Abstract
Industrial robotic arms utilized in contemporary industrial and collaborative environments must operate within increasingly congested and dynamically restricted workspaces while adhering to rigorous standards of safety, precision, and motion quality. This paper presents a two-stage framework for path planning and optimization of a 6-DOF industrial robotic arm navigating amid randomly distributed obstacles. A collision-free reference motion is initially created by integrating B-spline geometric interpolation with a bidirectional RRT-Connect planner, augmented by short-cutting and effective joint-space collision verification for a KUKA KR 4 R600 manipulator. The baseline trajectory is subsequently enhanced through two metaheuristic optimizers: a Whale Genetic hybrid algorithm (WGA) and the Grey Wolf Optimizer (GWO). These optimizers minimize a composite objective that incorporates end-effector trajectory length, joint-level energy consumption based on established motor characteristics, and trajectory smoothness measured by joint jerk. Simulation results indicate that, while the raw Bi-RRT trajectory is geometrically efficient and energy-efficient, it demonstrates excessively high jerk. The suggested enhancements based on WGA and GWO diminish the jerk index of the original Bi-RRT solution by roughly 94–96%, resulting in relatively slight increases in trajectory length and energy, while producing dynamically smooth, collision-free trajectories that adhere to all kinematic constraints. This work presents a comprehensive, implementation-ready methodology that compares sampling-based planning, and multi-objective metaheuristic optimization to produce executable, energy-efficient, and jerk-minimized motions for industrial manipulators in intricate environments.
Data availability
All data generated and analyzed during this study are included in this article.
References
Luo, L. et al. Collision-free path-planning for Six-DOF serial harvesting robot based on energy optimal and artificial potential field, Complexity, 1–12, 2018, (2018). https://doi.org/10.1155/2018/3563846
Gasparetto, A., Boscariol, A., Lanzutti & Vidoni, R. Path planning and trajectory planning algorithms: a general overview. Mech. Mach. Sci. 29, 3–27. https://doi.org/10.1007/978-3-319-14705-5_1 (2015).
Flores, F. G. & Kecskeméthy, A. Time-optimal path planning along specified trajectories. In Multibody System Dynamics, Robotics and Control (eds Gattringer, H. & Gerstmayr, J.) 1–16 (Springer Vienna, 2013). https://doi.org/10.1007/978-3-7091-1289-2_1.
Fang, S., Ma, X., Zhao, Y., Zhang, Q. & Li, Y. Trajectory planning for seven-DOF Robotic Arm Based on Quintic Polynormial, in Proceedings – 2019 11th International Conference on Intelligent Human-Machine Systems and Cybernetics, IHMSC 2019, Institute of Electrical and Electronics Engineers Inc., 198–201. (2019). https://doi.org/10.1109/IHMSC.2019.10142
Mei, J., Zhang, F., Zang, J., Zhao, Y. & Yan, H. Trajectory optimization of the 6-degrees-of-freedom high-speed parallel robot based on B-spline curve. Sci. Prog. 103 (1). https://doi.org/10.1177/0036850419880115 (2020).
Liu, H., Chen, X. & Li, C. Path Planning Optimization for Obstacle Avoidance in Unknown Environment, in 2024 36th Chinese Control and Decision Conference (CCDC), IEEE, May 5601–5606. (2024). https://doi.org/10.1109/CCDC62350.2024.10588054
Mousa, M. A. A., Elgohr, A. & Khater, H. Path planning for a 6 DoF robotic arm based on Whale optimization algorithm and genetic algorithm. J. Eng. Res. 7 (5), 160–168. https://doi.org/10.21608/erjeng.2023.237586.1256 (2023).
Cao, M., Mao, H., Tang, X., Sun, Y. & Chen, T. A novel RRT*-Connect algorithm for path planning on robotic arm collision avoidance. Sci. Rep. 15 (1). https://doi.org/10.1038/s41598-025-87113-5 (2025).
Yang, J., Lyu, M. & Zhang, J. Robotic arm path planning under static obstacles based on improved Informed RRT* algorithm, in 2024 36th Chinese Control and Decision Conference (CCDC), IEEE, May 5466–5470. (2024). https://doi.org/10.1109/CCDC62350.2024.10587619
Elgohr, A. T., Elhadidy, M. S., El-geneedy, M., Akram, S. & Mousa, M. A. A. Advancing Sign Language Recognition: A YOLO v.11-Based Deep Learning Framework for Alphabet and Transactional Hand Gesture Detection, Proceedings of the AAAI Symposium Series, 6, 1, 209–217, (2025). https://doi.org/10.1609/aaaiss.v6i1.36055
Elgohr, A. T. et al. The intelligence behind robotic arms: A deep dive into control evolution. J. Rob. Control (JRC). 6 (3), 1478–1501. https://doi.org/10.18196/jrc.v6i3.25604 (May 2025).
Hassan, O. H. et al. Performance Evaluation of a Standalone Solar-Powered Irrigation System in Desert Regions Using PVsyst: A Comprehensive Analysis, in 2024 25th International Middle East Power System Conference (MEPCON), IEEE, 1–6. (2024). https://doi.org/10.1109/MEPCON63025.2024.10850121
Mousa, M. A. A., Elgohr, A. T. & Khater, H. A. A novel hybrid deep neural network classifier for EEG emotional brain signals. Int. J. Adv. Comput. Sci. Appl. 15 (6). https://doi.org/10.14569/IJACSA.2024.01506107 (2024).
Elgohr, A. T., Khater, H. A. & Mousa, M. A. A. Trajectory optimization for 6 DOF robotic arm using WOA, GA, and novel WGA techniques. Results Eng. 25 https://doi.org/10.1016/j.rineng.2025.104511 (2025).
Hashemi, A. B. & Meybodi, M. R. Cellular PSO: A PSO for dynamic environments, 422–433. (2009). https://doi.org/10.1007/978-3-642-04843-2_45
Mousa, M. A. A., Elgohr, A. T. & Khater, H. A. Trajectory optimization for a 6 DOF robotic arm based on reachability time. Annals Emerg. Technol. Comput. 8 (1), 22–35. https://doi.org/10.33166/AETiC.2024.01.003 (2024).
Mousa, M. A. A., Elgohr, A. T. & Khater, H. A. Whale-Based trajectory optimization algorithm for 6 DOF robotic arm. Annals Emerg. Technol. Comput. (AETiC). 8 (4), 99–114. https://doi.org/10.33166/AETiC.2024.04.005 (2024).
Boscariol, A., Gasparetto, & Scalera, L. Path planning for special robotic operations. In Robot Design: from Theory To Service Applications (eds Carbone, G. & Laribi, M. A.) 69–95 (Springer International Publishing, 2023). https://doi.org/10.1007/978-3-031-11128-0_4.
Ugwoke, K. C., Nnanna, N. A. & Abdullahi, S. E. Y. Simulation-based review of classical, heuristic, and metaheuristic path planning algorithms. Sci. Rep. 15 (1, 12643, ). https://doi.org/10.1038/s41598-025-96614-2 (2025).
Wu, G., Wang, B., Qiu & Han, Y. A path planning and trajectory optimization method for robotic manipulators in industrial scenes with frame Obstacles. Symmetry (Basel). 17 (1, 1, ). https://doi.org/10.3390/sym17010001 (2024).
Wu, Y. et al. Robotic Arm Motion Planning for Obstacle Avoidance Based on the CMN-RRT * Method, in 2023 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 1–6. (2023). https://doi.org/10.1109/ROBIO58561.2023.10354552
Chen, Y. & Lin, H. Reconstructed informed RRT*algorithm for robotic manipulator trajectory planning. J. Phys. Conf. Ser. 3080 (1, 012190, ). https://doi.org/10.1088/1742-6596/3080/1/012190 (2025).
Yu, Y. H. & Zhang, Y. T. Collision avoidance and path planning for industrial manipulator using slice-based heuristic fast marching tree. Robot Comput. Integr. Manuf. 75 (102289). https://doi.org/10.1016/j.rcim.2021.102289 (2022).
Wu, B., Wu, X., Hui, N. & Han, X. Trajectory planning and singularity avoidance algorithm for robotic arm obstacle avoidance based on an improved fast marching tree. Appl. Sci. 14 (8, 3241, ). https://doi.org/10.3390/app14083241 (2024).
Gai, S. N., Sun, R., Chen, S. J. & Ji, S. 6-DOF Robotic Obstacle Avoidance Path Planning Based on Artificial Potential Field Method, in 2019 16th International Conference on Ubiquitous Robots (UR), IEEE, 165–168. (2019). https://doi.org/10.1109/URAI.2019.8768792
Tang, X., Zhou, H. & Xu, T. Obstacle avoidance path planning of 6-DOF robotic arm based on improved A* algorithm and artificial potential field method. Robotica 42 (2), 457–481. https://doi.org/10.1017/S0263574723001546 (2024).
Yao, Z., Gan, Y., Han, Z., Gao, H. & Li, A. An obstacle avoidance path planning algorithm for manipulator in deep crate Grasping, in 2023 China automation Congress (CAC), IEEE, 4715–4720. (2023). https://doi.org/10.1109/CAC59555.2023.10451398
Liu, W. et al. Study on Remote Operation Obstacle Avoidance of Robotic Arm by Fusing APF and RRT Algorithms, in 2024 IEEE 14th International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), IEEE, 1–6. (2024). https://doi.org/10.1109/CYBER63482.2024.10748898
Cesar Velez-Lopez, G. et al. Collision-Free path planning applied to Multi-Degree-of-Freedom robotic arms using homotopy methods. IEEE Access. 12, 150702–150718. https://doi.org/10.1109/ACCESS.2024.3479095 (2024).
Elgohr, A. T., Kasem, H. M. & Elhadidy, M. S. Comparative analysis of robotic arms path planning techniques: case study of the KUKA KR4 R600 using the Whale optimization algorithm. Int. J. Intell. Robot Appl. https://doi.org/10.1007/s41315-025-00501-y (2025).
Yan, C., Zhang, J., Lv, M., Gu, J. & Yahya, K. A Sampling-Based motion planning strategy for robotic manipulators in highly dynamic workspaces. Adv. Transdisciplinary Eng. https://doi.org/10.3233/ATDE250696 (2025).
Zhou, X., Wang, X., Xie, Z., Li, F. & Gu, X. Online obstacle avoidance path planning and application for Arc welding robot. Robot Comput. Integr. Manuf. 78 (102413). https://doi.org/10.1016/j.rcim.2022.102413 (2022).
Li, N., Gao, Z., Ouyang, Y. & Zeng, Y. Obstacle-Avoiding path planning for robotic manipulators based on recursive segmentation point migration optimization and progressive inverse kinematics. IEEE Trans. Autom. Sci. Eng. 22, 20876–20890. https://doi.org/10.1109/TASE.2025.3604604 (2025).
Kano, H. & Fujioka, H. B-Spline Trajectory Planning with Curvature Constraint, in Annual American Control Conference (ACC), IEEE, 2018, 1963–1968. (2018). https://doi.org/10.23919/ACC.2018.8431703
Huo, F., Zhu, S., Dong, H. & Ren, W. A new approach to smooth path planning of ackerman mobile robot based on improved ACO algorithm and B-spline curve. Rob. Auton. Syst. 175, 104655. https://doi.org/10.1016/j.robot.2024.104655 (May 2024).
Zhang, Y. et al. An obstacle avoidance path planning and evaluation method for intelligent vehicles based on the B-Spline algorithm. Sensors 23, 19, (8151). https://doi.org/10.3390/s23198151 (2023).
Elazab, M. A., Elbrashy, A., Elgohr, A. T. & Hussein, A. H. Innovative electrode design and catalytic enhancement for high-efficiency hydrogen production in renewable energy systems. Energy Sour. Part A Recover. Utilization Environ. Eff. 47 (1), 9394–9412. https://doi.org/10.1080/15567036.2025.2490800 (2025).
Liu, M. et al. A path planning algorithm for three-dimensional collision avoidance based on potential field and B-spline boundary curve. Aerosp. Sci. Technol. 144 (108763). https://doi.org/10.1016/j.ast.2023.108763 (2024).
Wang, J. et al. Obstacle-Avoidance Path-Planning algorithm for autonomous vehicles based on B-Spline algorithm. World Electr. Veh. J. 13, 12, (233). https://doi.org/10.3390/wevj13120233 (2022).
Zhang, M. et al. Path planning of the robotic manipulator based on an improved Bi-RRT. IEEE Sens. J. 24 (19), 31245–31261. https://doi.org/10.1109/JSEN.2024.3441622 (2024).
Zhuo, Z., Haiyan, H. & Miaomiao, Z. Obstacle Avoidance Path Planning for a 6-DOF Manipulator Based on Improved RRT Algorithm, in 2023 19th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), IEEE, 1–7. (2023). https://doi.org/10.1109/ICNC-FSKD59587.2023.10280813
Shi, W., Wang, K., Zhao, C. & Tian, M. Obstacle avoidance path planning for the Dual-Arm robot based on an improved RRT algorithm. Appl. Sci. 12 (8). https://doi.org/10.3390/app12084087 (2022).
Liu, Z., Sampurno, R. M., Abeyrathna, R. M. R. D., Nakaguchi, V. M. & Ahamed, T. Development of a Collision-Free path planning method for a 6-DoF orchard harvesting manipulator using RGB-D camera and Bi-RRT algorithm. Sensors 24 (24). https://doi.org/10.3390/s24248113 (2024).
Garg, D. & Kumar, M. Optimization techniques applied to multiple manipulators for path planning and torque minimization. Eng. Appl. Artif. Intell. 15, 241–252. https://doi.org/10.1016/S0952-1976(02)00067-2 (2002).
Bouhalassa, L., Benchikh, L., Ahmed-Foitih, Z. & Bouzgou, K. Path planning of the manipulator arm FANUC based on soft computing techniques. Int. Rev. Automatic Control (IREACO). 13 (4, 171, ). https://doi.org/10.15866/ireaco.v13i4.18506 (2020).
Mirjalili, S. & Lewis, A. The Whale optimization algorithm. Adv. Eng. Softw. 95, 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008 (May 2016).
Chhillar, A. & Choudhary, A. Mobile Robot Path Planning Based Upon Updated Whale Optimization Algorithm, in 2020 10th International Conference on Cloud Computing, Data Science & Engineering (Confluence), 684–691. (2020). https://doi.org/10.1109/Confluence47617.2020.9058323
Wang, T. et al. Optimal Trajectory Planning of Grinding Robot Based on Improved Whale Optimization Algorithm, Math Probl Eng, 3424313, 2020, (2020). https://doi.org/10.1155/2020/3424313
Lim, S. M., Sultan, A. B. M., Sulaiman, M. N., Mustapha, A. & Leong, K. Y. Crossover and mutation operators of genetic algorithms. Int. J. Mach. Learn. Comput. 7 (1), 9–12. https://doi.org/10.18178/ijmlc.2017.7.1.611 (2017).
Ziamanesh, S., Salimi, H. S., Tavana, A. & Ghavifekr, A. A. Parameter Tuning of Discontinues Lyapunov Based Controller Based on the Gray Wolf Optimization Algorithm Applied to a Robotic Manipulator, in 2022 8th Iranian Conference on Signal Processing and Intelligent Systems (ICSPIS), IEEE, 1–6. (2022). https://doi.org/10.1109/ICSPIS56952.2022.10043942
Ratiu, M. & Adriana Prichici, M. Industrial robot trajectory optimization- a review, in MATEC Web of Conferences, EDP Sciences, (2017). https://doi.org/10.1051/matecconf/201712602005
Gunantara, N. A review of multi-objective optimization: methods and its applications. Cogent Eng. 5 (1, 1502242, ). https://doi.org/10.1080/23311916.2018.1502242 (2018).
Al-Omari, A. et al. The role of automated technologies and industrial mechanisms in upgrading photovoltaic panel performance. Clean. Technol. Environ. Policy. https://doi.org/10.1007/s10098-025-03257-y (2025).
Kaur, M., Yanumula, V. K. & Sondhi, S. Trajectory planning and inverse kinematics solution of Kuka robot using COA along with pick and place application. Intell. Serv. Robot. 17, 2, 289–302. https://doi.org/10.1007/s11370-023-00501-6 (2024).
Elhadidy, M. S., Abdalla, W. S., Abdelrahman, A. A., Elnaggar, S. & Elhosseini, M. Assessing the accuracy and efficiency of kinematic analysis tools for six-DOF industrial manipulators: the KUKA robot case study. AIMS Math. 9 (6), 13944–13979. https://doi.org/10.3934/math.2024678 (2024).
Elgohr, A. T. et al. Particle swarm optimization vs. whale optimization algorithm for robotic arm path planning: A controlled study on the KUKA KR4 R600. Results Eng. 28 (108299). https://doi.org/10.1016/j.rineng.2025.108299 (2025).
Acknowledgements
We thank Horus University (Egypt) for its explicit support throughout this research and for providing access to KUKA robotic arm used in the case study. Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
Funding
Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
Author information
Authors and Affiliations
Contributions
Abdelrahman T. Elgohr conceptualized and designed the overall research framework, implemented the Bi-RRT with short-cutting and metaheuristic optimization, and performed the simulations. Maher Rashad contributed to the development of the optimization framework, integrating joint energy and jerk minimization strategies and providing expertise in mathematical modeling. Eman M. El-Gendy focused on B-spline time-parameterized trajectory generation, performance metrics design, and simulation analysis. Waleed Shaaban implemented the inverse kinematics solutions, integrated collision checking, and refined the optimization procedures. Mahmoud M. Saafan conducted the comparative analysis with related studies, assessing the advantages and limitations of the proposed method and optimizing robot motion dynamics. All authors contributed to the conceptualization, modeling, implementation, and revision of the manuscript, and approved the final version for publication.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Ethics approval and consent to participate
All applicable institutional and national guidelines were followed.
Consent for publication
Informed consent was obtained from all the co-authors of this publication.
Software
MATLAB software was used as a platform for modeling robotic arms and implementing the proposed algorithms.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Elgohr, A.T., Rashad, M., El-Gendy, E.M. et al. Dynamic quality aware path planning for 6 DoF robotic arms using BiRRT and metaheuristic optimization based on B spline paths. Sci Rep (2026). https://doi.org/10.1038/s41598-026-37676-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-026-37676-8
