IJAT Vol.15 No.5 pp. 621-630
doi: 10.20965/ijat.2021.p0621


Kinematic Tool-Path Smoothing for 6-Axis Industrial Machining Robots

Shingo Tajima, Satoshi Iwamoto, and Hayato Yoshioka

Tokyo Institute of Technology
4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8503, Japan

Corresponding author

February 25, 2021
April 27, 2021
September 5, 2021
robot machining, trajectory generation, corner smoothing, industrial robots, numerical control

The demands for machining by industrial robots have been increasing owing to their low installation cost and high flexibility. A novel trajectory generation algorithm for high-speed and high-accuracy machining by industrial robots is proposed in this paper. Linear interpolation in the workspace and smooth trajectory generation at the corners are important in industrial machining robots. Because industrial robots are composed of rotational joints, the joint space has a nonlinear relationship with the workspace. Therefore, linear interpolation in the joint space, which has been widely used in conventional machine tools, does not guarantee linear interpolation in the actual machining workspace. This results in the degradation of the machining surface. The proposed trajectory generation algorithm based on the decoupled approach can achieve linear interpolation in the workspace by separating the position commands into Cartesian coordinates and the orientation commands into spherical coordinates. In addition, a novel corner smoothing method that generates a smooth and continuous trajectory from discrete commands is proposed in this paper. The proposed kinematic local corner smoothing generates a smooth trajectory by using a 3-segmented constant jerk profile at the corners in the joint space. The sharp corners can thereby be replaced by smooth curves. The resulting cornering error is controlled by varying the cornering duration. The simulation results demonstrate the effectiveness of the proposed kinematic smoothing algorithm in achieving linear tool motion in straight sections and in generating smooth trajectories at corner sections within the user-defined tolerance.

Cite this article as:
Shingo Tajima, Satoshi Iwamoto, and Hayato Yoshioka, “Kinematic Tool-Path Smoothing for 6-Axis Industrial Machining Robots,” Int. J. Automation Technol., Vol.15, No.5, pp. 621-630, 2021.
Data files:
  1. [1] C. S. Chen and S. K. Chen, “Synchronization of tool tip trajectory and attitude based on the surface characteristics of workpiece for 6-DOF robot manipulator,” Robotics and Computer-Integrated Manufacturing, Vol.59, pp. 13-27, 2019.
  2. [2] Y. Chen and F. Dong, “Robot machining: recent development and future research issues,” Int. J. of Advanced Manufacturing Technology, Vol.66, pp. 1489-1497, 2013.
  3. [3] A. Verl, A. Valente, S. Melkote, C. Brecher, E. Ozturk, and L. T. Tunc, “Robots in machining,” CIRP Annals, Vol.68, Issue 2, pp. 799-822, 2019.
  4. [4] M. Beschi, S. Mutti, G. Nicola, M. Faroni, P. Magnoni, E. Villagrossi, and N. Pedrocchi, “Optimal robot motion planning of redundant robots in machining and additive manufacturing applications,” Electronics, Vol.8, Issue 12, 1437, 2019.
  5. [5] B. Greenway, “Robot accuracy,” Ind. Robot, Vol.27, pp. 257-265, 2000.
  6. [6] M. Dupac, “Smooth trajectory generation for rotating extensible manipulators,” Mathematical Methods in the Applied Sciences, Vol.41, Issue 6, pp. 2281-2286, 2018.
  7. [7] Y. Zhou, Z. Chen, and J. Tang, “A new method of designing the tooth surfaces of spiral bevel gears with ruled surface for their accurate five-axis flank milling,” J. Manuf. Sci. Eng., Vol.139, No.6, 61004, 2017.
  8. [8] F. Xiea, L. Chenb, Z. Lia, and K. Tang, “Path smoothing and feed rate planning for robotic curved layer additive manufacturing,” Robotics and Computer Integrated Manufacturing, Vol.65, 101967, 2020.
  9. [9] W. Wang, C. Hu, K. Zhou, S. He, and L. Zhu, “Local asymmetrical corner trajectory smoothing with bidirectional planning and adjusting algorithm for CNC machining,” Robotics and Computer Integrated Manufacturing, Vol.68, 102058, 2021.
  10. [10] L. Biagiotti and C. Melchiorri, “Online trajectory planning and filtering for robotic applications via B-spline smoothing filters,” Proc. of 2013 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 5668-5673, 2013.
  11. [11] M. A. Funes-Lora, E. A. Portilla-Flores, E. Vega-Alvarado, R. Rivera Blas, E. A. Merchán Cruz, and M. F. Carbajal Romero, “A Novel Mesh Following Technique Based on a Non-Approximant Surface Reconstruction for Industrial Robotic Path Generation,” IEEE Access, Vol.7, pp. 22807-22817, 2019.
  12. [12] S. Tajima and B. Sencer, “Kinematic corner smoothing for high speed machine tools,” Int. J. of Machine Tools and Manufacture, Vol.108, pp. 27-43, 2016.
  13. [13] R. Béarée and A. Olabi, “Dissociated jerk-limited trajectory applied to time-varying vibration reduction,” Robotics and Computer-Integrated Manufacturing, Vol.29, Issue 2, pp. 444-453, 2013.
  14. [14] Y. Fang, J. Qi, J. Hu, W. Wang, and Y. Peng, “An approach for jerk-continuous trajectory generation of robotic manipulators with kinematical constraints,” Mechanism and Machine Theory, Vol.153, 103957, 2020.
  15. [15] S. Tajima and B. Sencer, “Accurate real-time interpolation of 5-axis tool-paths with local corner smoothing,” Int. J. of Machine Tools and Manufacture, Vol.142, pp. 1-15, 2019.
  16. [16] Y. Chen and B. Li, “A Piecewise Acceleration-Optimal and Smooth-Jerk Trajectory Planning Method for Robot Manipulator along a Predefined Path,” Int. J. of Advanced Robotic Systems, Vol.8, Issue 4, pp. 184-193, 2011.
  17. [17] Q. B. Xiao, M. Wan, Y. Liu, X. B. Qin, and W. H. Zhang, “Space corner smoothing of CNC machine tools through developing 3D general clothoid,” Robotics and Computer-Integrated Manufacturing, Vol.64, 101949, 2020.
  18. [18] W. Wang, C. Hu, K. Zhou, and S. He, “Corner trajectory smoothing with asymmetrical transition profile for CNC machine tools,” Int. J. of Machine Tools and Manufacture, Vol.144, 103423, 2019.
  19. [19] T. Haas, S. Weikert, and K. Wegener, “MPCC-based set point optimisation for machine tools,” Int. J. Automation Technol., Vol.13, No.3, pp. 407-418, 2019.
  20. [20] K. Nakamoto and Y. Takeuchi, “Recent advances in multiaxis control and multitasking machining,” Int. J. Automation Technol., Vol.11, No.2, pp. 140-154, 2017.
  21. [21] F. Sellmann, T. Haas, H. Nguyen, S. Weikert, and K. Wegener, “Geometry optimisation for 2D cutting: A quadratic programming approach,” Int. J. Automation Technol., Vol.10, No.2, pp. 272-281, 2016.
  22. [22] L. Zhang, K. Zhang, and Y. Yan, “Local corner smoothing transition algorithm based on double cubic NURBS for five-axis linear tool path,” J. Mech. Eng., Vol.62, pp. 647-656, 2016.
  23. [23] R. Sato, K. Morishita, I. Nishida, K. Shirase, M. Hasegawa, A. Saito, and T. Iwasaki, “Improvement of simultaneous 5-axis controlled machining accuracy by CL-data modification,” Int. J. Automation Technol., Vol.13, No.5, pp. 583-592, 2019.
  24. [24] F. Chen, J. Liao, J. Xiong, S. Yin, S. Huang, and Q. Tang, “High-precision trajectory tracking design and simulation for six degree of freedom robot based on improved active disturbance rejection control,” J. of Mechanical Engineering Science, Vol.233, No.10, pp. 3659-3669, 2019.
  25. [25] M. X. Kong, C. Ji, Z. S. Chen, and R. F. Li, “Smooth and near time-optimal trajectory planning of robotic manipulator with smooth constraint based on cubic B-spline,” Proc. of 2013 IEEE Int. Conf. on Robotics and Biomimetics (ROBIO), pp. 2328-2333, 2013.
  26. [26] R. Zhao and S. Ratchev, “On-line trajectory planning with time-variant motion constraints for industrial robot manipulators,” Proc. of 2017 IEEE Int. Conf. on Robotics and Automation (ICRA), pp. 3748-3753, 2017.
  27. [27] B. Boyacioglu and S. Ertugrul, “Time-optimal Smoothing of RRT-given Path for Manipulators,” Proc. of the 13th Int. Conf. on Informatics in Control, Automation and Robotics, Vol.2, pp. 406-411, 2016.
  28. [28] D. Verscheure, B. Demeulenaere, J. Swevers, J. D. Schutter, and M. Diehl, “Time-Optimal Path Tracking for Robots a Convex Optimization Approach,” IEEE Trans. on Automatic Control, Vol.54, No.10, pp. 2318-2327, 2009.
  29. [29] K. Hu, Y. Dong, and D. Wu, “Smooth time-optimal path tracking for robot manipulators with kinematic constraints,” Proc. of ASME 2020 Int. Mechanical Engineering Congress and Exposition, Vol.7B, V07BT07A038, doi: 10.1115/IMECE2020-23637, 2020.
  30. [30] J. Yang, D. Li, C. Ye, and H. Ding, “An-analytical C3 continuous tool path corner smoothing algorithm for 6R robot manipulator,” Robotics and Computer Integrated Manufacturing, Vol.64, 101947, 2020.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Sep. 19, 2021