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In particular, safe and efficient social navigation is a key challenge, requiring AI not only to avoid collisions and deadlocks but also to interact intuitively and predictably with its surroundings. To date, methods based on probabilistic models and the generation of conformal safety regions have shown promising results in defining safety regions with a controlled margin of error, primarily relying on classification approaches and explicit rules to describe collision-free navigation conditions.\n<\/jats:p>\n          <jats:p>This work extends the existing perspective by investigating how topological features can contribute to the creation of explainable safety regions in social navigation scenarios, enabling the classification and characterization of different simulation behaviors. Rather than relying on behaviors parameters to generate safety regions, we leverage topological features through topological data analysis. We first utilize global rule-based classification to provide interpretable characterizations of different simulation behaviors, distinguishing between safe (free of collisions) and unsafe scenarios based on topological properties. Next, we define safety regions, <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$S_\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>S<\/mml:mi>\n                    <mml:mi>\u03b5<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>, representing zones in the topological feature space where collisions are avoided with a maximum classification error of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. These regions are constructed using adjustable SVM classifiers and order statistics, ensuring a robust and scalable decision boundary. To enhance interpretability, we extract local rules from these safety regions, ensuring that the decision-making process remains transparent and comprehensible.<\/jats:p>\n          <jats:p>Initially, we generate safety regions that separate simulations with and without collisions, achieving higher accuracy than methods that do not incorporate topological features. This approach also provides a deeper and more intuitive understanding of robot interactions within a navigable space. We then extend our methodology to design safety regions that ensure efficient simulations (i.e., free of deadlocks). Finally, we integrate both aspects to obtain comprehensive safety regions that guarantee both collision-free and deadlock-free simulations, defining an overall compliant simulation space.<\/jats:p>","DOI":"10.1007\/978-3-032-08324-1_18","type":"book-chapter","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T08:49:14Z","timestamp":1760518154000},"page":"396-421","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Safe and\u00a0Efficient Social Navigation Through Explainable Safety Regions Based on\u00a0Topological Features"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-1316-9026","authenticated-orcid":false,"given":"Victor","family":"Toscano-Duran","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0579-647X","authenticated-orcid":false,"given":"Sara","family":"Narteni","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7206-5511","authenticated-orcid":false,"given":"Alberto","family":"Carlevaro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1263-4110","authenticated-orcid":false,"given":"J\u00e9r\u00f4me","family":"Guzzi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9937-0033","authenticated-orcid":false,"given":"Rocio","family":"Gonzalez-Diaz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6201-6225","authenticated-orcid":false,"given":"Maurizio","family":"Mongelli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,16]]},"reference":[{"key":"18_CR1","unstructured":"Anjomshoae, S., Najjar, A., Calvaresi, D., Fr\u00e4mling, K.: Explainable agents and robots: results from a systematic literature review. 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