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This work contributes to the existing literature by analyzing results from an experiment conducted in real museum settings. The experiment investigates the relation between robot\u2019s competence, willingness, and trustworthiness, as well as the impact of robot\u2019s actions explanation on the aforementioned dimensions. Specifically, it focuses on an adaptive robot capable of adopting a task delegated by the human at various autonomy levels and explaining the reasons behind its actions. The explanation is based on the human\u2019s mental states (Theory of Mind). Findings demonstrated that an adaptive robot that deviates from the human\u2019s explicitly stated expectations, is perceived as trustworthy if evaluated competent in the collaboration, regardless of the explanation provided. Additionally, a robot evaluated willing to interact with the human for achieving the delegated task is perceived as trustworthy when it is able to explain the mechanism beyond the task adoption process. Furthermore, we found that a human who accepts and comprehends the logic underlying the robot\u2019s explanation tends to evaluate the provided explanation positively. Taken together, these results contribute to assess the relationship between trustworthiness, competence, willingness, and explainability in adaptive robots.<\/jats:p>","DOI":"10.1007\/s12369-025-01257-y","type":"journal-article","created":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T05:42:58Z","timestamp":1745991778000},"page":"2199-2210","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Trustworthiness Assessment of an Adaptive and Explainable Robot in a Real Environment"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2972-9666","authenticated-orcid":false,"given":"Filippo","family":"Cantucci","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Marini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rino","family":"Falcone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,30]]},"reference":[{"issue":"3","key":"1257_CR1","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1145\/3173087","volume":"61","author":"B Kuipers","year":"2018","unstructured":"Kuipers B (2018) How can we trust a robot? 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