{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T21:32:19Z","timestamp":1781731939232,"version":"3.54.5"},"reference-count":53,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T00:00:00Z","timestamp":1685145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technology of China","award":["2018AAA0101301"],"award-info":[{"award-number":["2018AAA0101301"]}]},{"name":"Ministry of Science and Technology of China","award":["2019KZDZX1011"],"award-info":[{"award-number":["2019KZDZX1011"]}]},{"name":"Ministry of Science and Technology of China","award":["20211800904722"],"award-info":[{"award-number":["20211800904722"]}]},{"name":"Ministry of Science and Technology of China","award":["20221800500052"],"award-info":[{"award-number":["20221800500052"]}]},{"name":"Key Projects of Artificial Intelligence of High School in Guangdong Province","award":["2018AAA0101301"],"award-info":[{"award-number":["2018AAA0101301"]}]},{"name":"Key Projects of Artificial Intelligence of High School in Guangdong Province","award":["2019KZDZX1011"],"award-info":[{"award-number":["2019KZDZX1011"]}]},{"name":"Key Projects of Artificial Intelligence of High School in Guangdong Province","award":["20211800904722"],"award-info":[{"award-number":["20211800904722"]}]},{"name":"Key Projects of Artificial Intelligence of High School in Guangdong Province","award":["20221800500052"],"award-info":[{"award-number":["20221800500052"]}]},{"name":"Dongguan Social Development Science and Technology Project","award":["2018AAA0101301"],"award-info":[{"award-number":["2018AAA0101301"]}]},{"name":"Dongguan Social Development Science and Technology Project","award":["2019KZDZX1011"],"award-info":[{"award-number":["2019KZDZX1011"]}]},{"name":"Dongguan Social Development Science and Technology Project","award":["20211800904722"],"award-info":[{"award-number":["20211800904722"]}]},{"name":"Dongguan Social Development Science and Technology Project","award":["20221800500052"],"award-info":[{"award-number":["20221800500052"]}]},{"name":"Dongguan Science and Technology Special Commissioner Project","award":["2018AAA0101301"],"award-info":[{"award-number":["2018AAA0101301"]}]},{"name":"Dongguan Science and Technology Special Commissioner Project","award":["2019KZDZX1011"],"award-info":[{"award-number":["2019KZDZX1011"]}]},{"name":"Dongguan Science and Technology Special Commissioner Project","award":["20211800904722"],"award-info":[{"award-number":["20211800904722"]}]},{"name":"Dongguan Science and Technology Special Commissioner Project","award":["20221800500052"],"award-info":[{"award-number":["20221800500052"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Path planning is an important area of mobile robot research, and the ant colony optimization algorithm is essential for analyzing path planning. However, the current ant colony optimization algorithm applied to the path planning of mobile robots still has some limitations, including early blind search, slow convergence speed, and more turns. To overcome these problems, an improved ant colony optimization algorithm is proposed in this paper. In the improved algorithm, we introduce the idea of triangle inequality and a pseudo-random state transfer strategy to enhance the guidance of target points and improve the search efficiency and quality of the algorithm. In addition, we propose a pheromone update strategy based on the partition method with upper and lower limits on the pheromone concentration. This can not only improve the global search capability and convergence speed of the algorithm but also avoid the premature and stagnation phenomenon of the algorithm during the search. To prevent the ants from getting into a deadlock state, we introduce a backtracking mechanism to enable the ants to explore the solution space better. Finally, to verify the effectiveness of the proposed algorithm, the algorithm is compared with 11 existing methods for solving the robot path planning problem, including several ACO variants and two commonly used algorithms (A* algorithm and Dijkstra algorithm), and the experimental results show that the improved ACO algorithm can plan paths with faster convergence, shorter path lengths, and higher smoothness. Specifically, the algorithm produces the shortest path length with a standard deviation of zero while ensuring the most rapid convergence and the highest smoothness in the case of the shortest path in four different grid environments. These experimental results demonstrate the effectiveness of the proposed algorithm in path planning.<\/jats:p>","DOI":"10.3390\/axioms12060525","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:18:43Z","timestamp":1685204323000},"page":"525","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Application of Ant Colony Optimization Algorithm Based on Triangle Inequality Principle and Partition Method Strategy in Robot Path Planning"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-5824-6846","authenticated-orcid":false,"given":"Shuai","family":"Wu","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingxia","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer and Information, Dongguan City College, Dongguan 523419, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0881-459X","authenticated-orcid":false,"given":"Wenhong","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1016\/j.procs.2018.07.076","article-title":"Obstacle avoidance and navigation planning of a wheeled mobile robot using amended artificial potential field method","volume":"133","author":"Sudhakara","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.asoc.2017.03.035","article-title":"Mobile robot path planning with surrounding point set and path improvement","volume":"57","author":"Han","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"955179","DOI":"10.3389\/fnbot.2022.955179","article-title":"Research on smooth path planning method based on improved ant colony algorithm optimized by Floyd algorithm","volume":"16","author":"Wang","year":"2022","journal-title":"Front. Neurorobot."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A note on two problems in connexion with graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_5","first-page":"5939","article-title":"Improved Dijkstra Algorithm for Mobile Robot Path Planning and Obstacle Avoidance","volume":"72","author":"Alshammrei","year":"2022","journal-title":"Comput. Mater. Contin."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10846-019-01112-z","article-title":"Hybrid Path Planning Based on Safe A* Algorithm and Adaptive Window Approach for Mobile Robot in Large-Scale Dynamic Environment","volume":"99","author":"Zhong","year":"2020","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1049\/el.2020.1895","article-title":"Solving path planning problem based on logistic beetle algorithm search-pigeon-inspired optimisation algorithm","volume":"56","author":"Liu","year":"2022","journal-title":"Electron. Lett."},{"key":"ref_8","first-page":"662","article-title":"UAV indoor path planning based on improved D* algorithm","volume":"14","author":"Zhang","year":"2019","journal-title":"CAAI Trans. Intell. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"161920","DOI":"10.1109\/ACCESS.2020.3021073","article-title":"Research and Optimization of D-Start Lite Algorithm in Track Planning","volume":"8","author":"Xie","year":"2020","journal-title":"IEEE Access"},{"key":"ref_10","first-page":"123","article-title":"UAV Track Planning of Electric Tower Pole Inspection Based on Improved Artificial Potential Field Method","volume":"24","author":"Jiang","year":"2021","journal-title":"J. Appl. Sci. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1108\/IR-06-2021-0120","article-title":"Mechanical arm obstacle avoidance path planning based on improved artificial potential field method","volume":"49","author":"Xu","year":"2022","journal-title":"Ind. Robot"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1108\/AA-11-2015-094","article-title":"A new genetic algorithm approach to smooth path planning for mobile robots","volume":"36","author":"Song","year":"2016","journal-title":"Assem. Autom."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6177","DOI":"10.1007\/s12652-019-01635-1","article-title":"Path planning and control of soccer robot based on genetic algorithm","volume":"11","author":"Chen","year":"2020","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1017\/S026357472200114X","article-title":"Path planning for spot welding robots based on improved ant colony algorithm","volume":"41","author":"Tan","year":"2023","journal-title":"Robotica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6756","DOI":"10.3934\/mbe.2020352","article-title":"Application of improved ant colony optimization in mobile robot trajectory planning","volume":"17","author":"Li","year":"2020","journal-title":"Math. Biosci. Eng."},{"key":"ref_16","first-page":"1397","article-title":"Multi-Robots Global Path Planning Based on PSO Algorithm and Cubic Spline","volume":"29","author":"Qiang","year":"2017","journal-title":"J. Syst. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.neucom.2021.12.016","article-title":"A new approach to smooth path planning of mobile robot based on quartic Bezier transition curve and improved PSO algorithm","volume":"473","author":"Xu","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"89400","DOI":"10.1109\/ACCESS.2021.3090776","article-title":"Path Planning of UAV Based on Improved Adaptive Grey Wolf Optimization Algorithm","volume":"9","author":"Zhang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"121944","DOI":"10.1109\/ACCESS.2021.3108973","article-title":"An Improved Grey Wolf Optimization Algorithm and its Application in Path Planning","volume":"9","author":"Liu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_20","first-page":"303","article-title":"Path Planning of Mobile Robot Based on Improved Obstacle Avoidance Strategy and Double Optimization Ant Colony Algorithm","volume":"53","author":"Hao","year":"2022","journal-title":"Trans. Chin. Soc. Agric. Mach."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1007\/s00521-019-04172-2","article-title":"Research on path planning of mobile robot based on improved ant colony algorithm","volume":"32","author":"Luo","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5829","DOI":"10.1007\/s00500-016-2161-7","article-title":"An improved ant colony algorithm for robot path planning","volume":"21","author":"Liu","year":"2017","journal-title":"Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Akka, K., and Khaber, F. (2018). Mobile robot path planning using an improved ant colony optimization. Int. J. Adv. Robot. Syst., 15.","DOI":"10.1177\/1729881418774673"},{"key":"ref_24","first-page":"219","article-title":"Path Planning Based on Improved Ant Colony Algorithm with Multiple Inspired Factor","volume":"55","author":"Li","year":"2019","journal-title":"Comput. Eng. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5329","DOI":"10.3233\/JIFS-189018","article-title":"Path planning of mobile robot based on adaptive ant colony algorithm","volume":"39","author":"Zheng","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_26","first-page":"142","article-title":"Path planning for mobile robots based on improved ant colony algorithm","volume":"40","author":"Gao","year":"2022","journal-title":"Transducer Microsyst. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107230","DOI":"10.1016\/j.cie.2021.107230","article-title":"Path planning optimization of indoor mobile robot based on adaptive ant colony algorithm","volume":"156","author":"Miao","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24933","DOI":"10.1109\/ACCESS.2021.3056651","article-title":"An Adaptive Improved Ant Colony System Based on Population Information Entropy for Path Planning of Mobile Robot","volume":"9","author":"Zhang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_29","first-page":"764","article-title":"Improvement of ant colony algorithm in group teaching and its application in robot path planning","volume":"17","author":"Pu","year":"2022","journal-title":"CAAI Trans. Intell. Syst."},{"key":"ref_30","first-page":"287","article-title":"Improved Ant Colony Algorithm for Mobile Robot Path Planning","volume":"58","author":"Tang","year":"2022","journal-title":"Comput. Eng. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1177\/0020294020909129","article-title":"Path planning for unmanned wheeled robot based on improved ant colony optimization","volume":"53","author":"Wang","year":"2020","journal-title":"Meas. Control"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"236","DOI":"10.3103\/S0146411619030064","article-title":"Study on an Optimal Path Planning for a Robot Based on an Improved ANT Colony Algorithm","volume":"53","author":"Li","year":"2019","journal-title":"Autom. Control Comput. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1504\/IJCSM.2021.114182","article-title":"Research on robot optimal path planning method based on improved ant colony algorithm","volume":"13","author":"Tian","year":"2021","journal-title":"Int. J. Comput. Sci. Math."},{"key":"ref_34","first-page":"182","article-title":"Mobile robot dynamic path planning based on improved ant colony algorithm","volume":"44","author":"Ren","year":"2021","journal-title":"Mod. Electron. Tech."},{"key":"ref_35","first-page":"260","article-title":"Research of Improved Ant Colony Based Robot Path Planning Under Dynamic Environment","volume":"44","author":"Qu","year":"2015","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.robot.2016.08.001","article-title":"Heuristic approaches in robot path planning: A survey","volume":"86","author":"Mac","year":"2016","journal-title":"Robot. Auton. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.3390\/s20071880","article-title":"Grid-Based Mobile Robot Path Planning Using Aging-Based Ant Colony Optimization Algorithm in Static and Dynamic Environments","volume":"20","author":"Ajeil","year":"2020","journal-title":"Sensors"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"225","DOI":"10.3934\/mbe.2022012","article-title":"LF-ACO: An effective formation path planning for multi-mobile robot","volume":"19","author":"Yang","year":"2022","journal-title":"Math. Biosci. Eng."},{"key":"ref_39","first-page":"490","article-title":"A Path Planning Algorithm for Seeing Eye Robots Based on V-Graph","volume":"33","author":"Chen","year":"2014","journal-title":"Mech. Sci. Technol. Aerosp. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"106312","DOI":"10.1016\/j.asoc.2020.106312","article-title":"Multi-robot path planning using improved particle swarm optimization algorithm through novel evolutionary operators","volume":"92","author":"Das","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_41","first-page":"282","article-title":"Research on Improved Ant Colony Algorithm for Robot Global Path Planning","volume":"58","author":"Zhang","year":"2022","journal-title":"Comput. Eng. Appl."},{"key":"ref_42","first-page":"24","article-title":"Path Planning of Mobile Robot Based on Improved Ant Colony Algorithm","volume":"30","author":"Wu","year":"2023","journal-title":"J. Dongguan Univ. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3389\/fnbot.2019.00015","article-title":"Mobile Robot Path Planning Based on Ant Colony Algorithm With A* Heuristic Method","volume":"13","author":"Dai","year":"2019","journal-title":"Front. Neurorobot."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4149","DOI":"10.1177\/1729881419898979","article-title":"Path planning of lunar robot based on dynamic adaptive ant colony algorithm and obstacle avoidance","volume":"17","author":"Zhu","year":"2020","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_45","first-page":"76","article-title":"Path planning of mobile robot based on the improved grey wolf optimization algorithm","volume":"57","author":"Liu","year":"2020","journal-title":"Electr. Meas. Instrum."},{"key":"ref_46","first-page":"1705","article-title":"Research on path planning of mobile robot based on heterogeneous dual population and global vision ant colony algorithm","volume":"39","author":"Ma","year":"2022","journal-title":"Appl. Res. Comput."},{"key":"ref_47","first-page":"303","article-title":"Mobile robot path planning using improved double-layer ant colony algorithm","volume":"37","author":"Zhang","year":"2022","journal-title":"Control Decis."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Zhang, H., Lin, W., and Chen, A. (2018). Path Planning for the Mobile Robot: A Review. Symmetry, 10.","DOI":"10.3390\/sym10100450"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.sbspro.2010.03.064","article-title":"Teaching robot navigation in the presence of obstacles using a computer simulation program","volume":"2","author":"Erin","year":"2010","journal-title":"Procedia Soc. Behav. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"150775","DOI":"10.1109\/ACCESS.2019.2946448","article-title":"A Self-Heuristic Ant-based Method for Path Planning of Unmanned Aerial Vehicle in Complex 3-D Space with Dense U-type Obstacles","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_51","first-page":"276","article-title":"Application of Improved Ant Colony Optimization in Robot Path Planning","volume":"57","author":"He","year":"2021","journal-title":"Comput. Eng. Appl."},{"key":"ref_52","first-page":"38","article-title":"Optimal path planning of mobile robot based on improved ant colony algorithm","volume":"7","author":"Yuan","year":"2021","journal-title":"Mod. Manuf. Eng."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Wang, L., Kan, J., Guo, J., and Wang, C. (2019). 3D Path Planning for the Ground Robot with Improved Ant Colony Optimization. Sensors, 19.","DOI":"10.3390\/s19040815"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/6\/525\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:43:15Z","timestamp":1760125395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/6\/525"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,27]]},"references-count":53,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["axioms12060525"],"URL":"https:\/\/doi.org\/10.3390\/axioms12060525","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,27]]}}}