Skip to main content
SpringerLink
Log in

Symbolic Computation for Robot Design

  • Conference paper
Expert Systems and Robotics

Part of the book series: NATO ASI Series ((NATO ASI F,volume 71))

  • 111 Accesses

Abstract

This report presents the basic derivations needed to develop a CAD robot system devoted to automatic analysis and design of controlled mechanisms. The feedback laws required by sophisticated robot controllers are directly derived from the Lagrangian of mechanical systems by means of generating rules. The dynamical model is not explicitly needed in this derivation which only requires partial derivatives and matrix calculus. In addition it is shown how the dynamical model can be computed from the control laws so that dynamics of controlled and uncontrolled mechanisms can be derived in the same framework. Finally, the sampling rate to use in computerized servo-mechanisms is defined from a simple rule.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acaccia, G.; Callegari, M.; Michelini, R. and Molfino, R.: Architectural analysis of robotic industrial manipulators. Int. AFCET Conf. on Robotics and Artificial Intelligence, Toulouse, France, 1986

    Google Scholar 

  2. Acaccia, G.; Michelini, R.; Molfino, R. and Piaggio, P.: N-SIFIP: a knowledge-based special purpose simulator for the development of flexible manufacturing cells. IEEE Conf. on Robotics and Automation, San Francisco, April 19SG

    Google Scholar 

  3. Acaccia, G.; Anselmi, N.; Michelini, R.; Molfino, R. and Piaggio, P.: Expert simulation: a tool for exploiting flexible manufacturing. ASME Conf. in Computer in Engineering. New York, Aug 1987

    Google Scholar 

  4. Acaccia, G.; Michelini, R..; Molfino, R. and Piaggio, P.: Information data based structures for flexible-manufacturing simulators. Third IFIP Conf. on Advances in Production Management Systems. Winnipeg, Aug 1987

    Google Scholar 

  5. Acaccia, G.; Michelini, R. and 1\’1olfino, R.: Knowledge-based simulators in manufacturing engineeering. 2nd Conf. on Applications of Artificial Intelligence. Boston, Aug 1987

    Google Scholar 

  6. Acaccia, G.; Callegari, M.; Michelini, R.; Molfino, R. and Piaggio, P.: X-ARS: A consultation program for selecting the industrial robot architectures. Third Int. Conf. on Applied of AI in Engineering. Aug 8–11 1988 p (24)

    Google Scholar 

  7. Rieseler, H. and Wahl, F.: Fast symbolic computation of the inverse kinematics of robots. IEEE Conf. on Robotics and Automation, Cincinnati, 1990 pp 462–467

    Google Scholar 

  8. Edwall, J.; Pottinger and Ho.: Trajectory generation and control of a robot arm using spline functions. Proc. of Robot VI, Detroit 1982 pp 421–446

    Google Scholar 

  9. Goldenberg, A. and Lawrence, D.: End-effector path generation. Trans of the ASME, J. of Dyn., System, Meas., and Control, 1986 Vol los pp 158–162

    Google Scholar 

  10. Khatib, O. and Le Maitre, J-F.: Dynamic control of manipulators operating in a complex environment. 3rd CISM-IFToMM, Udine, Italy 1978

    Google Scholar 

  11. Khatib, O.: Commande dynamique clans l’espace opérationnel des robots manipulators en présence d’obstacles. Thèse Docteur-Ingénieur, ENSAE, Toulouse, France 1980

    Google Scholar 

  12. Khatib, O.: Dynamic control of manipulators in operational space. Sixth CISM-IFToMM Congress on Theory of Machines and Mechanisms, New Delhi, India 1983

    Google Scholar 

  13. Khatib, O. The operational space formulation in robot manipulator control. 15th ISIR, Tokyo, 1985 pp 165–172

    Google Scholar 

  14. Meystel, A. and Thomas, M.: Computer aided conceptual design in robotics. IEEE Conf. on Robotics and Automation. 1984 pp 220–229

    Google Scholar 

  15. Cotsaftis, M. and Vibet, C.: A derivation of robot control algorithms from the Lagrange formalism. Proc. 2nd Int. Conf. on Robotics and Factories of the Future’87, San Diego. Springer Verlag, 1988 pp 461–466

    Google Scholar 

  16. Cotsaftis, M. and Vibet, C.: A new method for the robot controller design. Robotics and Autonomous Systems, 1988, Vol 4, No 1, pp 237–242

    Article  Google Scholar 

  17. -Cotsaftis, M. and \Tibet, C.: Decoupling and control laws generation from Lagrange formalism. J. of Robotic Systems. 1988, Vol 5, No 5 pp 433–441

    Article  Google Scholar 

  18. Cotsaftis, M. and Vibet, C.: A direct application of the decoupling method to EulerLagrange’s formalism. 1989, Submitted to J. of Robotics Research

    Google Scholar 

  19. Cotsaftis, NI. and Vibet, C.: Modeling of robot system dynamics for CAD based robot programming. NATO ARV, CAD based programming for sensor based robots. 1988, Il Ciocco, Italy. Edited by B.Ravani, ASI, F50, Springer Verlag 493–509

    Google Scholar 

  20. Khosla, P.: Choosing sampling rates for robot control. IEEE Conf. on Robotics and Automation, 1987 pp 169–174

    Google Scholar 

  21. Vibet, C.: Guide to choosing the sampling rate in computerized controllers. Electr. Lett., 1987, Vol 23 No 7, 1002–1003

    Article  Google Scholar 

  22. -Paul, R.: Robot Manipulators: Mathematics, Programming and Control. MIT Press, 1981

    Google Scholar 

  23. Freund, E.: A nonlinear control concept for computer-controlled manipulators. Proc. of IFAC Symp. on Multivariable Techn. Systems, Fredericton, Canada, Pergamon Press, N.Y., 1977 pp 395–403

    Google Scholar 

  24. -Freund, E.: Fast nonlinear control with arbitrary pole-placement for industrial robots and manipulators. Robotic Research, 1981, Vol 1,No 1, pp 65–78

    Article  Google Scholar 

  25. Freund, E. The structure of decoupled nonlinear systems. Int. J. of Control, 1982, Vol 21, No 3 pp 441–450

    Google Scholar 

  26. Freund, E.: On the design of multirobots systems. IEEE Conf on Robotics and Automation, 1984, pp 477–490

    Google Scholar 

  27. Tarn, T.; Bejczy, A.; Isidori, A. and Chen, Y. Nonlinear feedback in robot arm control. Proc. of the 23nd IEEE Conf. on Decision and Control, Las Vegas, Nevada, 1984

    Google Scholar 

  28. Bejczy, A.; Tarn, T. and Chen, Y.: Robot arm dynamic control by computer. IEEE Conf. on Robotics and Automation, Saint Louis, MO, 1985 pp 960–970

    Google Scholar 

  29. Tarn, T.; Bejczy, A. and Yun, X. Nonlinear control algorithms for multiple robot arms. IEEE Tans. on Aerospace and Electronics Systems, 1958 Vol 24, No 5 pp 571–583

    Article  Google Scholar 

  30. Tarn, T.; Bejczy, A. and Yun, X.: Robot arm force control through system linearization by nonlinear feedback. IEEE Conf. on Robotics and Autom., 1988, pp’1618–1625

    Google Scholar 

  31. Bejczy, A. and Tarn, T.: Dynamic control of robot arms in task space using nonlinear feedback. Automatisierungstechnik at, 30, Jahrgang, Helf 10/1988 pp 374–388

    Google Scholar 

  32. Vibet, C.: Design of robot controllers. Advanced Robotics, 1987, Vol 2, No 1 pp 9–20

    Article  Google Scholar 

  33. Forrest-Barlach, F. and Babcock, S. Inverse dynamics position control of a compliant manipulator. 1986 IEEE Conf. on Robotics and Automation pp 196–205

    Google Scholar 

  34. Khosla, P.; Kanade, T.: Real-time implementation and evaluation of model-based controls on CMU DD Arm II. IEEE Conf. on Robotics and Automation, 1986 pp 15461555

    Google Scholar 

  35. Cotsaftis, M. and Vibet, C. Synthesis of the dynamical equations of mechanisms from their related control laws. Computer Methods in Applied Mech. and Engin. 1989, Vol 74 pp 29–40

    Article  MathSciNet  MATH  Google Scholar 

  36. Cotsaftis, M. and \Tibet, C. Simultaneous derivation of control laws and of dynamical model for controlled mechanisms. Real-time Integration Methods For Mechanical System Simulation. 1989 NATO AIM’, Snowbird. Utah

    Google Scholar 

  37. Vibet, C. Initial conditions and differential equations. Simulation, 1987 Vol 48, No 5 pp. 210–212

    Article  MATH  Google Scholar 

  38. Zheng, Y.: Collision effects on two coordinating robots in assembly and the effect minimization. IEEE Trans. on Syst. Man and Cybern., 1987, SMC 17, No 1 pp 108–116

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Paris XII, France

    C. Vibet

Authors
  1. C. Vibet
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, California State University, 1250 Bellflower Boulevard, 90840-5005, Long Beach, CA, USA

    Timothy Jordanides

  2. Department of Mechanical Engineering, California State University, 1250 Bellflower Boulevard, 90840-5005, Long Beach, CA, USA

    Bruce Torby

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vibet, C. (1991). Symbolic Computation for Robot Design. In: Jordanides, T., Torby, B. (eds) Expert Systems and Robotics. NATO ASI Series, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76465-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-76465-3_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76467-7

  • Online ISBN: 978-3-642-76465-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation