Journals / Gazi University Journal of Science Part A: Engineering and Innovation / 2026 / Volume: 13 Issue: 3

Energy-Efficient Trajectory Optimization for a 4-DOF Serial Manipulator Using Adaptive Dolphin-Eagle Algorithm with Joint-Aware Energy Weighting

Mehmet İrfan Gedik(OSTIM TECHNICAL UNIVERSITY)0000-0003-2836-2735
Fatih Baykal(OSTIM TECHNICAL UNIVERSITY)0000-0002-2842-584X
Burak Yenipınar(OSTIM TECHNICAL UNIVERSITY)0000-0002-5997-944X
Pages
—
Publication Date
2026-09-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Unlike baseline methods that plateau mid-run, ADEA exhibits sustained convergence, offering a robust framework for energy-aware motion planning in industrial tasks.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Energy efficiency in industrial robotic manipulators is vital for reducing operational costs and carbon footprints.
📊
Key Findings & Data:This paper presents the Adaptive Dolphin-Eagle Algorithm (ADEA), a hybrid metaheuristic for energy-optimal trajectory planning of a 4-DOF serial manipulator.
💡
Conclusion & Impact:Unlike baseline methods that plateau mid-run, ADEA exhibits sustained convergence, offering a robust framework for energy-aware motion planning in industrial tasks.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Energy-Efficient Trajectory Planning · Bio-Inspired Optimization · Adaptive Dolphin-Eagle Algorithm

Abstract

Energy efficiency in industrial robotic manipulators is vital for reducing operational costs and carbon footprints. This paper presents the Adaptive Dolphin-Eagle Algorithm (ADEA), a hybrid metaheuristic for energy-optimal trajectory planning of a 4-DOF serial manipulator. ADEA combines dolphin echolocation-based global exploration with eagle Lévy-flight exploitation. It is augmented by Joint-Aware Energy Weighting (JAEW), a physics-informed mechanism that amplifies search steps for high-activation joints, embedding dynamic load structures into the optimization without altering the fitness function. Based on a CAD-accurate robot model under full Newton-Euler inverse dynamics, trajectories are parameterized using quintic polynomial segments through two intermediate waypoints to minimize mechanical energy. Comparative evaluations against Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), and a JAEW-augmented Starfish Optimization (SFO) baseline across 30 independent runs demonstrate that ADEA achieves the lowest mean energy consumption. Significant performance gains are confirmed by Wilcoxon signed-rank tests (p < 0.05). Unlike baseline methods that plateau mid-run, ADEA exhibits sustained convergence, offering a robust framework for energy-aware motion planning in industrial tasks.

🔖

Cite This Article

Öğülmüş, A. S., Gedik, M. İ., Baykal, F., Yenipınar, B. (2026). Energy-Efficient Trajectory Optimization for a 4-DOF Serial Manipulator Using Adaptive Dolphin-Eagle Algorithm with Joint-Aware Energy Weighting. Gazi University Journal of Science Part A: Engineering and Innovation, Volume: 13 Issue: 3. https://doi.org/10.54287/gujsa.1962818

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. Carabin, G., & Scalera, L. (2020). On the trajectory planning for energy efficiency in industrial robotic systems. Robotics, 9(4), 89. https://doi.org/10.3390/robotics9040089
  2. Derrac, J., García, S., Molina, D., & Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1), 3–18. https://doi.org/10.1016/j.swevo.2011.02.002
  3. Elgohr, A. T., Elazab, M. A., Emam, A. Z., Mostafa, M. G., Al-Razgan, M., Kasem, H. M., & Elhadidy, M. S. (2025). Particle swarm optimization vs. whale optimization algorithm for robotic arm path planning: A controlled study on the KUKA KR4 R600. Results in Engineering, 28, 108299. https://doi.org/10.1016/j.rineng.2025.108299
  4. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks (ICNN'95) (27 November - 01 December 1995, Vol. 4, pp. 1942–1948), Perth, WA, Australia. https://doi.org/10.1109/ICNN.1995.488968
  5. Li, Y., Wang, Z., Yang, H., Zhang, H., & Wei, Y. (2023). Energy-optimal planning of robot trajectory based on dynamics. Arabian Journal for Science and Engineering, 48(3), 3523–3536. https://doi.org/10.1007/s13369-022-07185-7
  6. Lin, H.-I., Mandal, R., & Wibowo, F. S. (2024). BN-LSTM-based energy consumption modeling approach for an industrial robot manipulator. Robotics and Computer-Integrated Manufacturing, 85, 102629. https://doi.org/10.1016/j.rcim.2023.102629
  7. Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in Engineering Software, 95, 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
  8. Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
  9. Nonoyama, K., Liu, Z., Fujiwara, T., Alam, M. M., & Nishi, T. (2022). Energy-efficient robot configuration and motion planning using genetic algorithm and particle swarm optimization. Energies, 15(6), 2074. https://doi.org/10.3390/en15062074
  10. Öğülmüş, A. S., & Tınkır, M. (2023). Development and performance analysis of novel design 3-DOF non-integrated runner permanent magnet spherical motor. Engineering Science and Technology, an International Journal, 40, 101380. https://doi.org/10.1016/j.jestch.2023.101380
  11. Pu, Q.-c., Xu, X.-r., Li, Q.-q., & Zhang, H. (2024). Robotic arm time–jerk optimal trajectory based on improved dingo optimization. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46(4), 198. https://doi.org/10.1007/s40430-024-04694-4
  12. Rezali, B., Ibari, B., Hebali, M., Berka, M., Bennaoum, M., Bouzgou, K., Ayad, R., & Benchikh, L. (2025). Optimal trajectory planning for industrial robots: Minimizing time, jerk, and energy consumption using LSTM for energy profile modeling. Journal of Vibration and Control, 32(11–12), 2712–2735. https://doi.org/10.1177/10775463251333481
  13. Spong, M. W., Hutchinson, S., & Vidyasagar, M. (2006). Robot modeling and control. Wiley.
  14. Xu, J., Ren, C., & Chang, X. (2023). Robot time-optimal trajectory planning based on quintic polynomial interpolation and improved Harris Hawks algorithm. Axioms, 12(3), 245. https://doi.org/10.3390/axioms12030245
  15. Yin, S., Ji, W., & Wang, L. (2019). A machine learning based energy efficient trajectory planning approach for industrial robots. Procedia CIRP, 81, 429–434. https://doi.org/10.1016/j.procir.2019.03.074
  16. Zhang, M., & Yan, J. (2021). A data-driven method for optimizing the energy consumption of industrial robots. Journal of Cleaner Production, 285, 124862. https://doi.org/10.1016/j.jclepro.2020.124862
  17. Zhou, Y., Han, G., Wei, Z., Huang, Z., Chen, X., & Wu, J. (2024). Optimal trajectory planning of robot energy consumption based on improved sparrow search algorithm. Measurement and Control, 57(7), 1014–1021. https://doi.org/10.1177/00202940231220080