Skip to main content
SpringerLink
Log in

Different-Level Simultaneous Minimization of Joint-Velocity and Joint-Torque for Redundant Robot Manipulators

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

In J Robot Syst 13(3):177–185 (1996), Ma proposed an efficient technique to stabilize local torque optimization solution of redundant manipulators, which prevents occurrence of high joint-velocity and guarantees the final joint-velocity to be near zero. To prevent the same problems, a different-level simultaneous minimization scheme is proposed in this paper for robotic redundancy resolution, which combines the minimum two-norm joint-velocity and joint-torque solutions via two weighting factors. Physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are also taken into consideration in such a scheme-formulation. Moreover, the proposed different-level simultaneous minimization scheme is resolved at the joint-acceleration level and reformulated as a general quadratic program (QP). Computer-simulation results based on the PUMA560 robot manipulator performing different types of end-effector path-tracking tasks demonstrate the validity and advantage of the proposed different-level simultaneous minimization scheme. Furthermore, experimental verification conducted on a practical six-link planar robot manipulator substantiates the effectiveness and the physical realizability of the proposed scheme.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Siciliano, B., Khatib, O.: Springer Handbook of Robotics. Springer, Heidelberg (2008)

    Book  MATH  Google Scholar 

  2. Zhang, Y.: Analysis and design of recurrent neural networks and their applications to control and robotic systems. Ph.D. Thesis, Chinese University of Hong Kong, Hong Kong (2002)

    Google Scholar 

  3. Latash, M.L.: Control of Human Movement. Human Kinematics, Chicago (1993)

    Google Scholar 

  4. Cheng, F.-T., Chen, T.-H., Sun, Y.-Y.: Resolving manipulator redundancy under inequality constraints. IEEE Trans. Robot. Autom. 10(1), 65–71 (1994)

    Article  Google Scholar 

  5. Cheng, F.T., Sheu, R.J., Chen, T.H.: The improved compact QP method for resolving manipulator redundancy. IEEE Trans. Syst. Man Cybern. 25(11), 1521–1530 (1995)

    Article  Google Scholar 

  6. Cai, B., Zhang, Y.: Equivalence of velocity-level and acceleration-level redundancy-resolution of manipulators. Phys. Lett. A 373(38), 3450–3453 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. De Luca, A., Lanari, L., Oriolo, G.: Control of redundant robots on cyclic trajectories. In: Proc. IEEE Int. Conf. Robot. Autom., pp. 500–506 (1992)

  8. Ding H., Chan, S.P.: A real-time planning algorithm for obstacle avoidance of redundant robots. J. Intell. Robot. Syst. 16, 229–243 (1996)

    Article  Google Scholar 

  9. Janabi-Sharift, F., Wilson, W.J.: A fast approach for robot motion planning. J. Intell. Robot. Syst. 25, 187–212 (1999)

    Article  Google Scholar 

  10. Chung, C.Y., Lee, B.H., Kim, M.S., Lee, C.W.: Torque optimizing control with singularity-robustness for kinematically redundant robots. J. Intell. Robot. Syst. 28, 231–258 (2000)

    Article  MATH  Google Scholar 

  11. Tian, L., Collins, C.: Motion planning for redundant manipulators using a floating point genetic algorithm. J. Intell. Robot. Syst. 38, 297–312 (2003)

    Article  Google Scholar 

  12. Mayorga R.V., Sanongboon, P.: An artificial neural network approach for inverse kinematics computation and singularities prevention of redundant manipulators. J. Intell. Robot. Syst. 44, 1–23 (2005)

    Article  Google Scholar 

  13. Daachi, B., Benallegue, A.: A neural network adaptive controller for end-effector tracking of redundant robot manipulators. J. Intell. Robot. Syst. 46, 245–262 (2006)

    Article  Google Scholar 

  14. Lin, C.-J., Lee, K.-S.: Contour tracking of a redundant robot using integral variable structure control with output feedback. J. Intell. Robot. Syst. 62, 241–270 (2011)

    Article  Google Scholar 

  15. Khoogar, A.R., Tehrani, A.K., Tajdari, M.: A dual neural network for kinematic control of redundant manipulators using input pattern switching. J. Intell. Robot. Syst. 63, 101–113 (2011)

    Article  Google Scholar 

  16. Granvagne, I.A., Walker, I.D.: On the structure of minimum effort solutions with application to kinematic redundancy resolution. IEEE Trans. Robot. Autom. 16(6), 855–863 (2000)

    Article  Google Scholar 

  17. Hollerbach, J.M., Suh, K.C.: Redundancy resolution of manipulators through torque optimization. IEEE J. Robot. Autom. 3(4), 308–316 (1987)

    Article  Google Scholar 

  18. Hou, Z.-G., Cheng, L., Tan, M.: Multicriteria optimization for coordination of redundant robots using a dual neural network. IEEE Trans. Syst. Man Cybern., Part B 40(4), 1075–1087 (2010)

    Article  Google Scholar 

  19. Klein, C.A., Huang, C.H.: Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern., Part B 13(3), 245–250 (1983)

    Article  Google Scholar 

  20. Kazerounian, K., Nedungadi, A.: Redundancy resolution of serial manipulators based on robot dynamics. Mech. Mach. Theory 23(4), 295–303 (1988)

    Article  Google Scholar 

  21. Kang, H.J., Freeman, R.A.: Joint torque optimization or redundant manipulators via the null space damping method. In: Proc. IEEE Int. Conf. Robot. Autom., pp. 520–525 (1992)

  22. Khoukhi, A., Baron, L., Balazinski, M.: A projected gradient augmented Lagrangian approach to multi-objective trajectory planning of redundant robots. Trans. Can. Soc. Mech. Eng. 31(4), 391–405 (2007)

    Google Scholar 

  23. Ma, S.: A balancing technique to stabilize local torque optimization solution of redundant manipulators. J. Robot. Syst. 13(3), 177–185 (1996)

    Article  MATH  Google Scholar 

  24. Nedungadi, A., Kazerouinian, K.: A local solution with global characteristics for the joint torque optimization of a redundant manipulator. J. Robot. Syst. 6(5), 631–654 (1989)

    Article  Google Scholar 

  25. O’Neil, K.A.: Divergence of linear acceleration-based redundancy resolution schemes. IEEE Trans. Robot. Autom. 18(4), 625–631 (2002)

    Article  Google Scholar 

  26. Park, K.C., Chang, P.H., Kim, S.H.: The enhanced compact QP method for redundant manipulators using practical inequality constraints. In: Proc. IEEE Int. Conf. Robot. Autom., pp. 107–114 (1998)

  27. Roberts, R.G., Maciejewski, A.A.: Singularities, stable surfaces, and the repeatable behavior of kinematically redundant manipulators. Int. J. Rob. Res. 13(1), 70–81 (1994)

    Article  Google Scholar 

  28. Tang, W.S., Wang, J.: Two recurrent neural networks for local joint torque optimization of kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern., Part B 30(1), 120–128 (2000)

    Article  Google Scholar 

  29. Tan, J., Xi, N., Wang, Y.: A singularity-free motion control algorithm for robot manipulators—a hybrid system approach. Automatica 40(7), 1239–1245 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. Yoshikawa, T.: Manipulability of robotic mechanisms. Int. J. Rob. Res. 4(2), 3–9 (1985)

    Article  MathSciNet  Google Scholar 

  31. Yin, F., Wang, Y.-N., Wei, S.-N.: Inverse kinematic solution for robot manipulator based on electromagnetism-like and modified DFP algorithms. Acta Auto. Sin. 37(1), 74–82 (2011)

    Article  MathSciNet  Google Scholar 

  32. Zhang, Y., Wang, J.: A dual neural network for constrained joint torque optimization of kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern., Part B 32(5), 654–662 (2002)

    Article  Google Scholar 

  33. Zhang, Y., Wang, J., Xu, Y.: A dual neural network for bi-criteria kinematic control of redundant manipulators. IEEE Trans. Robot. Autom. 18(6), 923–931 (2002)

    Article  Google Scholar 

  34. Zhang, Y., Wang, J., Xia, Y.: A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits. IEEE Trans. Neural Netw. 14(3), 658–667 (2003)

    Article  Google Scholar 

  35. Zhang, Y., Ge, S.S., Lee, T.H.: A unified quadratic programming based dynamical system approach to joint torque optimization of physically constrained redundant manipulators. IEEE Trans. Syst. Man Cybern., Part B 34(5), 2126–2132 (2004)

    Article  Google Scholar 

  36. Zhang, Y., Ma, S.: Minimum-energy redundancy resolution of robot manipulators unified by quadratic programming and its online solution. In: Proc. IEEE Int. Conf. Mech. Autom., pp. 3132–3137 (2007)

  37. Zhang, Y., Lv, X., Li, Z., Yang, Z., Chen, K.: Repetitive motion planning of PA10 robot arm subject to joint physical limits and using LVI-based primal-dual neural network. Mechatronics 18(9), 475–485 (2008)

    Article  Google Scholar 

  38. Guo, D., Zhang, Y.: Different-level two-norm and infinity-norm minimization to remedy joint-torque instability/divergence for redundant robot manipulators. Robot. Auton. Syst. 60(6), 874–888 (2012)

    Article  Google Scholar 

  39. Zhang, Y., Ma, W., Li, X.-D., Tan, H.-Z., Chen, K.: MATLAB Simulink modeling and simulation of LVI-based primal-dual neural network for solving linear and quadratic programs. Neurocomputing 72(7-9), 1679–1687 (2009)

    Article  Google Scholar 

  40. Zhang, Y., Jiang, D., Wang, J.: A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Trans. Neural Netw. 13(5), 1053–1063 (2002)

    Article  Google Scholar 

  41. Zhang, Y., Ge, S.S.: Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans. Neural Netw. 16(6), 1477–1490 (2005)

    Article  Google Scholar 

  42. Zhang, Y., Guo, D.: Linear programming versus quadratic programming in robots’ repetitive redundancy resolution: a chattering phenomenon investigation. In: Proc. 4th IEEE Conf. Ind. Elec. Appl., pp. 2822–2827 (2009)

  43. Zhang, Y., Wu, H., Guo, D., Xiao, L.: Effective parameter range for equivalence of velocity-level and acceleration-level redundancy resolution schemes. Phys. Lett. A 376(21), 1736–1739 (2012)

    Article  Google Scholar 

  44. Mead, C.: Analog VLSI and Neural Systems. Addison-Wesley, Reading (1989)

    Book  MATH  Google Scholar 

  45. Li, K., Zhang, Y.: Fault-tolerant motion planning and control of redundant manipulator. Control Eng. Pract. 20(3), 282–292 (2012)

    Article  Google Scholar 

  46. Li, K., Zhang, Y.: Design and implementation of a zero-initial-velocity self-motion scheme on a six-DOF planar robot manipulator. Ind. Rob. 39(4), 401–411 (2012)

    Google Scholar 

  47. Li, K., Zhang, Y.: State adjustment of redundant robot manipulator based on quadratic programming. Robotica 30(3) 477–489 (2012)

    Article  Google Scholar 

  48. The MathWorks Inc.: Optimization Toolbox for Use with MATLAB, version 2.3 (2003)

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, 510006, China

    Yunong Zhang & Dongsheng Guo

  2. Department of Robotics, Ritsumeikan University, Shiga-ken, 525-8577, Japan

    Shugen Ma

Authors
  1. Yunong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongsheng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shugen Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunong Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Y., Guo, D. & Ma, S. Different-Level Simultaneous Minimization of Joint-Velocity and Joint-Torque for Redundant Robot Manipulators. J Intell Robot Syst 72, 301–323 (2013). https://doi.org/10.1007/s10846-013-9816-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-013-9816-8

Keywords

Search

Navigation