Advertisement

Journal of Intelligent & Robotic Systems

, Volume 82, Issue 2, pp 257–275 | Cite as

A Novel Trajectory Planning Scheme for Parallel Machining Robots Enhanced with NURBS Curves

  • Javad JahanpourEmail author
  • Mehdi Motallebi
  • Mojtaba Porghoveh
Article

Abstract

In this paper, a CAD-based trajectory planning scheme for parallel machining robots is introduced using the parametric Non-uniform rational basis spline (NURBS) curves. First, a trajectory is designed via a NURBS curve then, a motion scheduling architecture consisting of time-dependent and constant feedrate profiles is advised to generate the position commands on the represented NURBS curve as the tool path. Using the generated commands, the inverse kinematics is elaborated to obtain the joints motions of the parallel machining robot. This paper investigates the NURBS trajectory generation for a parallel robot with 4(UPS)-PU mechanism as the case study. In order to evaluate the effectiveness of the proposed method, the inverse kinematic results for the parallel machining robot of 4(UPS)-PU is compared with the simulation results obtained from the CATIA software. The results confirmed that the proposed trajectory planning scheme along with the advised motion planning architecture is not only feasible for the parallel machining robots but also yields a smooth trajectory with a satisfactory performance for all the joints.

Keywords

Trajectory planning Parallel machining robot Inverse kinematics NURBS curve CATIA DMU kinematics simulation tool 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cai, G.Q., Hu, M., Guo, C., Li, B., Wang, Q.M.: Development of a robotized grinding machine with tripod linkage. Manuf. Technol. Mach. Tool 435, 4–6 (1998)Google Scholar
  2. 2.
    Gough, V.E.: Contribution to discussion to papers on research in automobile stability and control and in type performance. Pro Auto Device Instruction Mech. Eng., 392–395 (1957)Google Scholar
  3. 3.
    Stewart, D.: A platform with six degree of freedom. Proc. In srn. Mech. Engrs. Part 1 180(15), 371–376 (1965)Google Scholar
  4. 4.
    Cleary, K., Brooks, T.: Kinematics analysis of a novel 6 DOFs parallel manipulator. In: IEEE Conference on Robotics and Automation, pp. 708–713 (1993)Google Scholar
  5. 5.
    Salcudean, S.E., Drexel, P.A., Ben-Dov, D., Tayor, A.J., Lawrence, P.D.: A six degree-of-freedom, hydraulic, one person motion simulator. In: IEEE Conference on Robotics and Automation, pp. 2437–2443 (1994)Google Scholar
  6. 6.
    Fattah, A., Kasaei, G.: Kinematics and dynamics of a parallel manipulator with a new architecture. Robotica 18, 535–543 (2000)CrossRefGoogle Scholar
  7. 7.
    Reboulet, C., Pigeyre, R.: Hybrid control of a 6-DOFs in-parallel actuated micro-manipulator mounted on a scara robot. Int. J. Robot. Autom. 7(1), 10–14 (1992)Google Scholar
  8. 8.
    Valenti, M.: Machine tools get smarter. ASME Mechanical Engineering 17(11), 70–75 (1995)Google Scholar
  9. 9.
    Cox, D.J., Tesar, D.: The Dynamic Modeling and Command Signal Formulation for Parallel Multi-Parameter Robotic, Devic Internal Rep. CIMAR, Univ. Florida, Gainesville (1981)Google Scholar
  10. 10.
    Hunt, K.J.: Structure kinematics of in-parallel actuated robot-arms. Tran. ASME, J. Mech. Trans. Auto Des. 105, 705–712 (1983)CrossRefGoogle Scholar
  11. 11.
    Earl, C.F., Rooney, J.: Some kinematic structure for robot manipulator design. Trans. ASME, J. Mech. Trans. Auto Des. 105, 15–22 (1983)CrossRefGoogle Scholar
  12. 12.
    Merlet, J.P.: Les robot parallels. Hermes, Paris (1990)Google Scholar
  13. 13.
    Griffis, M., Duffy, J.: A forward displacement analysis of a class of Stewart platform 6(6), 703–720 (1989)Google Scholar
  14. 14.
    Gosselin, C.M., Sefrioui, J., Richard, M.J.: On the direct kinematics of general spherical three-degree-of-freedom parallel manipulators. In: Proceedings of 22nd ASME Biennial Mechanisms Conference, vol. 45, pp. 7–11, Scottsdale, AZ (1992)Google Scholar
  15. 15.
    Wang, J., Tan, X.: Analysis and dimensional design of a novel hybrid machine tool. Int. J. Mach. Tools Manuf. 43, 647–655 (2003)CrossRefGoogle Scholar
  16. 16.
    Khan, W.A., Hayhurst, D.R., Cannings, C.: Determination of optimal path under approach and exit constraints. Eur. J. Oper. Res. 117(2), 310–325 (1999)CrossRefzbMATHGoogle Scholar
  17. 17.
    Castelino, K., D’Souza, R., Wright, P.: Toolpath optimization for minimizing airtime during machining. J. Manuf. Syst. 22(3), 173–180 (2003)CrossRefGoogle Scholar
  18. 18.
    DeBoor, C.: A Practical Guide to Splines. Springer, New York (1978)CrossRefGoogle Scholar
  19. 19.
    Rogers, D., Adams, J.A.: Mathematical Elements for Computer Graphics. McGraw-Hill (1976). L.JGoogle Scholar
  20. 20.
    Paul, R.P., Zong, H.: Robot motion trajectory specification and generation. In: 2nd International Symposium on Robotics Research, pp. 373–380, Kyoto (1984)Google Scholar
  21. 21.
    Taylor, R.: Planning and execution of straight line manipulator trajectories. In: Robot Motion. MIT Press (1983)Google Scholar
  22. 22.
    Gasparetto, A., Zanotto, V.: A technique for time-jerk optimal planning of robot trajectories. Robot. Comput. Integr. Manuf. 24, 415–426 (2008)CrossRefGoogle Scholar
  23. 23.
    Farouki, R.T., Tsai, Y.F.: Exact Taylor series coefficients for variable-feed rate CNC curve interpolators. Comput. Aided Des. 33, 155–165 (2001)CrossRefGoogle Scholar
  24. 24.
    Wang, Y.: B-spline path planning for manipulator in joint coordinates. Anhui Institute of Mechanical 15(2), 21–26 (2000)Google Scholar
  25. 25.
    Wang, Y.m., Xu, W.h.: Bézier path planning for manipulator in joint coordinates. Anhui Institute of Mechanical 15(3), 59–64 (2000)Google Scholar
  26. 26.
    Cheng, X.: Cubic trigonometric Bézier spline interpolation. Journal of Jiamusi University 27(3), 445–448 (2009)Google Scholar
  27. 27.
    Wang, Y.j., Xu, W.l., Sun, N.l.: Manipulator trajectory planning based on the cubic triangular Bézier spline. In: 8th World Congress on Intelligent Control and Automation (WCICA), pp. 6485–6488 (2010)Google Scholar
  28. 28.
    Wang, C.H., Horng, J.G.: Constrained minimum-time path planning for robot manipulators via virtual knots of the cubic B-Spline functions. IEEE Trans. Autom. Control 35(5), 573–577 (1990)CrossRefzbMATHGoogle Scholar
  29. 29.
    Chen, Y.C.: Solving robot trajectory planning problems with uniform cubic B-splines. Optimal Control Applications & Methods 12, 247–262 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Martin, B.J., Bobrow, J.E.: Minimum effort motions for open chain manipulators with task-dependent end-effector constraints. Int. J. Robot. Res. 18(2), 213–224 (1999)CrossRefGoogle Scholar
  31. 31.
    Gasparetto, A., Zanotto, V.: A new method for smooth trajectory planning of robot manipulators. Mech. Mach. Theory 42, 455–471 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Steuben, J., Steele, J., Turner, C.J.: NURBS for robot manipulator trajectory generation. In: Proceeding of the ASME International Design Engineering Technical Conferences & Computes and Information in Engineering Conference IDETC/CIE, pp. 1121–1130 (2011)Google Scholar
  33. 33.
    Aleotti, J., Caselli, S., Maccherozzi, G.: Trajectory reconstruction with NURBS curves for robot programming by demonstration. In: IEEE International Symposium on Computational Intelligence in Robotics and Automation, pp. 73–78, Helsinki (2005)Google Scholar
  34. 34.
    Aleotti, J., Caselli, S.: Trajectory clustering and stochastic approximation for robot programming by demonstration. In: Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1029–1034 (2005)Google Scholar
  35. 35.
    Andreas, J.S., Heinz, W.: Path planning for a humanoid using NURBS curves. In: IEEE International Conference on Automation Science and Engineering, pp. 351–356 (2005)Google Scholar
  36. 36.
    Zuo, Y.: Study on NURBS surface tool trajectory planning of 6R engraving robot. Adv. Mater. Res. 711, 422–425 (2013)CrossRefGoogle Scholar
  37. 37.
    Tatematsu, N., Ohnishi, K.: Tracking motion of mobile robot for moving target using NURBS curve. In: International Conference on Industrial Technology, pp. 245–249, San Francisco (2003)Google Scholar
  38. 38.
    Chuang, H.Y., Chien, K.H.: A real-time NURBS motion interpolator for position control of a slide equilateral triangle parallel manipulator. Int. J. Adv. Manuf. Technol. 34, 724–735 (2007)CrossRefGoogle Scholar
  39. 39.
    Singh, A.K., Aggarwal, A., Vashisht, M., Siddavatam, R.: Robot motion planning in a dynamic environment using offset non-uniform rational B-Splines (NURBS). In: IEEE International Conference on Industrial Technology (ICIT), pp. 312–317 (2011)Google Scholar
  40. 40.
    Chen, H., Sheng, W., Xi, N., Song, M., Chen, Y.: CAD-based automated robot trajectory planning for spray painting of free-form surfaces. Industrial Robot-an International Journal - IND ROBOT 29(5), 426–433 (2002)CrossRefGoogle Scholar
  41. 41.
    Andrzej, J.C., Paul, J.Z.M.: NURBS to avoid boundary orientation poses in serial manipulators. J. Field Rob. 20(12), 723–736 (2003)zbMATHGoogle Scholar
  42. 42.
    Spong, M.W.: Motion control of robot manipulators. In: Levine, W. (ed.) Handbook of Control, pp. 1339–1350. CRC Press (1996)Google Scholar
  43. 43.
    Piegl, L.A., Triller, W.: The NURBS book. In: Monographs in Visual Communications. 2nd edn. Springer, Berlin (1997)Google Scholar
  44. 44.
    Jahanpour, J., Tsai, M.C., Cheng, M.Y.: High-speed contouring control with NURBS-based C 2PH spline curves. Int. J. Adv. Manuf. Technol. 49(5), 663–674 (2010)CrossRefGoogle Scholar
  45. 45.
    Liu, X., Ahmad, F., Yamazaki, K., Mori, M.: Adaptive interpolation scheme for NURBS curve with the integration of machining dynamics. Int. J. Mach. Tools Manuf. 45(4-5), 433–444 (2005)CrossRefGoogle Scholar
  46. 46.
    Bhattacharjee, B., Azeem, A., Ali, S.M., Paul, S.K.: Development of a CNC interpolation scheme for CNC controller based on Runge-Kutta method. Int. J. Computer Aided Engineering and Technology 4(5), 445–464 (2012)CrossRefGoogle Scholar
  47. 47.
    Jahanpour, J., Alizadeh, M.R.: A novel acc-jerk-limited NURBS interpolation enhanced with an optimized S-shaped quantic feedrate scheduling scheme. Int. J. Adv. Manuf. Technol. 77, 1889–1905 (2015)CrossRefGoogle Scholar
  48. 48.
    Tsai, Y.F., Farouki, R.T., Feldman, B.: Performance analysis of CNC interpolators for time-dependent federates along PH curves. Comput. Aided Geom. Des. 18(3), 245–265 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Jahanpour, J., Ghadirifar, A.: The improved NURBS-based C2 PH spline curve contour following task with PDFF controller. Int. J. Adv. Manuf. Technol. 70, 995–1007 (2014)CrossRefGoogle Scholar
  50. 50.
    Jahanpour, J.: High speed contouring enhanced with C2 PH quintic spline curves. Scientia Iranica B 19(2), 311–31 (2012)CrossRefGoogle Scholar
  51. 51.
    Zhang, D., Lei, J.: Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach. Robot. Comput. Integr. Manuf. 27, 157–163 (2011)CrossRefGoogle Scholar
  52. 52.
    Gosselin, C.M., Sefrriouri, J., Richard, M.J.: On the direct kinematics of spherical three degree of freedom parallel manipulators of general architecture. ASME J. Mech. Des. 116(2), 594–598 (1994)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Javad Jahanpour
    • 1
    Email author
  • Mehdi Motallebi
    • 1
  • Mojtaba Porghoveh
    • 1
  1. 1.Department of Mechanical Engineering, Mashhad BranchIslamic Azad UniversityMashhadIran

Personalised recommendations