A trajectory, which determines the change of the displacement and posture of a robot with time, influences dynamic torque or energy during the operation. Although various methods for optimizing the trajectories have been proposed, most of them require the exact model that is difficult to construct. Previously, the authors proposed the method for optimizing the trajectories of an industrial robot without the dynamic model by using a heuristic algorithm. The proposed method can reduce the energy or peak current value consumed in the motor. However, the proposed method cannot be available for the operation where the required path of a robot often varies, because those cases need to explore the optimal trajectory with each path, and then a quite few numbers of driving the actual robot for exploring will be required. Therefore, this paper proposed a method for instantaneously optimizing the trajectories by using a neural network (NN) that is constructed by using the optimal trajectories obtained with the heuristic algorithm. In this paper, first, the optimal start position and the optimal operation times of an industrial robot is respectively explored by the heuristic algorithm using the average power consumed in the motor as the evaluation value. Next, a NN learned the parameters of the optimal trajectories explored by the heuristic algorithm for various paths. The constructs NN will generate optimal trajectories that reduce the evaluation values to the same extent as the trajectories explored by the heuristic algorithm. Namely, the proposed method using the NN can estimate the optimal trajectories in a shorter time than the method using the heuristic algorithm.

1. [1] H. Tachiya, Y. Matsui, T. Murakawa, and S. Akino, “Evaluation of robotic open loop mechanisms using dynamic characteristic charts,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.63, No.606, pp. 613-619, 1997 (in Japanese). https://doi.org/10.1299/kikaic.63.613
2. [2] A. Abe and S. Nemoto, “An energy saving feedforward control technique for a 2-DOF flexible manipulator,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.78, No.789, pp. 1325-1337, 2012 (in Japanese). https://doi.org/10.1299/kikaic.78.1325
3. [3] M. Pellicciari, G. Berselli, F. Leali, and A. Vergnano, “A method for reducing the energy consumption of pick-and-place industrial robots,” Mechatronics, Vol.23, No.3, pp. 326-334, 2013. https://doi.org/10.1016/j.mechatronics.2013.01.013
4. [4] P. M. Ho, N. Uchiyama, S. Sano, Y. Honda, A. Kato, and T. Yonezawa, “Simple motion trajectory generation for energy saving of industrial machines,” SICE J. of Control, Measurement, and System Integration, Vol.7, No.1, pp. 29-34, 2014. https://doi.org/10.1109/SII.2012.6427362
5. [5] Y. M. Kim and B. K. Kim, “Energy-efficient joint path-following for attitude-fixed space manipulators with bounds on completion time and motor voltage/current,” Intelligent Service Robotics, Vol.10, pp. 1-11, 2017. https://doi.org/10.1007/s11370-016-0211-8
6. [6] M. Hayashi, H. Tachiya, N. Asakawa, and T. Kawamura, “Determination method for power-saved driving motions of manipulators by heuristic algorithms (in case of PTP control),” J. of the Franklin Institute, Vol.348, No.1, pp. 101-111, 2011. https://doi.org/10.1016/j.jfranklin.2009.02.016
7. [7] S. Fujimoto, T. Ono, and K. Ohsaka, “Proposal of insertion type genetic algorithm and its application to based parameter identification for a robot manipulator,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.74, No.739, pp. 633-641, 2008 (in Japanese). https://doi.org/10.1299/kikaic.74.633
8. [8] A. Klimchik, B. Furet, S. Caro, and A. Pashkevich, “Identification of the manipulator stiffness model parameters in industrial environment,” Mechanism and Machine Theory, Vol.90, pp. 1-22, 2015. https://doi.org/10.1016/j.mechmachtheory.2015.03.002
9. [9] A. Montazeri, C. West, S. D. Monk, and C. J. Taylor, “Dynamic modelling and parameter estimation of a hydraulic robot manipulator using a multi-objective genetic algorithm,” Int. J. of Control, Vol.90, No.4, pp. 661-683, 2017. https://doi.org/10.1080/00207179.2016.1230231
10. [10] R. Miranda-Colorado and J. M. Valenzuela, “Experimental parameter identification of flexible joint robot manipulators,” Robotica, Vol.36, No.3, pp. 313-332, 2018. https://doi.org/10.1017/S0263574717000224
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] N. A. Theissen, M. K. Gonzalez, A. Barrios, and A. Archenti, “Quasi-static compliance calibration of serial articulated industrial manipulators,” Int. J. Automation Technol., Vol.15, No.5, pp. 590-598, 2021. https://doi.org/10.20965/ijat.2021.p0590
13. [13] M. M. Alam, S. Ibaraki, and K. Fukuda, “Kinematic modeling of six-axis industrial robot and its parameter identification: A tutorial,” Int. J. Automation Technol., Vol.15, No.5, pp. 599-610, 2021. https://doi.org/10.20965/ijat.2021.p0599
14. [14] 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
15. [15] H. Tachiya, H. Itani, M. Hayashi, H. Iga, and M. Higuchi, “Generating optimized trajectories of industrial robots in CP motion without kinetic models,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.79, No.805, pp. 3075-3087, 2013 (in Japanese). https://doi.org/10.1299/kikaic.79.3075
16. [16] A. R. J. Almusawi, L. C. Dülger, and S. Kapucu, “A new artificial neural network approach in solving inverse kinematics of robotic arm (Denso VP6242),” Computational Intelligence and Neuroscience, 2016. https://doi.org/10.1155/2016/5720163
17. [17] N. T. T. Vu, D. D. Bui, and H. T. Tran, “Artificial neural network based path planning of excavator arm,” Int. J. of Mechanical Engineering and Robotics Research, Vol.8, No.1, pp. 12-17, 2019. https://doi.org/10.18178/ijmerr.8.1.12-17
18. [18] S. Erkaya, “Effects of joint clearance on the motion accuracy of robotic manipulators,” J. of Mechanical Engineering, Vol.64, No.2, pp. 82-94, 2018. https://doi.org/10.5545/sv-jme.2017.4534
19. [19] M. Endo and B. Sencer, “Accurate prediction of machining cycle times by data-driven modelling of NC system’s interpolation dynamics,” CIRP Annals – Manufacturing Technology, Vol.71, No.1, pp. 405-408, 2022. https://doi.org/10.1016/j.cirp.2022.04.017
20. [20] S. H. Chien, B. Sencer, and R. Ward, “Accurate prediction of five-axis machining cycle times with deep neural networks using Bi-LSTM,” CIRP J. of Manufacturing Science and Technology, Vol.48, pp. 28-41, 2024. https://doi.org/10.1016/j.cirpj.2023.11.007
21. [21] J. Gregory, A. Olivares, and E. Staffetti, “Energy-optimal trajectory planning for robot manipulators with holonomic constraints,” Systems & Control Letters, Vol.61, No.2, pp. 279-291, 2012. https://doi.org/10.1016/j.sysconle.2011.11.005
22. [22] W. Aribowo and K. Terashima, “Cubic spline trajectory planning and vibration suppression of semiconductor wafer transfer robot Arm,” Int. J. Automation Technol., Vol.8, No.2, pp. 265-274, 2014. https://doi.org/10.20965/ijat.2014.p0265
23. [23] K. Erkorkmaz, A. Alzaydi, A. Elfizy, and S. Engin, “Time-optimized hole sequence planning for 5-axis on-the-fly laser drilling,” CIRP Annals – Manufacturing Technology, Vol.63, pp. 377-380, 2014. https://doi.org/10.20965/ijat.2014.p0265
24. [24] D. Kato, K. Yoshitsugu, 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
25. [25] S. Aoyagi, M. Suzuki, T. Takahashi, J. Fujioka, and Y. Kamiya, “Calibration of Kinematic parameters of robot arm using laser tracking system: Compensation for non-geometric errors by neural networks and selection of optimal measuring points by genetic algorithm,” Int. J. Automation Technol., Vol.6, No.1, pp. 29-37, 2012. https://doi.org/10.20965/ijat.2012.p0029
26. [26] 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
27. [27] T. Arai, “JIS tsukaikata shiri-zu sangyoyou robotto gengo “SLIM”,” Nihon Kikaku Kyokai, pp. 132-154, 1994 (in Japanese).
28. [28] S. Lin and B. W. Kernighan, “An effective heuristic algorithm for the Traveling-Salesman Problem,” Operations Research, Vol.21, No.2, pp. 498-516, 1973. https://doi.org/10.1287/opre.21.2.498
29. [29] Y. Ueno and H. Tachiya, “Suppressing residual vibration caused in objects carried by robots using a heuristic algorithm,” Precision Engineering, Vol.80, pp. 1-9, 2023. https://doi.org/10.1016/j.precisioneng.2022.11.009
30. [30] M. Hayashi, H. Tachiya, and N. Asakawa, “Determination of trajectory for a multi-DOF manipulator by heuristic algorithms (Implementation approach for the suppression of dynamic torque of a steel sheet handling manipulator),” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.75, No.750, pp. 262-269, 2009 (in Japanese).
31. [31] M. Taki, “Korenarawakaru shinsougakusyu,” Koudansha Ltd., 2017 (in Japanese).