{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:16Z","timestamp":1760060416916,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T00:00:00Z","timestamp":1756252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52402505","QN2024254","A202504"],"award-info":[{"award-number":["52402505","QN2024254","A202504"]}]},{"name":"Science and Technology Project of Hebei Education Department","award":["52402505","QN2024254","A202504"],"award-info":[{"award-number":["52402505","QN2024254","A202504"]}]},{"name":"National Engineering Research Center for Water Transport Safety","award":["52402505","QN2024254","A202504"],"award-info":[{"award-number":["52402505","QN2024254","A202504"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The widespread application of unmanned vehicles in logistics distribution and special transportation has made improving trajectory tracking accuracy and dynamic adaptability critical for operational efficiency. This article proposes a biologically inspired combination control strategy based on the Deep Deterministic Policy Gradient (DDPG) algorithm, enhanced by the Crayfish Optimization Algorithm (COA) to address limitations in generalization and dynamic adaptability. The proposed DDPG-COA controller embodies a symmetrical structure: DDPG acts as the primary controller for global trajectory tracking, while COA serves as a compensatory regulator, dynamically optimizing actions through a disturbance observation mechanism. This symmetrical balance between learning-based control (DDPG) and bio-inspired optimization (COA) ensures robust performance in complex scenarios. Experiments on symmetrical trajectories demonstrated significant improvements, with the average tracking errors reduced by 56.3 percent, 71.6 percent, and 74.6 percent, respectively. The results highlight how symmetry in control architecture and trajectory design synergistically enhances precision and adaptability for unmanned systems.<\/jats:p>","DOI":"10.3390\/sym17091396","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T09:14:05Z","timestamp":1756286045000},"page":"1396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Autonomous Vehicle Trajectory Tracking Control Based on Deep Deterministic Policy Gradient Algorithm and Crayfish Optimization Algorithm"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5485-1076","authenticated-orcid":false,"given":"Le","family":"Wang","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"},{"name":"Hebei Key Laboratory of Traffic Safety and Control, Shijiazhuang 050043, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-5223-9838","authenticated-orcid":false,"given":"Hongrui","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0537-6149","authenticated-orcid":false,"given":"Qingyang","family":"Su","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}]},{"given":"Yang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,27]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Feh\u00e9r, \u00c1., Aradi, S., Heged\u00fcs, F., B\u00e9csi, T., and G\u00e1sp\u00e1r, P. (2019, January 29\u201331). Hybrid DDPG approach for vehicle motion planning. Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics, Prague, Czech Republic.","key":"ref_1","DOI":"10.5220\/0007955504220429"},{"unstructured":"(China Transport News, 2024). 2023 Statistical Bulletin on the Development of the Transportation Industry\u2014Technical Report, China Transport News.","key":"ref_2"},{"key":"ref_3","first-page":"1","article-title":"Overview of Big Data and Cloud Control Technologies in the Field of Unmanned Ground Vehicles","volume":"41","author":"Ni","year":"2021","journal-title":"Sch. Mech. Eng. Inst. Technol."},{"key":"ref_4","first-page":"64","article-title":"A Study on Unmanned Intelligent Means of Transportation","volume":"1","author":"Zhang","year":"2022","journal-title":"Army Mil. Transp. Univ."},{"doi-asserted-by":"crossref","unstructured":"Zhao, Z. (2024). Trajectory Tracking of Unmanned Logistics Vehicle Based on Event-Triggered and Adaptive Optimization Parameters MPC. Processes, 12.","key":"ref_5","DOI":"10.3390\/pr12091878"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"69","DOI":"10.5391\/IJFIS.2022.22.1.69","article-title":"Trajectory-tracking control of a transport robot for smart logistics using the fuzzy controller","volume":"22","author":"Ryoo","year":"2022","journal-title":"Int. J. Fuzzy Log. Intell. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"221","DOI":"10.4271\/10-07-02-0014","article-title":"A survey of intelligent driving vehicle trajectory tracking based on vehicle dynamics","volume":"7","author":"Zha","year":"2023","journal-title":"SAE Int. J. Veh. Dyn. Stab. NVH"},{"unstructured":"Lei, M. (2017). Study on Lateral, Longitudinal andIntegrated Control Strategy of IntelligentVehicles Based on Dynamic Model. [Master\u2019s Thesis, Chongqing Jiaotong University].","key":"ref_8"},{"key":"ref_9","first-page":"3846","article-title":"Development of Intelligent Control Technology for Unmanned Vehicle","volume":"22","author":"Qian","year":"2022","journal-title":"Sci. Technol. Eng."},{"doi-asserted-by":"crossref","unstructured":"Chen, Y., Gai, J., He, S., Li, H., Cheng, C., and Zou, W. (2024). MPC-TD3 Trajectory Tracking Control for Electrically Driven Unmanned Tracked Vehicles. Electronics, 13.","key":"ref_10","DOI":"10.3390\/electronics13183747"},{"key":"ref_11","first-page":"72","article-title":"Research on lane change trajectory and tracking control of unmanned vehicle","volume":"38","author":"Ding","year":"2024","journal-title":"J. Chongqing Univ. Technol. Sci."},{"key":"ref_12","first-page":"257","article-title":"A Way-Point Tracking of Hovering AUV by PID Control","volume":"10","author":"Kim","year":"2015","journal-title":"IEMEK J. Embed. Syst. Appl."},{"doi-asserted-by":"crossref","unstructured":"Luo, Z., and Zheng, Y. (2024). Analyzing the Impact of Wind on Trajectory Tracking for Unmanned Vehicles Based on Road Adhesion Coefficient Estimation. Processes, 13.","key":"ref_13","DOI":"10.3390\/pr13010052"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1109\/TCST.2013.2281936","article-title":"A trajectory tracking robust controller of surface vessels with disturbance uncertainties","volume":"22","author":"Yang","year":"2013","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_15","first-page":"877","article-title":"Design and Simulation of Intelligent Vehicle Trajectory Tracking Control Algorithm Based on LQR and PID","volume":"53","author":"Xu","year":"2022","journal-title":"J. Taiyuan Univ. Technol."},{"key":"ref_16","first-page":"153","article-title":"Intelligent Vehicle Path Tracking Based on Lateral and Longitudinal Integrated Control","volume":"42","author":"Zhang","year":"2023","journal-title":"J. Chongqing Jiaotong Univ. Sci."},{"doi-asserted-by":"crossref","unstructured":"Jin, M., Li, J., and Chen, T. (2024). Method for the Trajectory Tracking Control of Unmanned Ground Vehicles Based on Chaotic Particle Swarm Optimization and Model Predictive Control. Symmetry, 16.","key":"ref_17","DOI":"10.3390\/sym16060708"},{"doi-asserted-by":"crossref","unstructured":"Wei, Z., Sun, T., and Zhou, M. (2024). LIRL: Latent Imagination-Based Reinforcement Learning for Efficient Coverage Path Planning. Symmetry, 16.","key":"ref_18","DOI":"10.3390\/sym16111537"},{"key":"ref_19","first-page":"68","article-title":"Anti Collision Control Strategy of Unmanned Vehicle Based on DDPG Algorithm","volume":"43","author":"Lai","year":"2021","journal-title":"J. Wuhan Univ. Technol."},{"key":"ref_20","first-page":"335","article-title":"Trajectory Tracking Control of Intelligent Vehicle Based on DDPG Method of Reinforcement Learning","volume":"34","author":"He","year":"2021","journal-title":"China J. Highw. Transp."},{"key":"ref_21","first-page":"1","article-title":"Hierarchical Decision-Making For UAV Air Combat Based on DDQN-D3PG","volume":"279","author":"Wang","year":"2025","journal-title":"Acta Armamentarii"},{"key":"ref_22","first-page":"18","article-title":"Path Tracking Control of Rice Pollination Robot Based on DDPG+MPC","volume":"47","author":"Wen","year":"2025","journal-title":"J. Agric. Mech. Res."},{"key":"ref_23","first-page":"259","article-title":"Trajectory tracking control of intelligent vehicles based on deep reinforcement learning and rolling horizon optimization","volume":"24","author":"Xie","year":"2024","journal-title":"J. Traffic Transp. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e13076","DOI":"10.1111\/exsy.13076","article-title":"Combining reinforcement learning and conventional control to improve automatic guided vehicles tracking of complex trajectories","volume":"41","author":"Santos","year":"2024","journal-title":"Expert Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6962","DOI":"10.1109\/TSMC.2020.2966631","article-title":"Multi-kernel online reinforcement learning for path tracking control of intelligent vehicles","volume":"51","author":"Liu","year":"2020","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.1109\/TCYB.2017.2667680","article-title":"Adaptive neural control of uncertain nonlinear systems using disturbance observer","volume":"47","author":"Chen","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1109\/TMECH.2021.3051835","article-title":"Event-triggered-based discrete-time neural control for a quadrotor UAV using disturbance observer","volume":"26","author":"Shao","year":"2021","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1007\/s10462-023-10567-4","article-title":"Crayfish optimization algorithm","volume":"56","author":"Jia","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10462-024-10738-x","article-title":"Modified crayfish optimization algorithm for solving multiple engineering application problems","volume":"57","author":"Jia","year":"2024","journal-title":"Artif. Intell. Rev."},{"doi-asserted-by":"crossref","unstructured":"Elhosseny, M., Abdel-Salam, M., and El-Hasnony, I.M. (2025). Adaptive dynamic crayfish algorithm with multi-enhanced strategy for global high-dimensional optimization and real-engineering problems. Sci. Rep., 15.","key":"ref_30","DOI":"10.1038\/s41598-024-81144-0"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"28621","DOI":"10.1109\/ACCESS.2024.3366495","article-title":"BinCOA: An efficient binary crayfish optimization algorithm for feature selection","volume":"12","author":"Shikoun","year":"2024","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.procs.2018.01.054","article-title":"Grid Path Planning with Deep Reinforcement Learning: Preliminary Results","volume":"123","author":"Panov","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_33","first-page":"128","article-title":"The Path Planning for Unmanned Ship Based on the Prioritized Experience Replay of Deep Q-networks","volume":"126","author":"Wen","year":"2020","journal-title":"Basic Clin. Pharmacol. Toxicol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s42154-023-00281-w","article-title":"Double Deep Q-Networks Based Game-Theoretic Equilibrium Control of Automated Vehicles at Autonomous Intersection","volume":"7","author":"Hu","year":"2024","journal-title":"Automot. Innov."},{"key":"ref_35","first-page":"3089","article-title":"Improved particle swarm optimization algorithm for mobile robot path planning","volume":"38","author":"Hu","year":"2021","journal-title":"Appl. Res. Comput."},{"key":"ref_36","first-page":"30","article-title":"Comprehensive Review of Grey Wolf Optimization Algorithm","volume":"46","author":"Zhang","year":"2019","journal-title":"Comput. Sci."},{"key":"ref_37","first-page":"49","article-title":"Path Planning of Mobile Robot Based on TGWO Algorithm","volume":"56","author":"Liu","year":"2022","journal-title":"J. Xi\u2019an Jiaotong Univ."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/9\/1396\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:33:33Z","timestamp":1760034813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/9\/1396"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,27]]},"references-count":37,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["sym17091396"],"URL":"https:\/\/doi.org\/10.3390\/sym17091396","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,8,27]]}}}