{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T01:43:48Z","timestamp":1774143828560,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,1,26]],"date-time":"2023-01-26T00:00:00Z","timestamp":1674691200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency","doi-asserted-by":"publisher","award":["N2-0153"],"award-info":[{"award-number":["N2-0153"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Human\u2013robot collaboration is one of the most challenging fields in robotics, as robots must understand human intentions and suitably cooperate with them in the given circumstances. But although this is one of the most investigated research areas in robotics, it is still in its infancy. In this paper, human\u2013robot collaboration is addressed by applying a phase state system, guided by stable heteroclinic channel networks, to a humanoid robot. The base mathematical model is first defined and illustrated on a simple three-state system. Further on, an eight-state system is applied to a humanoid robot to guide it and make it perform different movements according to the forces exerted on its grippers. The movements presented in this paper are squatting, standing up, and walking forwards and backward, while the motion velocity depends on the magnitude of the applied forces. The method presented in this paper proves to be a suitable way of controlling robots by means of physical human-robot interaction. As the phase state system and the robot movements can both be further extended to make the robot execute many other tasks, the proposed method seems to provide a promising way for further investigation and realization of physical human\u2013robot interaction.<\/jats:p>","DOI":"10.3390\/s23031396","type":"journal-article","created":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T01:27:58Z","timestamp":1674782878000},"page":"1396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Stable Heteroclinic Channel Networks for Physical Human\u2013Humanoid Robot Collaboration"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0297-8286","authenticated-orcid":false,"given":"Tilen","family":"Brecelj","sequence":"first","affiliation":[{"name":"Department of Automatics, Biocybernetics and Robotics, Jo\u017eef Stefan Institute, Jamova Cesta 39, 1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3407-4206","authenticated-orcid":false,"given":"Tadej","family":"Petri\u010d","sequence":"additional","affiliation":[{"name":"Department of Automatics, Biocybernetics and Robotics, Jo\u017eef Stefan Institute, Jamova Cesta 39, 1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1037\/0012-1649.41.2.328","article-title":"Unwilling versus unable: Infants\u2019 understanding of intentional action","volume":"41","author":"Behne","year":"2005","journal-title":"Dev. 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