Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Recursive linearizing and decoupling control of robots

  • 43 Accesses


A control structure is considered for decoupling and linearizing the dynamic behavior of a robotic manipulator. Since computational efficiency is a crucial consideration in implementation of this control system, a fast recursive algorithm is presented for the necessary digital computations, and the computational requirements are studied in terms of the number of degrees of freedom of a general and open-chain robotic manipulator. An important feature of the algorithm is that decoupling is realized without employing matrix inversion. The sequential recursive algorithm is restructured into a parallel algorithm. A significant improvement in the computational speed is achieved in this manner. The computing requirements of the parallel algorithm are compared with those of the serial algorithm. For a six-degrees-of-freedom robot, the computational cost of the parallel algorithm is approximately 23 % of that of the original serial algorithm. Finally, the processor loads in some regions of the parallel algorithm are redistributed to achieve a balanced scheme. The resulting parallel algorithm requires approximately 17% of the computational effort of the serial algorithm, for a six-degrees-of-freedom robot.

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


  1. 1.

    K. Van Brussel and L. Vastmans, “A compensation method for the dynamic control of robots,” inProc. Conf Robotics Res., Bethlehem, PA, MS84-487, August 1984.

  2. 2.

    C.W. de Silva, “A motion control scheme for robotic manipulators,” inProc. 1984 Canadian CAD/CAM Robotics Conf., Toronto, 13.1–7, June 1984.

  3. 3.

    J.J. Craig,Introduction to Robotics. Addison-Wesley: Reading, MA, 1986.

  4. 4.

    J.R. Hewit and J.S. Burdess, “Fast dynamic decoupled control for robotics using active force control,” Mech. Machine Theory, vol.16, no. 5, pp. 535–542, 1981.

  5. 5.

    C.W. de Silva,Control Sensors and Actuators. Prentice-Hall: Englewood Cliffs, NJ, 1989.

  6. 6.

    C.W. de Silva and A.G.J. MacFarlane, “Knowledge-based control approach for robotic manipulators,”Int. J. Control, vol. 50, no. 1, pp. 249–273, 1989.

  7. 7.

    C. Li, “A new Lagrangian formulation of dynamics for robot manipulators,”J. Dynam. Syst. Meas. Control, Trans. ASME, vol. 111, pp. 559–567, 1989.

  8. 8.

    H. Hemami, “A state space model for interconnected rigid bodies,“IEEE Trans. Automat. Control, vol. AC-27, no. 2, pp. 376–382, April 1982.

  9. 9.

    J.M. Hollerback, “A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity,”IEEE Trans. Syst. Man Cybernet., vol. SMC-10, no. 11, pp. 730–736, November 1980.

  10. 10.

    R.W. Hockney and C.R. Jesshope,Parallel Computers. IOP Publishers: Philadelphia, PA, 1988.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

de Silva, C.W. Recursive linearizing and decoupling control of robots. Dynamics and Control 2, 401–414 (1992). https://doi.org/10.1007/BF02172224

Download citation


  • Control System
  • Computational Cost
  • Dynamic Behavior
  • Computational Effort
  • Control Structure