Skip to main content
SpringerLink
Log in

Smooth trajectory planning for a parallel manipulator with joint friction and jerk constraints

  • Regular Papers
  • Robot and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In order to achieve better tracking accuracy effectively, a new smooth and near time-optimal trajectory planning approach is proposed for a parallel manipulator subject to kinematic and dynamic constraints. The complete dynamic model is constructed with consideration of all joint frictions. The presented planning problem can be solved efficiently by formulating a new limitation curve for dynamic constraints and a reduced form for jerk constraints. The motion trajectory is planned with quartic and quintic polynomial splines in Cartesian space and septuple polynomial splines in joint space. Experimental results show that smaller tracking error can be obtained. The developed method can be applied to any robots with analytical inverse kinematic and dynamic solutions.

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. J. E. Bobrow, S. Dubowsky, and J. S. Gibson, “Timeoptimal control of robotic manipulators along specified paths,” The Int. J. Robot. Res., vol. 4, no. 3, pp. 3–17, Sept. 1985. [click]

    Article  Google Scholar 

  2. K. G. Shin and N. D. McKay, “Minimum-time control of robotic manipulators with geometric path constraints,” IEEE Trans. Autom. Contr., vol. 30, no. 5, pp. 531–541, Jun. 1985. [click]

    Article  MATH  Google Scholar 

  3. Z. Shiller and H. H. Lu, “Computation of path constrained time optimal motions with dynamic singularities,” ASME J.Dyn. Syst., Meas., Contr., vol. 114, no. 1, pp. 34–40, Mar. 1992. [click]

    Article  MATH  Google Scholar 

  4. J. T. Betts and W. P Huffman, “Path-constrained trajectory optimization using sparse sequential quadratic programming,” J. Guid., Contr.,Dyn., vol. 16, no.1, pp. 59–68, January 1993. [click]

    Article  MATH  Google Scholar 

  5. M. Tarkiainen and Z. Shiller, “Time optimal motions of manipulators with actuator dynamics,” Proc. of the IEEE Int. Conf. Robot. Autom., pp. 725–730, 1993. [click]

    Chapter  Google Scholar 

  6. Z. Shiller, “On singular time-optimal control along specified paths,” IEEE Trans. on Robot. Autom., vol. 10, no. 4, pp. 561–566, Aug. 1994. [click]

    Article  Google Scholar 

  7. J. H. Lee, “A dynamic programming approach to near minimum-time trajectory planning for two robots,” IEEE Trans. Robot. Autom., vol. 11, no. 1, pp. 160–164, Feb. 1995. [click]

    Article  Google Scholar 

  8. J. Gregory, A. Olivares, and E. Staffetti, “Energy-optimal trajectory planning for robot manipulators with holonomic constraints,” Syst. & Contr. Letters, vol. 61, no. 2, pp. 279–291, Feb. 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Li, R.W. Longman, V. H. Schultz, and H. G. Bock, “Implementing time optimal robot maneuvers using realistic actuator constraints and learning control,” Adv. Astronaut. Sci., vol. 99, no.1, pp. 355–374, Feb. 1998.

    Google Scholar 

  10. D. Constantinescu, E. A. Croft, “Smooth and time-optimal trajectory planning for industrial manipulators along specified paths,” J. Robot. Syst., vol. 17, no. 5, pp. 233–249, May 2000. [click]

    Article  MATH  Google Scholar 

  11. D. Verscheure, B. Demeulenaere, J. Swevers, J. D. Schutter, and M. Diehl, “Time-optimal path tracking for robots: a convex optimization approach,” IEEE Trans. Autom. Contr., vol. 54, no. 10, pp. 2318–2327, Oct. 2009. [click]

    Article  MathSciNet  Google Scholar 

  12. A. Gasparetto, and V. Zanotto, “A new method for smooth trajectory planning of robot manipulators,” Mech. Mach. Theory, vol. 42, no. 4, pp. 455–471, Apr. 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Dong, P. M. Ferreira, and J. A. Stori, “Feed-rate optimization with jerk constraints for generating minimumtime trajectories,” Int. J. Mach. Tools Manuf., vol. 47, no. 12-13, pp. 1941–1955, Oct. 2007. [click]

    Article  Google Scholar 

  14. K. J. Kyriakopoulos and G. N. Saridis, “Minimum jerk for trajectory planning and control,” Robotica, vol. 12, no. 2, pp. 109–113, Mar. 1994. [click]

    Article  Google Scholar 

  15. A. Piazzi and A. Visioli, “Global minimum-jerk trajectory planning of robot manipulators,” IEEE Trans. Indus. Elect., vol. 47, no. 1, pp. 140–149, Feb. 2000. [click]

    Article  Google Scholar 

  16. P. F. Huang, Y. S. Xu, and B. Liang, “Global minimum-jerk trajectory planning of space manipulator,” Int. J. Contr., Autom., Syst., vol. 4, no. 4, pp. 405–413, Aug. 2006.

    Google Scholar 

  17. G. Lini, A. Piazzi, and L. Consolini, “Algebraic solution to minimum-time velocity planning,” Int. J. Contr., Autom. Syst., vol. 11, no. 4, pp. 805–814, Aug. 2013. [click]

  18. T. Huang, P. F. Wang, J. P. Mei, X. M. Zhao, and D. G. Chetwynd, “Time minimum trajectory planning of a 2-DOF translational parallel robot for pick-and-place operations,” CIRP Annals-Manuf. Techn., vol. 56, no. 1, pp. 365–368, 2007. [click]

    Article  Google Scholar 

  19. Y. Q. Xiao, Z. J. Du, and W. Dong, “Smooth and near timeoptimal trajectory planning of industrial robots for online applications,” Ind. Robot: An Inter. J., vol. 39, no. 2, pp. 169–177, March 2012. [click]

    Article  Google Scholar 

  20. Y. Yun and Y. M. Li, “Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace,” Robot. Compu.-Integr. Manuf., vol. 27, no. 6, pp. 977–985, Dec. 2011. [click]

    Article  Google Scholar 

  21. L. W. Tsai, Robot Analysis: The Mechanics of Serial and Parallel Manipulator, Wiley, New York, 1999.

    Google Scholar 

  22. R. Waiboer, R. Aarts, and B. Jonker, “Velocity dependence of joint friction in robotic manipulators with gear transmissions,” Proc. of ECCOMAS Thematic Conf. Multibody Dyn., Adv. in Comput. Multibody Dyn., pp. 1–19, 2005.

    Google Scholar 

  23. B. Li, Y. M. Li, X. H. Zhao, and W. M. Ge, “Kinematic analysis of a novel 3-CRU translational parallel mechanism,” Mechanical Sciences, vol.6, pp.57–64, 2015. [click]

    Article  Google Scholar 

  24. Y. M. Li and S. Staicu, “Inverse dynamics of a 3-PRC parallel kinematic machine,” Nonlin. Dyn., vol. 67, no. 2, pp. 1031–1041, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  25. H. Lim, S.-H. Lee, and B.-J. Yi, “Design of a new 6-DOF parallel mechanism with a suspended platform,” Int. J. Contr., Autom., Syst., vol. 13, no. 4, pp.942–950, 2015. [click]

    Article  Google Scholar 

  26. B. Li, Y. M. Li, W. M. Ge, X. H. Zhao, and Y. W. Yang, “Dynamics analysis of a novel over-constrained three-DOF parallel manipulator,” Proc. of IEEE Int. Conf. Mechatron. Autom., Tianjin, China, Aug. 3-6, 2014, pp.828–833. [click]

    Google Scholar 

  27. Y. M. Li, Y. Liu, X. P. Liu, and Z. Y. Peng, “Parameter identification and vibration control in modular manipulators,” IEEE/ASME Trans. Mechatron., vol. 9. no. 4, pp. 700–705, Dec., 2004. [click]

    Article  Google Scholar 

  28. Y. Liu and Y. M. Li, “Dynamic modeling and adaptive neural-fuzzy control for nonholonomic mobile manipulators moving on a slope,” Int. J. Contr., Autom., Syst., vol. 4, no. 2, pp. 197–203, 2006.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, 92 Weijin St., Nankai, Tianjin, China

    Liang Liu & Chaoying Chen

  2. Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of Technology, 391 Binshuixi St., Xiqing, Tianjin, China

    Xinhua Zhao

  3. Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Av. Da Universidade E11, Taipa, Macao, China

    Yangmin Li

Authors
  1. Liang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chaoying Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinhua Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yangmin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xinhua Zhao or Yangmin Li.

Additional information

Recommended by Associate Editor Seul Jung under the direction of Editor Hyouk Ryeol Choi. This work was supported by the National Natural Science Foundation of China (No. 51275353, 51265289 and 51575544), Tianjin Natural Science Foundation of China (No. 14JCZDJC39100 and 12JCYBJC12200), Macao Science and Technology Development Fund (108/2012/A3 and 110/2013/A3), and Research Committee of University of Macau (MYRG2015-00194-FST and MYRG203(Y1-L4)-FST11-LYM).

Liang Liu received his B.S. degree in Electrical Engineering in 2001 and his M.S. degree in Electrical Engineering in 2006 from the School of Electrical Engineering both at Tianjin University of Technology, China. He received the second M.S. degree in Mechanical Engineering from Tianjin University of Technology in 2010. He is currently pursuing a Ph.D. from the School of Mechanical Engineering at Tianjin University, China. His research interests include robotics, mulitbody dynamics, and motion control.

Chaoying Chen received his B.S. degree in computer science in 1982 from the Harbin Institute of Technology, China and his M.S. degree in computer science in 1988 from the Free University of Brussels, Belgium. His research interests include robotics and inertial navigation.

Xinhua Zhao received his B.S. degree in Machinery Manufacturing Technolog-y in 1985 and his M.S. degree in Mechanical Engineering in 1988, both from Northeast Heavy Machinery Institute, China. He received his Ph.D. in Mechanical Design and Theory in 2000 from Tianjin University, China. He then joined the School of Mechanical Engineering at Tianjin University of Technology, China. He developed 3-RRRU parallel manipulator, 2-RRU&RRS parallel manipulator, and 2-PPU&PPS parallel manipulator. His research interests are robotics, mechanical design, dynamics, and control.

Yangmin Li received the B.S. and M.S. degrees from Jilin University, Changchun, China, in 1985 and 1988, respectively, and the Ph.D. degree from Tianjin University, Tianjin, China, in 1994, all in mechanical engineering. He is currently a Full Professor of electromechanical engineering with the University of Macau, Macau, China, he is the Director of the Mechatronics Laboratory. He is also a Tianjin Thousands of Talents Plan Chair Professor with the Tianjin University of Technology. He has authored or coauthored 356 scientific papers in journals and conferences. His research interests include micro-/nanomanipulation, nanorobotics, micromanipulators, mobile robots, modular robots, multibody dynamics, and control. He is a member of the American Society of Mechanical Engineers and a senior member of IEEE. From 2009 to 2012, he served as the Technical Editor of the IEEE/ASME Transactions on Mechatronics. He served as an Associate Editor of the IEEE Transactions on Automation Science Engineering from 2009 to 2013.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, L., Chen, C., Zhao, X. et al. Smooth trajectory planning for a parallel manipulator with joint friction and jerk constraints. Int. J. Control Autom. Syst. 14, 1022–1036 (2016). https://doi.org/10.1007/s12555-014-0495-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-014-0495-4

Keywords

Search

Navigation