{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:16:29Z","timestamp":1777533389398,"version":"3.51.4"},"reference-count":65,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,6,8]],"date-time":"2020-06-08T00:00:00Z","timestamp":1591574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The ability to plan a multiple-target path that goes through places considered important is desirable for autonomous mobile robots that perform tasks in industrial environments. This characteristic is necessary for inspection robots that monitor the critical conditions of sectors in thermal, nuclear, and hydropower plants. This ability is also useful for applications such as service at home, victim rescue, museum guidance, land mine detection, and so forth. Multiple-target collision-free path planning is a topic that has not been very studied because of the complexity that it implies. Usually, this issue is left in second place because, commonly, it is solved by segmentation using the point-to-point strategy. Nevertheless, this approach exhibits a poor performance, in terms of path length, due to unnecessary turnings and redundant segments present in the found path. In this paper, a multiple-target method based on homotopy continuation capable to calculate a collision-free path in a single execution for complex environments is presented. This method exhibits a better performance, both in speed and efficiency, and robustness compared to the original Homotopic Path Planning Method (HPPM). Among the new schemes that improve their performance are the Double Spherical Tracking (DST), the dummy obstacle scheme, and a systematic criterion to a selection of repulsion parameter. The case studies show its effectiveness to find a solution path for office-like environments in just a few milliseconds, even if they have narrow corridors and hundreds of obstacles. Additionally, a comparison between the proposed method and sampling-based planning algorithms (SBP) with the best performance is presented. Furthermore, the results of case studies show that the proposed method exhibits a better performance than SBP algorithms for execution time, memory, and in some cases path length metrics. Finally, to validate the feasibility of the paths calculated by the proposed planner; two simulations using the pure-pursuit controlled and differential drive robot model contained in the Robotics System Toolbox of MATLAB are presented.<\/jats:p>","DOI":"10.3390\/s20113265","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T06:34:16Z","timestamp":1591684456000},"page":"3265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Multiple-Target Homotopic Quasi-Complete Path Planning Method for Mobile Robot Using a Piecewise Linear Approach"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8144-6615","authenticated-orcid":false,"given":"Gerardo","family":"Diaz-Arango","sequence":"first","affiliation":[{"name":"Engineering School, University of Xalapa, Km. 2 Carretera Xalapa-Veracruz, Xalapa, Veracruz 91190, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7785-5272","authenticated-orcid":false,"given":"Hector","family":"Vazquez-Leal","sequence":"additional","affiliation":[{"name":"Facultad de Instrumentacion Electronica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltran S\/N, Xalapa, Veracruz 91000, Mexico"},{"name":"Consejo Veracruzano de Investigacion Cientifica y Desarrollo Tecnologico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Cuauhtemoc, Xalapa, Veracruz 91069, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"Hernandez-Martinez","sequence":"additional","affiliation":[{"name":"Electronics Department, National Institute for Astrophysics, Optics and Electronics, Sta. Mar\u00eda Tonantzintla, Puebla 72840, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor Manuel","family":"Jimenez-Fernandez","sequence":"additional","affiliation":[{"name":"Facultad de Instrumentacion Electronica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltran S\/N, Xalapa, Veracruz 91000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1537-3910","authenticated-orcid":false,"given":"Aurelio","family":"Heredia-Jimenez","sequence":"additional","affiliation":[{"name":"Electronics Department, UPAEP, 21 Sur 1103, Puebla 72410, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4942-6320","authenticated-orcid":false,"given":"Roberto C.","family":"Ambrosio","sequence":"additional","affiliation":[{"name":"Faculty of Electronics Science Meritorious University Autonomous of Puebla, 4 Sur 104 Centro, Puebla 72000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2803-0645","authenticated-orcid":false,"given":"Jesus","family":"Huerta-Chua","sequence":"additional","affiliation":[{"name":"Instituto Tecnologico Superior de Poza Rica, Tecnologico Nacional de Mexico, Luis Donaldo Colosio Murrieta S\/N, Arroyo del Maiz,  Poza Rica, Veracruz 93230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hector","family":"De Cos-Cholula","sequence":"additional","affiliation":[{"name":"Electronics Department, National Institute for Astrophysics, Optics and Electronics, Sta. Mar\u00eda Tonantzintla, Puebla 72840, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Hernandez-Mendez","sequence":"additional","affiliation":[{"name":"Engineering School, University of Xalapa, Km. 2 Carretera Xalapa-Veracruz, Xalapa, Veracruz 91190, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TRO.2011.2160466","article-title":"A Sampling-Based Tree Planner for Systems with Complex Dynamics","volume":"28","author":"Kavraki","year":"2012","journal-title":"IEEE Trans. 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