Vertically articulated industrial robots are suitable for machining purposes owing to their advantages over multi-axis machine tools, such as larger workspace, easier installation, and lower cost. However, the rigidity and positioning accuracy of industrial robots are inferior to those of machine tools, which renders it difficult to maintain the robot posture required for machining operations. This study focuses on improving the accuracy of robot machining based on posture optimization by exploiting the kinematic redundancy of a six-axis vertically articulated robot. To decrease positioning errors caused by static and dynamic external forces during machining, this study proposes a path generation method for a redundant joint that simultaneously considers the static and dynamic rigidity of the machining robot. The relationships between the static and dynamic mechanical characteristics of the machining robot and the redundant angle are illustrated using two maps: a static stiffness map and a natural frequency map. Using these two maps in the proposed path generation method, the redundant angle that can be selected for the robot posture with arbitrary mechanical characteristics is selected. Experimental results confirm that the proposed path generation method can control the priority of reducing static positioning error and vibration amplitude by changing the weight coefficients. In addition, the proposed method can improve positioning accuracy compared with conventional trajectory generation methods for redundant robots.

1. [1] 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. https://doi.org/10.1016/j.cirp.2019.05.009
2. [2] V. Milenkovic and B. Huang, “Kinematics of Major Robot Linkages,” Robotics Int. of SME, Vol.2, pp. 16-31, 1983.
3. [3] Y. Chen and F. Dong, “Robot machining: recent development and future research issues,” The Int. J. of Advanced Manufacturing Technology, Vol.66, No.9, pp. 1489-1497, 2013. https://doi.org/10.1007/s00170-012-4433-4
4. [4] S. Tajima, S. Iwamoto, and H. Yoshioka, “Kinematic tool-path smoothing for 6-axis industrial machining robots,” Int. J. Automation Technol., Vol.15, No.5, pp. 621-630, 2021. https://doi.org/10.20965/ijat.2021.p0621
5. [5] 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. https://doi.org/10.1016/j.rcim.2019.01.016
6. [6] 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. https://doi.org/10.3390/electronics8121437
7. [7] M. Dupac, “Smooth trajectory generation for rotating extensible manipulators,” Mathematical Methods in the Applied Sciences, Vol.41, Issue 6, pp. 2281-2286, 2018. https://doi.org/10.1002/mma.4210
8. [8] S. Mousavi, V. Gagnol, B. C. Bouzgarrou, and P. Ray, “Dynamic modeling and stability prediction in robotic machining,” Int. J. Adv. Manuf. Technol., Vol.88, No.9, pp. 3053-3065, 2017. https://doi.org/10.1007/s00170-016-8938-0
9. [9] S. Ibaraki, N. A. Theissen, A. Archenti, and M. M. Alam, “Evaluation of kinematic and compliance calibration of serial articulated industrial manipulators,” Int. J. Automation Technol., Vol.15, No.5, pp. 567-580, 2021. https://doi.org/10.20965/ijat.2021.p0567
10. [10] D. Kato, K. Yoshitsugu, N. Maeda, T. Hirogaki, E. Aoyama, and K. Takahashi, “Positioning Error Calibration of Industrial Robots Based on Random Forest,” Int. J. Automation Technol., Vol.15, No.5, pp. 581-589, 2021. https://doi.org/10.20965/ijat.2021.p0581
11. [11] R. Sato, Y. Ito, S. Mizuura, and K. Shirase, “Vibration Mode and Motion Trajectory Simulations of an Articulated Robot by a Dynamic Model Considering Joint Bearing Stiffness,” Int. J. Automation Technol., Vol.15, No.5, pp. 631-640, 2021. https://doi.org/10.20965/ijat.2021.p0631
12. [12] S. Mejri, V. Gagnol, T. P. Le, L. Sabourin, P. Ray, and P. Paultre, “Dynamic characterization of machining robot and stability analysis,” The Int. J. of Advanced Manufacturing Technology, Vol.82, pp. 351-359, 2016. https://doi.org/10.1007/s00170-015-7336-3
13. [13] A. Karim, J. Hitzer, A. Lechler, and A. Verl, “Analysis of the dynamic behavior of a six-axis industrial robot within the entire workspace in respect of machining tasks,” 2017 IEEE Int. Conf. on Advanced Intelligent Mechatronics (AIM), pp. 670-675, 2017. https://doi.org/10.1109/AIM.2017.8014094
14. [14] J. R. Diaz Posada, U. Schneider, A. Sridhar, and A. Verl, “Automatic motion generation for robotic milling optimizing stiffness with sample-based planning,” Machines, Vol.5, No.1, 3, 2017. https://doi.org/10.3390/machines5010003
15. [15] H. Celikag, N. D. Sims, and E. Ozturk, “Cartesian stiffness optimization for serial arm robots,” Procedia CIRP, Vol.77, pp. 566-569, 2018. https://doi.org/10.1016/j.procir.2018.08.222
16. [16] L. Sabourin, K. Subrin, R. Cousturier, G. Gogu, and Y. Mezouar, “Redundancy-based optimization approach to optimize robotic cell behaviour: application to robotic machining,” Industrial Robot, Vol.42, Issue 2, pp. 167-178, 2015. https://doi.org/10.1108/IR-07-2014-0371
17. [17] D. Busson, R. Bearee, and A. Olabi, “Task-oriented rigidity optimization for 7 DOF redundant manipulators,” IFAC PapersOnLine, Vol.50, Issue 1, pp. 14588-14593, 2017. https://doi.org/10.1016/j.ifacol.2017.08.2108
18. [18] S. Mousavi, V. Gagnol, B. C. Bouzgarroua, and P. Ray, “Stability optimization in robotic milling through the control of functional redundancies,” Robotics and Computer–Integrated Manufacturing, Vol.50, pp. 181-192, 2018. https://doi.org/10.1016/j.rcim.2017.09.004
19. [19] L. B. da Silva, H. Yoshioka, H. Shinno, and J. Zhu, “Tool orientation angle optimization for a multi-axis robotic milling system,” Int. J. Automation Technol., Vol.13, No.5, pp. 574-582, 2019. 10.20965/ijat.2019.p0574
20. [20] E. K. Xidias, “Time-optimal trajectory planning for hyper-redundant manipulators in 3D workspaces,” Robotics and Computer-Integrated Manufacturing, Vol.50, pp. 286-298, 2018. https://doi.org/10.1016/j.rcim.2017.10.005
21. [21] M. Weghe, D. Ferguson, and S. Srinivasa, “Randomized Path Planning for Redundant Manipulators without Inverse Kinematics,” IEEE-RAS Int. Conf. on Humanoid Robots, pp. 477-482, 2007. 10.1109/ICHR.2007.4813913
22. [22] Y. Altintas and E. Budak, “Analytical Prediction of Stability Lobes in Milling,” Annals of the ClRP, Vol.44, Issue 1, pp. 357-362, 1995. https://doi.org/10.1016/S0007-8506(07)62342-7
23. [23] T. S. Lee and E. A. Alandoli, “A critical review of modelling methods for fexible and rigid link manipulators,” J. of the Brazilian Society of Mechanical Sciences and Engineering, Vol.42, Issue 10, 508, 2020. https://doi.org/10.1007/s40430-020-02602-0
24. [24] E. A. Alandoli and T. S. Lee, “A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators,” Robotica, Vol.38, No.12, pp. 2239-2265, 2020. https://doi.org/10.1017/S0263574720000223
25. [25] G. Sherif, S. Ahmad, S. A. Mohamad, and G. Fayez, “Dynamic Modelling with a Modified PID Controller of a Three Link Rigid Manipulator,” Int. J. of Computer Applications, Vol.179, pp. 37-42, 2018. https://doi.org/10.5120/IJCA2018916772
26. [26] S. Joo and H. Mayeda, “Joint Stiffness Measurements of Multi-joint Type Robot Manipulators with Serial Mechanisms,” J. of the Robotics Society of Japan, Vol.13, Issue 3, pp. 390-396, 1995 (in Japanese). https://doi.org/10.7210/jrsj.13.390
27. [27] T. Tsumugiwa, R. Yokogawa, and K. Hara, “Measurement for Compliance of Vertical-Multi-Articulated Robot,” Trans. of the Japan society of mechanical engineers. C, Vol.69, No.688, pp. 3293-3300, 2003 (in Japanese). https://doi.org/10.1299/kikaic.69.3293
28. [28] M. Galicki, “Time-optimal controls of kinematically redundant manipulators with geometric constraints,” IEEE Trans. on Robotics and Automation, Vol.16, No.1, pp. 89-93, 2000. https://doi.org/10.1109/70.833194
29. [29] M. Minami, X. Li, T. Matsuno, and A. Yanou, “Dynamic reconfiguration manipulability for redundant manipulators,” J. of Mechanisms and Robotics, Vol.8, Issue 6, 061004, 2016. https://doi.org/10.1115/1.4033667