.: A parallel algorithm and architecture for the control of kinematically redundant manipulators,IEEE Trans. Robotics and Automat. 10(4) (August 1994), 405–415.

    Google Scholar 

  12. Yeung, T. B. and Lee, G. S. G.: Efficient parallel algorithms and VLSI architectures for manipulator Jacobian computation,IEEE Trans. Syst., Man, and Cybernetics 19(5) (Sept./Oct. 1989), 1154–1166.

    Google Scholar 

  13. Peled, A. and Liu, B.: A new hardware realization of digital filters,IEEE Trans. Acoustics, Speech and Signal Processing ASSP-22(6) (Dec. 1974), 456–462.

    Google Scholar 

  14. White, S. A.: Applications of distributed arithmetic to digital signal processing: A tutorial review,IEEE ASSP Magazine 6(3) (July 1989), 4–19.

    Google Scholar 

  15. Wang, S. and Bowron, P.: Microcontroller implementation of digital filters based on distributed arithmetic,Int. J. Electronics 72(1) (Jan. 1992), 67–71.

    Google Scholar 

  16. Burleson and Scharf, L.: A VLSI design methodology for distributed arithmetic,J. VLSI Signal Processing (2) (1991), 235–252.

  17. Parhi, K. K.: A systematic approach for design of digit-serial signal processing architectures,IEEE Trans. Circuits and Systems 38(4) (April 1991), 358–375.

    Google Scholar 

  18. Fu, K. S., Gonzalez, R. C. and Lee, C. S. G.:Robotics: Control, Sensing, Vision, and Intelligence, McGraw-Hill, 1987.

  19. Graig, J. J.:Introduction to Robotics: Mechanics and Control, Addison-Wesley, Reading, MA, 1987.

    Google Scholar 

  20. Wolovich, W. A.:Robotics: Basic Analysis and Design, Halt, Rinehart and Winston, New York, 1987.

    Google Scholar 

  21. Snyder, W. E.:Industrial Robots: Computer Interfacing and Control, Prentice-Hall, Englewood Cliffs, NJ, 1985.

    Google Scholar 

  22. Hwang, K.:Advance Computer Architecturers: Parallelism, Scalability and Programmability, Computer Science Series, McGraw-Hill, New York, 1993.

    Google Scholar 

  23. Hayes, J. P.:Computer Architecture and Organization, Computer Science Series, McGraw-Hill, New York, 1983.

    Google Scholar 

  24. Almasi, G. S. and Gottlied, A.:High Parallel Computing, Benjamin/Cummings, 1989.

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Authors and Affiliations

  1. Automatic Control Systems Laboratory, Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100, Xanthi, Greece

    G. K. Grigoriadis & B. G. Mertzios

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  1. G. K. Grigoriadis
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  2. B. G. Mertzios
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Grigoriadis, G.K., Mertzios, B.G. Implementation of the velocities of the end-effector with the distributed arithmetic architecture. J Intell Robot Syst 17, 387–417 (1996). https://doi.org/10.1007/BF00571700

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  • DOI: https://doi.org/10.1007/BF00571700

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