Fractional-Order Artificial Potential Field with Global Guidance for Bidirectional and Adaptive Path Planning in Mobile Robots

Qi  Yang; Dongwei  Li; Minghao  Li; Xin  Zhang; Zhicheng  Cao; Shengbing  Sun; Jianxi  Huang

doi:10.6180/jase.202608_31.013

Fractional-Order Artificial Potential Field with Global Guidance for Bidirectional and Adaptive Path Planning in Mobile Robots

Qi Yang¹, Dongwei Li¹, Minghao Li¹This email address is being protected from spambots. You need JavaScript enabled to view it., Xin Zhang¹, Zhicheng Cao¹, Shengbing Sun¹, and Jianxi Huang²

¹School of Mechanical Engineering, Shenyang Ligong University, Shenyang, Liaoning, China

²School of Advanced Manufacturing, Fuzhou University, Fuzhou, Fujian, China

Received: January 2, 2026
Accepted: January 13, 2026
Publication Date: February 3, 2026

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202608_31.013

To address the limitations of the traditional A^∗ algorithm, including excessive node expansion and non-smooth paths, this paper proposes a bidirectional dynamic A^∗ algorithm guided by an improved fractional-order artificial potential field (FO-APF). The core innovation involves reformulating the potential field using fractional order calculus to generate a superior guiding force that dynamically constrains the search neighborhood, thereby minimizing redundant expansions. The algorithm further integrates adaptive heuristic weights and a bidirectional strategy to accelerate convergence, with subsequent path smoothing achieved via Bézier curve fitting. MATLAB simulations on 30×30 and 50×50 maps demonstrate significant reductions in search time (up to 47.31%), expanded nodes (33.46%), and number of turns. These results confirm the method’s efficacy in enhancing path planning efficiency and quality, particularly in complex environments.

Keywords: Fractional-order artificial potential field; A∗ algorithm; Path planning; Bidirectional search

[1] L. Liu, X. Wang, X. Yang, H. Liu, J. Li, and P. Wang, (2023) “Path planning techniques for mobile robots: Re view and prospect" Expert Systems with Applications 227: 120254. DOI: https: //doi.org/10.1016/j.eswa.2023.120254.
[2] H.-y. Zhang, W.-m. Lin, and A.-x. Chen, (2018) “Path planning for the mobile robot: A review" Symmetry 10(10): 450. DOI: 10.3390/sym10100450.
[3] Z. Wang, G. Li, and J. Ren, (2021) “Dynamic path planning for unmanned surface vehicle in complex offshore areas based on hybrid algorithm" Computer Communications 166: 49–56. DOI: https: //doi.org/10.1016/j.comcom.2020.11.012.
[4] F.-F. Li, Y. Du, and K.-J. Jia, (2022) “Path planning and smoothing of mobile robot based on improved artificial fish swarm algorithm" Scientific reports 12(1): 659. DOI: 10.1038/s41598-021-04506-y.
[5] S. Shan, J. Shao, H. Zhang, S. Xie, and F. Sun, (2024) “Research and validation of self-driving path planning algorithm based on optimized A*-artificial potential field method" IEEE Sensors Journal 24(15): 24708–24722. DOI: 10.1109/JSEN.2024.3410271.
[6] X. Chi, H. Li, and J. Fei, (2021) “Research on robot random obstacle avoidance method based on fusion of improved A* algorithm and dynamic window method" Chinese Journal of Scientific Instrument 42(3): 132–140.
[7] B. Zhang, T. Gao, Y. Chen, X. Jin, T. Feng, and X. Chen, (2023) “Research on unmanned transfer vehicle path planning for raw grain warehousing" Journal of Intelligent & Fuzzy Systems 45(4): 6513–6533. DOI: 10.3233/JIFS-232780.
[8] S. Erke, D. Bin, N. Yiming, Z. Qi, X. Liang, and Z. Dawei, (2020) “An improved A-Star based path planning algorithm for autonomous land vehicles" International Journal of Advanced Robotic Systems 17(5): 1729881420962263. DOI: 10.1177/1729881420962263.
[9] G. Tang, C. Tang, C. Claramunt, X. Hu, and P. Zhou, (2021) “Geometric A-star algorithm: An improved A-star algorithm for AGV path planning in a port environment" IEEE access 9: 59196–59210. DOI: 10.1109/ACCESS. 2021.3070054.
[10] R. Song, Y. Liu, and R. Bucknall, (2019) “Smoothed A* algorithm for practical unmanned surface vehicle path planning" Applied Ocean Research 83: 9–20. DOI: https: //doi.org/10.1016/j.apor.2018.12.001.
[11] X. Fan, Y. Guo, H. Liu, B. Wei, and W. Lyu, (2020) “Improved artificial potential field method applied for AUV path planning" Mathematical Problems in Engineering 2020(1): 6523158. DOI: https: //doi.org/10.1155/2020/6523158.
[12] D. Xu, H. Yue, Y. Zhao, F. Yang, J. Wu, X. Pan, T. Tang, and Y. Zhang, (2024) “Improved A* Algorithm for Path Planning Based on CubeSats In-Orbit Electromagnetic Transfer System" Aerospace 11(5): 394. DOI: 10.3390/aerospace11050394.
[13] L. Chu, Y. Wang, S. Li, Z. Guo, W. Du, J. Li, and Z. Jiang, (2024) “Intelligent vehicle path planning based on optimized a* algorithm" Sensors 24(10): 3149. DOI: 10.3390/s24103149.
[14] Y. Liu, X. Gao, B. Wang, J. Fan, Q. Li, and W. Dai, (2024) “A passage time–cost optimal A* algorithm for cross-country path planning" International Journal of Applied Earth Observation and Geoinformation 130: 103907. DOI: https: //doi.org/10.1016/j.jag.2024.103907.
[15] Z. An, X. Rui, and C. Gao, (2024) “Improved A* navigation path-planning algorithm based on hexagonal grid" ISPRS International Journal of Geo-Information 13(5): 166. DOI: 10.3390/ijgi13050166.
[16] G. Xie, L. Fang, X. Su, D. Guo, Z. Qi, Y. Li, and J. Che, (2024) “A Path-Planning Approach for an Unmanned Vehicle in an Off-Road Environment Based on an Improved A* Algorithm" World Electric Vehicle Journal 15(6): 234. DOI: 10.3390/wevj15060234.
[17] X. Meng, D. Duan, and T. Feng, (2022) “Multi-vehicle multi-sensor occupancy grid map fusion in vehicular net works" IET communications 16(1): 67–74.
[18] J. S. Obando-Ceron, V. Romero-Cano, and S. Mon teiro, (2023) “Probabilistic multi-modal depth estimation based on camera–LiDAR sensor fusion" Machine Vision and Applications 34(5): 79. DOI: 10.1007/s00138-023 01426-x.
[19] L. Zhang and Y. Li, (2021) “Mobile robot path planning algorithm based on improved a star" 1848(1): 012013. DOI: 10.1088/1742-6596/1848/1/012013.
[20] Y. Zhang and Q. Zhao, (2024) “Complex Environment Based on Improved A* Algorithm Research on Path Planning of Inspection Robots" Processes 12(5): 855. DOI: 10.3390/pr12050855.
[21] T. Li and Z. Wang, (2024) “Multi objective optimization scheduling of unmanned warehouse handling robots based on Astar algorithm" Concurrency and Computation: Practice and Experience 36(13): e8064. DOI: https: //doi.org/10.1002/cpe.8064.
[22] J.-X. Zhang, X. Zhang, D. Boutat, and D. -Y.Liu, (2025) “Fractional-order complex systems: Advanced control, intelligent estimation and reinforcement learning image processing algorithms" Fractal and Fractional 9(2): 67. DOI: 10.3390/fractalfract9020067.
[23] X. Wang, X. Zhang, W. Pedrycz, S.-H. Yang, and D. Boutat, (2024) “Consensus of TS fuzzy fractional-order, singular perturbation, multi-agent systems" Fractal and Fractional 8(9): 523. DOI: 10.3390/fractalfract8090523.
[24] X. Zhang, R. Liu, J. Ren, and Q. Gui, (2022) “Adaptive fractional image enhancement algorithm based on rough set and particle swarm optimization" Fractal and Fractional 6(2): 100. DOI: 10.3390/fractalfract6020100.
[25] X. Zhang and L. Dai, (2022) “Image enhancement based on rough set and fractional order differentiator" Fractal and Fractional 6(4): 214. DOI: 10.3390/fractalfract6040214.
[26] X.ZhangandY.Chen,(2018)“Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: The 0< α< 1 case" ISA transactions 82: 42–50. DOI: https: //doi.org/10.1016/j.isatra.2017.03.008.
[27] B. Fu, L. Chen, Y. Zhou, D. Zheng, Z. Wei, J. Dai, and H. Pan, (2018) “An improved A* algorithm for the industrial robot path planning with high success rate and short length" Robotics and Autonomous Systems 106: 26–37.
[28] X. Wu, L. Xu, R. Zhen, and X. Wu, (2020) “Bi directional adaptive A* algorithm toward optimal path planning for large-scale UAV under multi-constraints" IEEE Access 8: 85431–85440. DOI: 10.1109/ACCESS. 2020.2990153.
[29] B. ZhangandD.Zhu,(2021) “A new method on motion planning for mobile robots using jump point search and Bezier curves" International Journal of Advanced Robotic Systems 18(4): 17298814211019220. DOI: 10.1177/17298814211019220.