{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T04:34:54Z","timestamp":1766378094527,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,5,26]],"date-time":"2022-05-26T00:00:00Z","timestamp":1653523200000},"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>Achieving the smart motion of any autonomous or semi-autonomous robot requires an efficient algorithm to determine a feasible collision-free path. In this paper, a novel collision-free path homotopy-based path-planning algorithm applied to planar robotic arms is presented. The algorithm utilizes homotopy continuation methods (HCMs) to solve the non-linear algebraic equations system (NAES) that models the robot\u2019s workspace. The method was validated with three case studies with robotic arms in different configurations. For the first case, a robot arm with three links must enter a narrow corridor with two obstacles. For the second case, a six-link robot arm with a gripper is required to take an object inside a narrow corridor with two obstacles. For the third case, a twenty-link arm must take an object inside a maze-like environment. These case studies validated, by simulation, the versatility and capacity of the proposed path-planning algorithm. The results show that the CPU time is dozens of milliseconds with a memory consumption less than 4.5 kB for the first two cases. For the third case, the CPU time is around 2.7 s and the memory consumption around 18 kB. Finally, the method\u2019s performance was further validated using the industrial robot arm CRS CataLyst-5 by Thermo Electron.<\/jats:p>","DOI":"10.3390\/s22114022","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T02:30:06Z","timestamp":1653964206000},"page":"4022","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Novel Collision-Free Homotopy Path Planning for Planar Robotic Arms"],"prefix":"10.3390","volume":"22","author":[{"given":"Gerardo C.","family":"Velez-Lopez","sequence":"first","affiliation":[{"name":"Electronics Department, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, Santa Mar\u00eda Tonantzintla, Cholula 72840, Puebla, 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 91000, Veracruz, Mexico"},{"name":"Consejo Veracruzano de Investigacion Cientifica y Desarrollo Tecnologico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Xalapa 91069, Veracruz, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"Hernandez-Martinez","sequence":"additional","affiliation":[{"name":"Electronics Department, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, Santa Mar\u00eda Tonantzintla, Cholula 72840, Puebla, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arturo","family":"Sarmiento-Reyes","sequence":"additional","affiliation":[{"name":"Electronics Department, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, Santa Mar\u00eda Tonantzintla, Cholula 72840, Puebla, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8144-6615","authenticated-orcid":false,"given":"Gerardo","family":"Diaz-Arango","sequence":"additional","affiliation":[{"name":"Instituto Tecnologico Superior de Poza Rica, Tecnologico Nacional de Mexico, Luis Donaldo Colosio Murrieta S\/N, Poza Rica 93230, Veracruz, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Poza Rica 93230, Veracruz, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hector D.","family":"Rico-Aniles","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, North Central College, 30 N. Brainard St., Naperville, IL 60540, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor M.","family":"Jimenez-Fernandez","sequence":"additional","affiliation":[{"name":"Facultad de Instrumentacion Electronica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltran S\/N, Xalapa 91000, Veracruz, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Baek, D., Hwang, M., Kim, H., and Kwon, D.S. (2018, January 26\u201330). Path planning for automation of surgery robot based on probabilistic roadmap and reinforcement learning. 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