{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T18:18:06Z","timestamp":1789669086467,"version":"4.0.1"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T00:00:00Z","timestamp":1765324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42502223"],"award-info":[{"award-number":["42502223"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013142","name":"Key research and development project of Hainan province","doi-asserted-by":"crossref","award":["ZDYF2024GXJS025"],"award-info":[{"award-number":["ZDYF2024GXJS025"]}],"id":[{"id":"10.13039\/501100013142","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Independent Innovation Fund of Tianjin University-Hainan University","award":["XJ2300003470"],"award-info":[{"award-number":["XJ2300003470"]}]},{"name":"Research Startup Fund of Hainan University","award":["RZ2300002747"],"award-info":[{"award-number":["RZ2300002747"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>Snake-like robots, characterized by their high flexibility and multi-joint structure, exhibit exceptional adaptability to complex terrains such as snowfields, jungles, deserts, and underwater environments. Their ability to navigate narrow spaces and circumvent obstacles makes them ideal for operations in confined or rugged environments. However, efficient motion in such conditions requires not only mechanical flexibility but also effective path planning to ensure safety, energy efficiency, and overall task performance. Most existing path planning algorithms for snake-like robots focus primarily on finding the shortest path between the start and target positions while neglecting the optimization of energy consumption during real operations. To address this limitation, this study proposes an energy-efficient path planning method based on an improved A* algorithm enhanced with deep reinforcement learning: Dueling Double-Deep Q-Network (D3QN). An Energy Consumption Estimation Model (ECEM) is first developed to evaluate the energetic cost of snake robot motion in three-dimensional space. This model is then integrated into a new heuristic function to guide the A* search toward energy-optimal trajectories. Simulation experiments were conducted in a 3D environment to assess the performance of the proposed approach. The results demonstrate that the improved A* algorithm effectively reduces the energy consumption of the snake robot compared with conventional algorithms. Specifically, the proposed method achieves an energy consumption of 68.79 J, which is 3.39%, 27.26%, and 5.91% lower than that of the traditional A* algorithm (71.20 J), the bidirectional A* algorithm (94.61 J), and the weighted improved A* algorithm (73.11 J), respectively. These findings confirm that integrating deep reinforcement learning with an adaptive heuristic function significantly enhances both the energy efficiency and practical applicability of snake robot path planning in complex 3D environments.<\/jats:p>","DOI":"10.3390\/biomimetics10120826","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T16:11:18Z","timestamp":1765383078000},"page":"826","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Energy-Efficient Path Planning for Snake Robots Using a Deep Reinforcement Learning-Enhanced A* Algorithm"],"prefix":"10.3390","volume":"10","author":[{"given":"Yang","family":"Gu","sequence":"first","affiliation":[{"name":"School of Information and Communication Engineering, Hainan University, Haikou 570228, China"},{"name":"State Key Laboratory of Marine Resources Utilization in South China Sea, Hainan University, Haikou 570228, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zelin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Hainan University, Haikou 570228, China"},{"name":"State Key Laboratory of Marine Resources Utilization in South China Sea, Hainan University, Haikou 570228, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1263-9464","authenticated-orcid":false,"given":"Zhong","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Hainan University, Haikou 570228, China"},{"name":"State Key Laboratory of Marine Resources Utilization in South China Sea, Hainan University, Haikou 570228, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ge, H., Ying, Z., Chen, Z., Zu, W., Liu, C., and Jin, Y. (2023). Improved A* algorithm for path planning of spherical robot considering energy consumption. Sensors, 23.","DOI":"10.3390\/s23167115"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, B., Dong, C., Chen, Q., Mu, Y., Fan, Z., Wang, Q., and Chen, X. (2020, January 2\u20134). Path planning of mobile robots based on an improved A* algorithm. Proceedings of the 2020 4th High Performance Computing and Cluster Technologies Conference & 2020 3rd International Conference on Big Data and Artificial Intelligence, New York City, NY, USA.","DOI":"10.1145\/3409501.3409524"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cui, J. (2024, January 18\u201319). Optimization of Spinal Surgery Robot Path Planning Using Deep Reinforcement Learning. Proceedings of the 2024 First International Conference on Software, Systems and Information Technology, Tumkur, India.","DOI":"10.1109\/SSITCON62437.2024.10797118"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"119","DOI":"10.3901\/JME.2004.10.119","article-title":"Study on turning and sidewise motion of a snake-like robot","volume":"40","author":"Ye","year":"2004","journal-title":"J. Mech. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.measurement.2015.04.021","article-title":"Development of an obstacle-avoidance algorithm for snake-like robots","volume":"73","year":"2015","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Rykkje, T.R., and Impelluso, T.J. (2024). A Kinematic Variable for Analyzing Snake Robot Dynamics. AI Comput. Sci. Robot. Technol.","DOI":"10.5772\/acrt.32"},{"key":"ref_7","unstructured":"Zhang, F., Gu, C., and Yang, F. (2020, January 23\u201325). An improved algorithm of robot path planning in complex environment based on Double DQN. Proceedings of the Advances in Guidance, Navigation and Control: Proceedings of 2020 International Conference on Guidance, Navigation and Control, ICGNC 2020, Tianjin, China."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hanssen, K.G., Transeth, A.A., Sanfilippo, F., Liljeb\u00e4ck, P., and Stavdahl, \u00d8 (2020, January 14\u201316). Path planning for perception-driven obstacle-aided snake robot locomotion. Proceedings of the 2020 IEEE 16th International Workshop on Advanced Motion Control (AMC), Kristiansand, Norway.","DOI":"10.1109\/AMC44022.2020.9244366"},{"key":"ref_9","unstructured":"Keselman, A., Ten, S., Ghazali, A., and Jubeh, M. (2018). Reinforcement learning with a* and a deep heuristic. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1163\/156855395X00193","article-title":"Sensor-based motion planning in three dimensions for a highly redundant snake robot","volume":"9","author":"Reznik","year":"1994","journal-title":"Adv. Robot."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kabir, R., Watanobe, Y., Islam, M.R., and Naruse, K. (2024). Enhanced Robot Motion Block of A-Star Algorithm for Robotic Path Planning. Sensors, 24.","DOI":"10.3390\/s24051422"},{"key":"ref_12","unstructured":"Mudiyanselage, H., and Herath, K.P. (2020). Design, Realization and Control of an Aquatic Snake Robot, Politecnico di Milano."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11929","DOI":"10.1109\/TII.2023.3254534","article-title":"Anti-disturbance path-following control for snake robots with spiral motion","volume":"19","author":"Li","year":"2023","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_14","unstructured":"Quinones-Ramirez, M., Rios-Martinez, J., and Uc-Cetina, V. (2023). Robot path planning using deep reinforcement learning. arXiv."},{"key":"ref_15","first-page":"18","article-title":"Practical search techniques in path planning for autonomous driving","volume":"1001","author":"Dolgov","year":"2008","journal-title":"Ann Arbor"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Yin, Y., Chen, Z., Liu, G., and Guo, J. (2023). A mapless local path planning approach using deep reinforcement learning framework. Sensors, 23.","DOI":"10.3390\/s23042036"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7664","DOI":"10.1109\/ACCESS.2021.3139534","article-title":"Quality-oriented hybrid path planning based on A* and Q-learning for unmanned aerial vehicle","volume":"10","author":"Li","year":"2021","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1007\/s12652-019-01531-8","article-title":"An improved ant colony optimization algorithm based on particle swarm optimization algorithm for path planning of autonomous underwater vehicle","volume":"11","author":"Che","year":"2020","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"041013","DOI":"10.1115\/1.4043683","article-title":"Modeling and mechanical analysis of snake robots on cylinders","volume":"11","author":"Tang","year":"2019","journal-title":"J. Mech. Robot."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6962","DOI":"10.1109\/JSEN.2020.3039275","article-title":"Mobile robot path planning based on improved localized particle swarm optimization","volume":"21","author":"Zhang","year":"2020","journal-title":"IEEE Sens. 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