Research on mathematical optimization-driven A<sup>*</sup> search, DWA improvement, and intelligent robot path planning

Le Gao; Yuying Zhang; Pinjie Liu; Xiaoying Ou; Jinglong Cheng; Ying Zhu; Le Gao; Yuying Zhang; Pinjie Liu; Xiaoying Ou; Jinglong Cheng; Ying Zhu

doi:10.3934/math.20251355

AIMS Mathematics

2025, Volume 10, Issue 12: 30879-30904. doi: 10.3934/math.20251355

Previous Article Next Article

Research article

Research on mathematical optimization-driven A^* search, DWA improvement, and intelligent robot path planning

1.
School of Computer Engineering, Guangzhou Huali College, Guangzhou 510000, China
2.
Center for Earth Environment and Earth Resources, Sun Yat-sen University, Zhuhai 519000, China
3.
School of Intelligent Manufacturing, Guangzhou Huali College, Jiangmen 529000, China

Received: 08 November 2025 Revised: 13 December 2025 Accepted: 24 December 2025 Published: 30 December 2025
MSC : 90B06, 90C90

Mobile robots encounter issues like low global search efficiency and insufficient static path safety in path planning within complex dynamic environments. This paper proposes a fusion strategy integrating a mathematically optimized improved A^* algorithm (ImpA^*) and an enhanced Dynamic Window Approach (ImpDWA). At the global planning layer, path quality and efficiency are improved through optimizations such as obstacle ratio quantification and dynamic weighting of heuristic functions. At the local planning layer, the DWA evaluation system is optimized by adding a target point cost sub-function and dynamically adjusting weights. At the fusion layer, dual-algorithm collaboration is achieved via global path segmentation and key sub-target transmission. MATLAB simulations show that the ImpA^* algorithm significantly optimizes path length and runtime. The fusion algorithm (ImpA^*-ImpDWA) achieves an obstacle avoidance success rate exceeding 96.5% in dynamic environments, with comprehensive performance superior to other mainstream schemes. It realizes the coordinated balance of core indicators including safety and smoothness, providing reliable support for autonomous robot navigation.
- mathematical optimization,
- improved A^* algorithm,
- dynamic window approach,
- mobile robot,
- path planning
Citation: Le Gao, Yuying Zhang, Pinjie Liu, Xiaoying Ou, Jinglong Cheng, Ying Zhu. Research on mathematical optimization-driven A* search, DWA improvement, and intelligent robot path planning[J]. AIMS Mathematics, 2025, 10(12): 30879-30904. doi: 10.3934/math.20251355

Related Papers:

Abstract

Mobile robots encounter issues like low global search efficiency and insufficient static path safety in path planning within complex dynamic environments. This paper proposes a fusion strategy integrating a mathematically optimized improved A^* algorithm (ImpA^*) and an enhanced Dynamic Window Approach (ImpDWA). At the global planning layer, path quality and efficiency are improved through optimizations such as obstacle ratio quantification and dynamic weighting of heuristic functions. At the local planning layer, the DWA evaluation system is optimized by adding a target point cost sub-function and dynamically adjusting weights. At the fusion layer, dual-algorithm collaboration is achieved via global path segmentation and key sub-target transmission. MATLAB simulations show that the ImpA^* algorithm significantly optimizes path length and runtime. The fusion algorithm (ImpA^*-ImpDWA) achieves an obstacle avoidance success rate exceeding 96.5% in dynamic environments, with comprehensive performance superior to other mainstream schemes. It realizes the coordinated balance of core indicators including safety and smoothness, providing reliable support for autonomous robot navigation.

References

[1]	M. A. Ferreira, L. C. Moreira, A. M. Lopes, Autonomous navigation system for a differential drive mobile robot, J. Test. Eval., 52 (2024), 841–852. https://doi.org/10.1520/JTE20230191 doi: 10.1520/JTE20230191
[2]	A. Amin, X. C. Wang, Y. N. Zhang, T. H. Li, Y. Y. Chen, J. M. Zhang, A comprehensive review of applications of robotics and artificial intelligence in agricultural operations, Stud. Inform. Control, 32 (2023), 59–70.
[3]	T. Chen, S. Q. Li, Z. P. Zeng, Z. H. Liang, Y. X. Chen, W. S. Guo, An empirical investigation of users' switching intention to public service robots: From the perspective of PPM framework, Gov. Inform. Q., 41 (2024), 101933. https://doi.org/10.1016/j.giq.2024.101933 doi: 10.1016/j.giq.2024.101933
[4]	H. W. Qin, S. L. Shao, T. Wang, X. T. Yu, Y. Jiang, Z. H. Cao, Review of autonomous path planning algorithms for mobile robots, Drones, 7 (2023), 211. https://doi.org/10.3390/drones7030211 doi: 10.3390/drones7030211
[5]	O. Misir, Dynamic local path planning method based on neutrosophic set theory for a mobile robot, J. Braz. Soc. Mech. Sci. Eng., 45 (2023), 127. https://doi.org/10.1007/s40430-023-04048-6 doi: 10.1007/s40430-023-04048-6
[6]	Q. Zhang, J. Zhao, L. Pan, X. Wu, Y. Y. Hou, X. Q. Qi, Optimal path planning for mobile robots in complex environments based on the gray wolf algorithm and self-powered sensors, IEEE Sens. J., 23 (2023), 20756–20765. https://doi.org/10.1109/JSEN.2023.3252635 doi: 10.1109/JSEN.2023.3252635
[7]	L. Gao, J. Z. Zhang, J. X. Yu, X. Zhang, Z. Q. Zeng, BPA: A decentralized payment system that balances privacy and auditability, AIMS Mathematics, 9 (2024), 6183–6206. https://doi.org/10.3934/math.2024302 doi: 10.3934/math.2024302
[8]	X. M. Liu, X. H. Chang, L. W. Hou, Attack-dependent adaptive event-triggered security fuzzy control for nonlinear networked cascade control systems under deception attacks, Mathematics, 12 (2024), 3385. https://doi.org/10.3390/math12213385 doi: 10.3390/math12213385
[9]	X. He, C. Guo, Research on multi-strategy fusion of the chimpanzee optimization algorithm and its application in path planning, Appl. Sci., 15 (2025), 608. https://doi.org/10.3390/app15020608 doi: 10.3390/app15020608
[10]	B. Guo, Z. Kuang, J. H. Guan, M. T. Hu, L. X. Rao, X. Q. Sun, An improved A-star algorithm for complete coverage path planning of unmanned ships, Int. J. Pattern Recogn., 36 (2022), 2259009. https://doi.org/10.1142/S0218001422590091 doi: 10.1142/S0218001422590091
[11]	J. Jason, M. Siever, A. Valentino, K. M. Suryaningrum, R. Yunanda, Dijkstra's algorithm to find the nearest vaccine location, Procedia Computer Science, 216 (2023), 5–12. https://doi.org/10.1016/j.procs.2022.12.105 doi: 10.1016/j.procs.2022.12.105
[12]	Y. Zhang, L. L. Li, H. C. Lin, Z. W. Ma, J. Zhao, Development of path planning approach using improved a-star algorithm in AGV system, J. Internet Technol., 20 (2019), 915–924. https://doi.org/10.3966/160792642019052003023 doi: 10.3966/160792642019052003023
[13]	C. G. Liu, Q. Z. Mao, X. M. Chu, S. Xie, An improved a-star algorithm considering water current, traffic separation and berthing for vessel path planning, Appl. Sci., 9 (2019), 1057. https://doi.org/10.3390/app9061057 doi: 10.3390/app9061057
[14]	Y. Dai, W. J. Lv, S. K. Li, M. Y. Zong, Improving the Lifelong Planning A-star algorithm to satisfy path planning for space truss cellular robots with dynamic obstacles, Robotica, 43 (2025), 1243–1257. https://doi.org/10.1017/S0263574725000256 doi: 10.1017/S0263574725000256
[15]	W. Z. Li, J. J. Liu, S. L. Yao, An improved Dijkstra's algorithm for shortest path planning on 2D grid maps, 2019 IEEE 9th International Conference on Electronics Information and Emergency Communication (ICEIEC), Beijing, China, 2019,438–441. https://doi.org/10.1109/iceiec.2019.8784487
[16]	C. G. Liu, K. Zhang, Z. B. He, L. H. Lai, X. M. Chu, Clustering Theta^* based segmented path planning method for vessels in inland waterways, Ocean Eng., 309 (2024), 118249. https://doi.org/10.1016/j.oceaneng.2024.118249 doi: 10.1016/j.oceaneng.2024.118249
[17]	M. Kobayashi, N. Motoi, Local path planning: dynamic window approach with virtual manipulators considering dynamic obstacles, IEEE Access, 10 (2022), 17018–17029. https://doi.org/10.1109/ACCESS.2022.3150036 doi: 10.1109/ACCESS.2022.3150036
[18]	R. Zhou, K. Zhou, L. N. Wang, B. R. Wang, An improved dynamic window path planning algorithm using multi-algorithm fusion, Int. J. Control Autom. Syst., 22 (2024), 1005–1020. https://doi.org/10.1007/s12555-022-0495-8 doi: 10.1007/s12555-022-0495-8
[19]	M. Yao, H. G. Deng, X. Y. Feng, P. G. Li, Y. F. Li, H. Y. Liu, Improved dynamic window approach based on energy consumption management and fuzzy logic control for local path planning of mobile robots, Comput. Ind. Eng., 187 (2024), 109767. https://doi.org/10.1016/j.cie.2023.109767 doi: 10.1016/j.cie.2023.109767
[20]	J. Moon, B. Y. Lee, M. J. Tahk, A hybrid dynamic window approach for collision avoidance of VTOL UAVs, Int. J. Aeronaut. Space Sci., 19 (2018), 889–903. https://doi.org/10.1007/s42405-018-0061-z doi: 10.1007/s42405-018-0061-z
[21]	M. E. Miyombo, Y. K. Liu, C. M. Mulenga, A. Siamulonga, M. C. Kabanda, P. Shaba, et al., Optimal path planning in a real-world radioactive environment: A comparative study of A-star and Dijkstra algorithms, Nucl. Eng. Des., 420 (2024), 113039. https://doi.org/10.1016/j.nucengdes.2024.113039 doi: 10.1016/j.nucengdes.2024.113039
[22]	L. Morin, P. Gilormini, K. Derrien, Generalized euclidean distances for elasticity tensors, J. Elast., 138 (2020), 221–232. https://doi.org/10.1007/s10659-019-09741-z doi: 10.1007/s10659-019-09741-z
[23]	X. Liu, W. T. Chen, L. Peng, D. Luo, L. K. Jia, G. Xu, et al., Secure computation protocol of Chebyshev distance under the malicious model, Sci. Rep., 14 (2024), 17115. https://doi.org/10.1038/s41598-024-67907-9 doi: 10.1038/s41598-024-67907-9
[24]	C. D. Wang, J. L. Yang, B. Q. Zhang, A fault diagnosis method using improved prototypical network and weighting similarity-Manhattan distance with insufficient noisy data, Measurement, 226 (2024), 114171. https://doi.org/10.1016/j.measurement.2024.114171 doi: 10.1016/j.measurement.2024.114171
[25]	Z. B. Zeng, H. Dong, Y. L. Xu, W. Zhang, H. C. Yu, X. P. Li, Teaching-learning-based optimization algorithm with dynamic neighborhood and crossover search mechanism for numerical optimization, Appl. Soft Comput., 154 (2024), 111332. https://doi.org/10.1016/j.asoc.2024.111332 doi: 10.1016/j.asoc.2024.111332
[26]	J. Ahmad, M. Wahab, Enhancing the safety and smoothness of path planning through an integration of Dijkstra's algorithm and piecewise cubic Bezier optimization, Expert Syst. Appl., 289 (2025), 128315. https://doi.org/10.1016/j.eswa.2025.128315 doi: 10.1016/j.eswa.2025.128315
[27]	Y. D. Ji, Q. Q. Liu, C. Zhou, Z. J. Han, W. Wu, Hybrid swarm intelligence and human-inspired optimization for urban drone path planning, Biomimetics, 10 (2025), 180. https://doi.org/10.3390/biomimetics10030180 doi: 10.3390/biomimetics10030180
[28]	H. F. Bao, J. Fang, C. H. Wang, Z. B. Li, J. S. Zhang, C. S. Wang, Research on static/dynamic global path planning based on improved A^* algorithm for mobile robots, J. Robot., 2023 (2023), 5098156. https://doi.org/10.1155/2023/5098156 doi: 10.1155/2023/5098156
[29]	B. P. Wang, D. Y. Ju, F. Z. Xu, C. Feng, G.L. Xun, CAF-BRT^: A 2D path planning algorithm based on circular arc fillet method, IEEE Access*, 10 (2022), 127168–127181. https://doi.org/10.1109/ACCESS.2022.3226465 doi: 10.1109/ACCESS.2022.3226465
[30]	M. Y. Wu, E. L. M. Su, C. F. Yeong, B. Dong, W. Holderbaum, C. G. Yang, A hybrid path planning algorithm combining A^* and improved ant colony optimization with dynamic window approach for enhancing energy efficiency in warehouse environments, PeerJ Computer Science, 10 (2024), e2629. https://doi.org/10.7717/peerj-cs.2629 doi: 10.7717/peerj-cs.2629
[31]	J. T. Chen, Q. Zhou, H. R. Ren, H. Y. Li, Partition and planning: a human-like motion decision for UAV in trap environment, Sci. China Technol. Sci., 67 (2024), 1226–1237. https://doi.org/10.1007/s11431-023-2605-7 doi: 10.1007/s11431-023-2605-7
[32]	Y. H. Li, J. W. Ye, L. Gao, M. Cai, CoDAC: autonomous obstacle avoidance optimization for unmanned surface vehicle clusters via multi-modal dynamic perception and collaborative community detection, IEEE Access, 13 (2025), 134552–134569. https://doi.org/10.1109/ACCESS.2025.3593236 doi: 10.1109/ACCESS.2025.3593236
[33]	J. T. Chen, H. R. Ren, Q. Zhou, H. Y. Li, Fast unfolding-based indoor space partitioning and rapid complementary search planning for high-rise fire rescue, IEEE T. Autom. Sci. Eng., 22 (2025), 18750–18760. https://doi.org/10.1109/TASE.2025.3590419 doi: 10.1109/TASE.2025.3590419

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)