{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:37:19Z","timestamp":1764175039563,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T00:00:00Z","timestamp":1623888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","award":["001"],"award-info":[{"award-number":["001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The planning of safe paths is an important issue for autonomous robot systems. The Probabilistic Foam method (PFM) is a planner that guarantees safe paths bounded by a sequence of structures called bubbles that provides safe regions. This method performs the planning by covering the free configuration space with bubbles, an approach analogous to a breadth-first search. To improve the propagation process and keep the safety, we present three algorithms based on Probabilistic Foam: Goal-biased Probabilistic Foam (GBPF), Radius-biased Probabilistic Foam (RBPF), and Heuristic-guided Probabilistic Foam (HPF); the last two are proposed in this work. The variant GBPF is fast, HPF finds short paths, and RBPF finds high-clearance paths. Some simulations were performed using four different maps to analyze the behavior and performance of the methods. Besides, the safety was analyzed considering the new propagation strategies.<\/jats:p>","DOI":"10.3390\/s21124156","type":"journal-article","created":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T11:20:26Z","timestamp":1623928826000},"page":"4156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Safe Path Planning Algorithms for Mobile Robots Based on Probabilistic Foam"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1699-4535","authenticated-orcid":false,"given":"Lu\u00eds B. P.","family":"Nascimento","sequence":"first","affiliation":[{"name":"Department of Computer Engineering and Automation, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil"},{"name":"Federal Institute of Rio Grande do Norte, Parnamirim 59143-455, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7482-3390","authenticated-orcid":false,"given":"Dennis","family":"Barrios-Aranibar","sequence":"additional","affiliation":[{"name":"Electrical and Electronics Engineering Department, Universidad Cat\u00f3lica San Pablo, Arequipa 04001, Peru"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4530-9568","authenticated-orcid":false,"given":"Vitor G.","family":"Santos","sequence":"additional","affiliation":[{"name":"Federal Institute of Rio Grande do Norte, Parnamirim 59143-455, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6658-1854","authenticated-orcid":false,"given":"Diego S.","family":"Pereira","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering and Automation, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil"},{"name":"Federal Institute of Rio Grande do Norte, Parnamirim 59143-455, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9753-4038","authenticated-orcid":false,"given":"William C.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering and Automation, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2882-5237","authenticated-orcid":false,"given":"Pablo J.","family":"Alsina","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering and Automation, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1109\/TPAMI.1984.4767480","article-title":"Planning Collision-Free Paths for Robotic Arm Among Obstacles","volume":"6","author":"Chien","year":"1984","journal-title":"IEEE Trans. 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