{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:55:28Z","timestamp":1759334128545,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:00:00Z","timestamp":1759190400000},"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":["52025111","52401365"],"award-info":[{"award-number":["52025111","52401365"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2024QE371"],"award-info":[{"award-number":["ZR2024QE371"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Stable Supporting Fund of National Key Laboratory of Autonomous Marine Vehicle Technology","award":["2024-HYHXQ-WDZC05"],"award-info":[{"award-number":["2024-HYHXQ-WDZC05"]}]},{"DOI":"10.13039\/501100014206","name":"National Key Laboratory Foundation","doi-asserted-by":"publisher","award":["WDZC20255290305"],"award-info":[{"award-number":["WDZC20255290305"]}],"id":[{"id":"10.13039\/501100014206","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Robotics"],"abstract":"<jats:p>To address the limited adaptability of traditional fixed-parameter strategies for hexapod robots operating in multi-material terrain environments, this study proposes a terrain-aware gait optimization method based on an improved particle swarm optimization algorithm that incorporates foot-end sinking perception. This method establishes a ground sinking detection mechanism based on foot-end position sensors, constructs a dynamic weight allocation strategy based on ground bearing capacity, and develops a Terrain-aware Ground Particle Swarm Optimization algorithm (TGPSO) that integrates Latin hypercube sampling, linearly decreasing inertia weights, and stagnation exploration mechanisms. Furthermore, it establishes a unified terrain-based reward function framework to achieve dynamic adjustment of weights for velocity, stability, and transportation efficiency. Simulink simulation verification demonstrates that TGPSO achieves superior optimization performance compared to traditional strategies across three typical terrain types, while exhibiting faster convergence speed and enhanced stability. The research findings provide theoretical foundations and technical support for intelligent motion control of hexapod robots across varying material properties, achieving targeted optimization of locomotion performance under diverse terrain conditions.<\/jats:p>","DOI":"10.3390\/robotics14100139","type":"journal-article","created":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T09:12:23Z","timestamp":1759223543000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["TGPSO: An Adaptive Gait Optimization Algorithm for Hexapod Robots in Multi-Terrain Environments"],"prefix":"10.3390","volume":"14","author":[{"given":"Guiqiang","family":"Bai","sequence":"first","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150000, China"},{"name":"National Key Laboratory of Autonomous Marine Vehicle Technology, Harbin Engineering University, Harbin 150000, China"},{"name":"Qingdao Innovation and Development Center, Harbin Engineering University, Qingdao 266000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-6356-2085","authenticated-orcid":false,"given":"Weixu","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150000, China"},{"name":"National Key Laboratory of Autonomous Marine Vehicle Technology, Harbin Engineering University, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-4079-6492","authenticated-orcid":false,"given":"Jingang","family":"Du","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150000, China"},{"name":"National Key Laboratory of Autonomous Marine Vehicle Technology, Harbin Engineering University, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150000, China"},{"name":"National Key Laboratory of Autonomous Marine Vehicle Technology, Harbin Engineering University, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanting","family":"Luo","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Equipment State Sensing and Smart Support, National University of Defense Technology, Changsha 410073, China"},{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongde","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.robot.2017.05.007","article-title":"Gait and Trajectory Rolling Planning and Control of Hexapod Robots for Disaster Rescue Applications","volume":"95","author":"Deng","year":"2017","journal-title":"Robot. Auton. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jadeja, R., Trivedi, T., and Surve, J. (2024). Survivor Detection Approach for Post Earthquake Search and Rescue Missions Based on Deep Learning Inspired Algorithms. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-75156-z"},{"key":"ref_3","unstructured":"Lee, S., Azhari, M.B., Kang, G., G\u00fcnes, O., Han, D., and Shim, D.H. (2024). A Collaborative Team of UAV-Hexapod for an Autonomous Retrieval System in GNSS-Denied Maritime Environments. arXiv."},{"key":"ref_4","unstructured":"Kuo, L.S., Lin, Y., Sheng, V.S., Kuo, L.S., and Jheng, S.J. (2008). Development an Intelligent Power Detection System for Mobile Robots. Proceedings of the 2008 27th Chinese Control Conference, Kunming, China, 16-18 July 2008, IEEE."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/s11370-023-00508-z","article-title":"Autonomous Gait Switching Method and Experiments of a Hexapod Walking Robot for Mars Environment with Multiple Terrains","volume":"17","author":"Chen","year":"2024","journal-title":"Intel. Serv. Robot."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Guo, Y.-Q., Luo, W.-H., Xu, Z.-D., Shu, B.-M., and Yang, D.-K. (2023). Research on the Design and Gait Planning of a Hexapod Robot Based on Improved Triangular Gait for Lunar Exploration. Appl. Sci., 14.","DOI":"10.3390\/app14010260"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Coelho, J., Ribeiro, F., Dias, B., Lopes, G., and Flores, P. (2021). Trends in the Control of Hexapod Robots: A Survey. Robotics, 10.","DOI":"10.3390\/robotics10030100"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Roennau, A., Heppner, G., Nowicki, M., and Dillmann, R. (2014, January 8\u201311). LAURON V: A Versatile Six-Legged Walking Robot with Advanced Maneuverability. Proceedings of the 2014 IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, Besacon, France.","DOI":"10.1109\/AIM.2014.6878051"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"129328","DOI":"10.1016\/j.neucom.2024.129328","article-title":"Enhancing Hexapod Robot Mobility on Challenging Terrains: Optimizing CPG-Generated Gait with Reinforcement Learning","volume":"622","author":"Huang","year":"2025","journal-title":"Neurocomputing"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ouyang, W., Chi, H., Pang, J., Liang, W., and Ren, Q. (2021). Adaptive Locomotion Control of a Hexapod Robot via Bio-Inspired Learning. Front. Neurorobot., 15.","DOI":"10.3389\/fnbot.2021.627157"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1186\/s10033-024-01000-0","article-title":"Smart Gait: A Gait Optimization Framework for Hexapod Robots","volume":"37","author":"Yin","year":"2024","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, Z., He, W., Wu, F., Quesada, L., and Xiang, L. (2024). Development of a Bionic Hexapod Robot with Adaptive Gait and Clearance for Enhanced Agricultural Field Scouting. Front. Robot. AI, 11.","DOI":"10.3389\/frobt.2024.1426269"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Liu, Y., Fan, X., Ding, L., Wang, J., Liu, T., and Gao, H. (2020). Fault-Tolerant Tripod Gait Planning and Verification of a Hexapod Robot. Appl. Sci., 10.","DOI":"10.3390\/app10082959"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sun, Y., Zong, C., Pancheri, F., Chen, T., and Lueth, T.C. (2023). Design of Topology Optimized Compliant Legs for Bio-Inspired Quadruped Robots. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-32106-5"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, L., Li, R., Wang, X., Gao, W., and Chen, Y. (2025). A Motion Control Strategy for a Blind Hexapod Robot Based on Reinforcement Learning and Central Pattern Generator. Symmetry, 17.","DOI":"10.3390\/sym17071058"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s11370-020-00340-9","article-title":"A Hybrid Tactile Sensor-Based Obstacle Overcoming Method for Hexapod Walking Robots","volume":"14","author":"Luneckas","year":"2021","journal-title":"Intel. Serv. Robot."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"8091","DOI":"10.1007\/s11042-020-10139-6","article-title":"A Review on Genetic Algorithm: Past, Present, and Future","volume":"80","author":"Katoch","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"15522","DOI":"10.1039\/D4SC02934H","article-title":"Augmenting Genetic Algorithms with Machine Learning for Inverse Molecular Design","volume":"15","author":"Kneiding","year":"2024","journal-title":"Chem. Sci."},{"key":"ref_19","unstructured":"Shi, Y., and Eberhart, R. (1998, January 4\u20139). A Modified Particle Swarm Optimizer. Proceedings of the 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), Anchorage, AK, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1007\/s10033-017-0110-8","article-title":"Energy Expenditure of Trotting Gait Under Different Gait Parameters","volume":"30","author":"Chen","year":"2017","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Tao, C., Xue, J., Zhang, Z., Cao, F., Li, C., and Gao, H. (2021). Gait Optimization Method for Humanoid Robots Based on Parallel Comprehensive Learning Particle Swarm Optimizer Algorithm. Front. Neurorobot., 14.","DOI":"10.3389\/fnbot.2020.600885"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Walas, K., Schmidt, A., Kraft, M., and Fularz, M. (2013, January 3\u20135). Hardware Implementation of Ground Classification for a Walking Robot. Proceedings of the 9th International Workshop on Robot Motion and Control, Kuslin, Poland.","DOI":"10.1109\/RoMoCo.2013.6614594"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10514-006-7230-9","article-title":"Visual Wheel Sinkage Measurement for Planetary Rover Mobility Characterization","volume":"21","author":"Brooks","year":"2006","journal-title":"Auton. Robot."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1177\/02783640122067570","article-title":"RHex: A Simple and Highly Mobile Hexapod Robot","volume":"20","author":"Saranli","year":"2001","journal-title":"Int. J. Robot. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"eade2256","DOI":"10.1126\/scirobotics.ade2256","article-title":"Learning Quadrupedal Locomotion on Deformable Terrain","volume":"8","author":"Choi","year":"2023","journal-title":"Sci. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.jterra.2020.12.002","article-title":"Recurrent and Convolutional Neural Networks for Deep Terrain Classification by Autonomous Robots","volume":"96","author":"Vulpi","year":"2021","journal-title":"J. Terramechanics"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Vangen, A., Barnwal, T., Olsen, J.A., and Alexis, K. (2023, January 5). Terrain Recognition and Contact Force Estimation Through a Sensorized Paw for Legged Robots. Proceedings of the 2023 21st International Conference on Advanced Robotics (ICAR), Abu Dhabi, United Arab Emirates.","DOI":"10.1109\/ICAR58858.2023.10407030"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Johnson, K.L. (1985). Contact Mechanics, Cambridge University Press.","DOI":"10.1017\/CBO9781139171731"},{"key":"ref_29","unstructured":"Inman, D.J. (2014). Engineering Vibration, Pearson. [4th ed.]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1177\/0278364913498122","article-title":"Foot\u2013Terrain Interaction Mechanics for Legged Robots: Modeling and Experimental Validation","volume":"32","author":"Ding","year":"2013","journal-title":"Int. J. Robot. Res."},{"key":"ref_31","first-page":"14","article-title":"Research and Analysis on Energy Consumption of Underwater Hexapod Robot Based on Typical Gait","volume":"Volume 13015","author":"Liu","year":"2021","journal-title":"Intelligent Robotics and Applications"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Brodoline, I., Sauvageot, E., Viollet, S., and Serres, J.R. (2024). Shaping the Energy Curves of a Servomotor-Based Hexapod Robot. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-62184-y"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Luneckas, M., Luneckas, T., Kriau\u010di\u016bnas, J., Udris, D., Plonis, D., Dama\u0161evi\u010dius, R., and Maskeli\u016bnas, R. (2021). Hexapod Robot Gait Switching for Energy Consumption and Cost of Transport Management Using Heuristic Algorithms. Appl. Sci., 11.","DOI":"10.3390\/app11031339"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey Wolf Optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"162059","DOI":"10.1109\/ACCESS.2021.3133286","article-title":"Northern Goshawk Optimization: A New Swarm-Based Algorithm for Solving Optimization Problems","volume":"9","author":"Dehghani","year":"2021","journal-title":"IEEE Access"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/10\/139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T09:55:24Z","timestamp":1759226124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/10\/139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,30]]},"references-count":35,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["robotics14100139"],"URL":"https:\/\/doi.org\/10.3390\/robotics14100139","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2025,9,30]]}}}