{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T19:52:29Z","timestamp":1773085949764,"version":"3.50.1"},"reference-count":79,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:00:00Z","timestamp":1759795200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T00:00:00Z","timestamp":1759795200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100013000","name":"Politecnico di Torino","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100013000","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Robot integration in daily life demands research on both safety and social acceptance. Current methods focus on safety, but social factors are understudied. Moreover, existing studies lack deep analysis of human perception towards robot movement. Here, we present a novel navigation approach based on the combination of Game Theory and the Social Force Model (GTSFM) to bridge these gaps. We model navigation as a non-cooperative game to consider both pedestrians and robot as rational agents influencing each other\u2019s choices. We evaluate the social acceptability of the GTSFM algorithm from both quantitative and qualitative perspectives. In both evaluations, the GTSFM is compared against two state-of-the-art algorithms: the social force model (SFM) and the optimal reciprocal collision avoidance (ORCA). According to the quantitative analysis performed in simulation, the GTSFM outperforms the SFM in all considered performance metrics and ensures higher performance than ORCA considering the smoothness of the trajectories and the proximity to pedestrians. The qualitative measurement is performed through a real-world experiment using a questionnaire administered to a pool of 76 participants. Our qualitative analysis revealed no statistically significant differences in performance between the algorithms tested. This lack of distinction may be due to unaccounted factors. The robot\u2019s appearance and the limited velocity of the real robot could have obscured the distinction between the algorithms. These results represent a significant milestone in advancing the integration of robots into social environments also leave important hints for future research.<\/jats:p>","DOI":"10.1007\/s10846-025-02318-0","type":"journal-article","created":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:07:40Z","timestamp":1759835260000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Game of Social Forces: Integrating Non-cooperative Game Theory with Social Force Model for a Socially-acceptable Mobile Robot Navigation"],"prefix":"10.1007","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0694-6609","authenticated-orcid":false,"given":"Giada","family":"Galati","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0215-3080","authenticated-orcid":false,"given":"Andrea","family":"Usai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0002-8394-4156","authenticated-orcid":false,"given":"Giacomo","family":"Vignolo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2946-4784","authenticated-orcid":false,"given":"Simone","family":"Macr\u00ec","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2386-3146","authenticated-orcid":false,"given":"Alessandro","family":"Rizzo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,7]]},"reference":[{"issue":"8","key":"2318_CR1","doi-asserted-by":"publisher","first-page":"1767","DOI":"10.1007\/s12369-022-00904-y","volume":"14","author":"M Hellou","year":"2022","unstructured":"Hellou, M., Lim, J., Gasteiger, N., Jang, M., Ahn, H.S.: Technical methods for social robots in museum settings: an overview of the literature. Int. J. Soc. Robot. 14(8), 1767\u20131786 (2022)","journal-title":"Int. J. Soc. Robot."},{"key":"2318_CR2","doi-asserted-by":"crossref","unstructured":"Zhao, Z., Chen, W., Peter, C.C. , Wu, X.: A novel navigation system for indoor cleaning robot. In: 2016 IEEE international conference on Robotics and Biomimetics (ROBIO), pp.\u00a02159\u20132164. IEEE (2016)","DOI":"10.1109\/ROBIO.2016.7866649"},{"issue":"7","key":"2318_CR3","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1016\/j.robot.2010.03.010","volume":"58","author":"M Takahashi","year":"2010","unstructured":"Takahashi, M., Suzuki, T., Shitamoto, H., Moriguchi, T., Yoshida, K.: Developing a mobile robot for transport applications in the hospital domain. Robot. Auton. Syst. 58(7), 889\u2013899 (2010)","journal-title":"Robot. Auton. Syst."},{"issue":"4","key":"2318_CR4","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1002\/rob.21534","volume":"32","author":"R K\u00fcmmerle","year":"2015","unstructured":"K\u00fcmmerle, R., Ruhnke, M., Steder, B., Stachniss, C., Burgard, W.: Autonomous robot navigation in highly populated pedestrian zones. J. Field Robot. 32(4), 565\u2013589 (2015)","journal-title":"J. Field Robot."},{"issue":"19","key":"2318_CR5","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.ifacol.2015.12.032","volume":"48","author":"AR Araujo","year":"2015","unstructured":"Araujo, A.R., Caminhas, D.D., Pereira, G.A.: An architecture for navigation of service robots in human-populated office-like environments. IFAC-PapersOnLine 48(19), 189\u2013194 (2015)","journal-title":"IFAC-PapersOnLine"},{"issue":"12","key":"2318_CR6","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1016\/j.robot.2013.05.007","volume":"61","author":"T Kruse","year":"2013","unstructured":"Kruse, T., Pandey, A.K., Alami, R., Kirsch, A.: Human-aware robot navigation: a survey. Robot. Auton. Syst. 61(12), 1726\u20131743 (2013)","journal-title":"Robot. Auton. Syst."},{"key":"2318_CR7","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1109\/OJIES.2022.3179617","volume":"3","author":"H Hewawasam","year":"2022","unstructured":"Hewawasam, H., Ibrahim, M.Y., Appuhamillage, G.K.: Past, present and future of path-planning algorithms for mobile robot navigation in dynamic environments. IEEE Open J. Ind. Electron. Soc. 3, 353\u2013365 (2022)","journal-title":"IEEE Open J. Ind. Electron. Soc."},{"key":"2318_CR8","unstructured":"Kivrak, H., Cakmak, F., Kose, H., Yavuz, S.: Social navigation framework for assistive robots in human inhabited unknown environments. Eng. Sci. Technol. Int J. 100 (2020)"},{"issue":"3","key":"2318_CR9","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1177\/0278364914557874","volume":"34","author":"P Trautman","year":"2015","unstructured":"Trautman, P., Ma, J., Murray, R.M., Krause, A.: Robot navigation in dense human crowds: statistical models and experimental studies of human-robot cooperation. Int. J. Robot. Res. 34(3), 335\u2013356 (2015)","journal-title":"Int. J. Robot. Res."},{"key":"2318_CR10","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s12369-018-0487-2","volume":"11","author":"A Turnwald","year":"2019","unstructured":"Turnwald, A., Wollherr, D.: Human-like motion planning based on game theoretic decision making. Int. J. Soc. Robot. 11, 151\u2013170 (2019)","journal-title":"Int. J. Soc. Robot."},{"issue":"5","key":"2318_CR11","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1109\/TRO.2007.904911","volume":"23","author":"EA Sisbot","year":"2007","unstructured":"Sisbot, E.A., Marin-Urias, L.F., Alami, R., Simeon, T.: A human aware mobile robot motion planner. IEEE Trans. Rob. 23(5), 874\u2013883 (2007)","journal-title":"IEEE Trans. Rob."},{"issue":"3","key":"2318_CR12","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/s12369-014-0238-y","volume":"6","author":"M Shiomi","year":"2014","unstructured":"Shiomi, M., Zanlungo, F., Hayashi, K., Kanda, T.: Towards a socially acceptable collision avoidance for a mobile robot navigating among pedestrians using a pedestrian model. Int. J. Soc. Robot. 6(3), 443\u2013455 (2014)","journal-title":"Int. J. Soc. Robot."},{"key":"2318_CR13","doi-asserted-by":"crossref","unstructured":"Chen, Y.F., Everett, M., Liu, M., How, J.\u00a0P.: Socially aware motion planning with deep reinforcement learning. In: 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp.\u00a01343\u20131350. IEEE (2017)","DOI":"10.1109\/IROS.2017.8202312"},{"key":"2318_CR14","doi-asserted-by":"crossref","unstructured":"Nash, J.: Non-cooperative games. Ann. Math. 286\u2013295 (1951)","DOI":"10.2307\/1969529"},{"issue":"1","key":"2318_CR15","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1109\/MCS.2016.2621479","volume":"37","author":"N Quijano","year":"2017","unstructured":"Quijano, N., et al.: The role of population games and evolutionary dynamics in distributed control systems: the advantages of evolutionary game theory. IEEE Control Syst. Mag. 37(1), 70\u201397 (2017)","journal-title":"IEEE Control Syst. Mag."},{"issue":"2","key":"2318_CR16","doi-asserted-by":"publisher","first-page":"024314","DOI":"10.1103\/PhysRevE.104.024314","volume":"104","author":"M Ye","year":"2021","unstructured":"Ye, M., Zino, L., Rizzo, A., Cao, M.: Game-theoretic modeling of collective decision making during epidemics. Phys. Rev. E 104(2), 024314 (2021)","journal-title":"Phys. Rev. E"},{"issue":"24","key":"2318_CR17","doi-asserted-by":"publisher","first-page":"5611","DOI":"10.1016\/j.physa.2010.08.032","volume":"389","author":"J Tanimoto","year":"2010","unstructured":"Tanimoto, J., Hagishima, A., Tanaka, Y.: Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory. XXPhys. A 389(24), 5611\u20135618 (2010)","journal-title":"XXPhys. A"},{"key":"2318_CR18","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/j.ssci.2016.03.018","volume":"87","author":"BL Mesmer","year":"2016","unstructured":"Mesmer, B.L., Bloebaum, C.L.: Modeling decision and game theory based pedestrian velocity vector decisions with interacting individuals. Saf. Sci. 87, 116\u2013130 (2016)","journal-title":"Saf. Sci."},{"issue":"9","key":"2318_CR19","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1177\/0361198120931513","volume":"2674","author":"Y Rahmati","year":"2020","unstructured":"Rahmati, Y., Talebpour, A., Mittal, A., Fishelson, J.: Game theory-based framework for modeling human-vehicle interactions on the road. Transp. Res. Rec. 2674(9), 701\u2013713 (2020)","journal-title":"Transp. Res. Rec."},{"issue":"10","key":"2318_CR20","doi-asserted-by":"publisher","first-page":"2827","DOI":"10.3390\/s20102827","volume":"20","author":"C Kim","year":"2020","unstructured":"Kim, C., Won, J.-S.: A fuzzy analytic hierarchy process and cooperative game theory combined multiple mobile robot navigation algorithm. Sensors 20(10), 2827 (2020)","journal-title":"Sensors"},{"key":"2318_CR21","doi-asserted-by":"crossref","unstructured":"LaValle, S.\u00a0M., Hutchinson, S.: Game theory as a unifying structure for a variety of robot tasks. In: Proceedings of 8th IEEE international symposium on intelligent control, pp.\u00a0429\u2013434. IEEE (1993)","DOI":"10.1109\/ISIC.1993.397675"},{"issue":"4","key":"2318_CR22","doi-asserted-by":"publisher","first-page":"44","DOI":"10.5772\/6232","volume":"5","author":"Y Meng","year":"2008","unstructured":"Meng, Y.: Multi-robot searching using game-theory based approach. Int. J. Adv. Rob. Syst. 5(4), 44 (2008)","journal-title":"Int. J. Adv. Rob. Syst."},{"issue":"5","key":"2318_CR23","doi-asserted-by":"publisher","first-page":"4282","DOI":"10.1103\/PhysRevE.51.4282","volume":"51","author":"D Helbing","year":"1995","unstructured":"Helbing, D., Molnar, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51(5), 4282 (1995)","journal-title":"Phys. Rev. E"},{"key":"2318_CR24","doi-asserted-by":"crossref","unstructured":"Tadokoro, S., Hayashi, M., Manabe, Y., Nakami, Y., Takamori, T.: On motion planning of mobile robots which coexist and cooperate with human. In: Proceedings 1995 IEEE\/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots, vol.\u00a02, pp.\u00a0518\u2013523. IEEE (1995)","DOI":"10.1109\/IROS.1995.526265"},{"key":"2318_CR25","doi-asserted-by":"crossref","unstructured":"Hoeller, F., Schulz, D., Moors, M., Schneider, F.\u00a0E.: Accompanying persons with a mobile robot using motion prediction and probabilistic roadmaps. In: 2007 IEEE\/RSJ international conference on intelligent robots and systems, pp.\u00a01260\u20131265. IEEE (2007)","DOI":"10.1109\/IROS.2007.4399194"},{"issue":"1","key":"2318_CR26","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1177\/0278364904048962","volume":"24","author":"M Bennewitz","year":"2005","unstructured":"Bennewitz, M., Burgard, W., Cielniak, G., Thrun, S.: Learning motion patterns of people for compliant robot motion. Int. J. Robot. Res. 24(1), 31\u201348 (2005)","journal-title":"Int. J. Robot. Res."},{"key":"2318_CR27","doi-asserted-by":"crossref","unstructured":"Alahi, A., Goel, K., Ramanathan, V., Robicquet, A., Fei-Fei, L., Savarese, S.: Social lstm: human trajectory prediction in crowded spaces. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp.\u00a0961\u2013971. (2016)","DOI":"10.1109\/CVPR.2016.110"},{"key":"2318_CR28","doi-asserted-by":"crossref","unstructured":"Gupta, A., Johnson, J., Fei-Fei, L., Savarese, S., Alahi, A.: Social gan: Socially acceptable trajectories with generative adversarial networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp.\u00a02255\u20132264. (2018)","DOI":"10.1109\/CVPR.2018.00240"},{"key":"2318_CR29","doi-asserted-by":"crossref","unstructured":"Liang, J., Jiang, L., Niebles, J.\u00a0C., Hauptmann, A.\u00a0G. , Fei-Fei, L.: Peeking into the future: predicting future person activities and locations in videos. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp.\u00a05725\u20135734. (2019)","DOI":"10.1109\/CVPRW.2019.00358"},{"issue":"2","key":"2318_CR30","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s12369-016-0342-2","volume":"8","author":"A Turnwald","year":"2016","unstructured":"Turnwald, A., Althoff, D., Wollherr, D., Buss, M.: Understanding human avoidance behavior: interaction-aware decision making based on game theory. Int. J. Soc. Robot. 8(2), 331\u2013351 (2016)","journal-title":"Int. J. Soc. Robot."},{"issue":"1","key":"2318_CR31","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TEVC.2010.2059031","volume":"15","author":"S Das","year":"2010","unstructured":"Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4\u201331 (2010)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"3","key":"2318_CR32","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1177\/1745691610369336","volume":"5","author":"A Waytz","year":"2010","unstructured":"Waytz, A., Cacioppo, J., Epley, N.: Who sees human? the stability and importance of individual differences in anthropomorphism. Perspect. Psychol. Sci. 5(3), 219\u2013232 (2010)","journal-title":"Perspect. Psychol. Sci."},{"key":"2318_CR33","doi-asserted-by":"crossref","unstructured":"Fink, J.: Anthropomorphism and human likeness in the design of robots and human-robot interaction. In: International conference on social robotics, pp.\u00a0199\u2013208. Springer (2012)","DOI":"10.1007\/978-3-642-34103-8_20"},{"key":"2318_CR34","doi-asserted-by":"crossref","unstructured":"Van Den\u00a0Berg, J., Guy, S.\u00a0J., Lin, M., Manocha, D.: Reciprocal n-body collision avoidance. In: Robotics Research: The 14th International Symposium ISRR, pp.\u00a03\u201319. Springer (2011)","DOI":"10.1007\/978-3-642-19457-3_1"},{"key":"2318_CR35","unstructured":"Antonucci, A., et\u00a0al.: Socially aware robot navigation. Tesi di dottorato. (2022)"},{"issue":"1","key":"2318_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s40648-015-0033-z","volume":"2","author":"P Ratsamee","year":"2015","unstructured":"Ratsamee, P., Mae, Y., Kamiyama, K., Horade, M., Kojima, M., Arai, T.: Social interactive robot navigation based on human intention analysis from face orientation and human path prediction. Robomech J. 2(1), 1\u201318 (2015)","journal-title":"Robomech J."},{"issue":"4","key":"2318_CR37","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1007\/s10514-016-9584-y","volume":"41","author":"G Ferrer","year":"2017","unstructured":"Ferrer, G., Zulueta, A.G., Cotarelo, F.H., Sanfeliu, A.: Robot social-aware navigation framework to accompany people walking side-by-side. Auton. Robot. 41(4), 775\u2013793 (2017)","journal-title":"Auton. Robot."},{"issue":"7","key":"2318_CR38","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1177\/027836499801700706","volume":"17","author":"P Fiorini","year":"1998","unstructured":"Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using velocity obstacles. Int. J. Robot. Res. 17(7), 760\u2013772 (1998)","journal-title":"Int. J. Robot. Res."},{"key":"2318_CR39","doi-asserted-by":"crossref","unstructured":"Van\u00a0den Berg, J., Lin, M., Manocha, D.: Reciprocal velocity obstacles for real-time multi-agent navigation. In: 2008 IEEE international conference on robotics and automation, pp.\u00a01928\u20131935. IEEE (2008)","DOI":"10.1109\/ROBOT.2008.4543489"},{"issue":"1","key":"2318_CR40","doi-asserted-by":"publisher","first-page":"21976","DOI":"10.1038\/s41598-022-25438-1","volume":"12","author":"G Galati","year":"2022","unstructured":"Galati, G., Primatesta, S., Grammatico, S., Macr\u00ec, S., Rizzo, A.: Game theoretical trajectory planning enhances social acceptability of robots by humans. Sci. Rep. 12(1), 21976 (2022)","journal-title":"Sci. Rep."},{"issue":"1","key":"2318_CR41","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s11370-018-0260-2","volume":"12","author":"NH Singh","year":"2019","unstructured":"Singh, N.H., Thongam, K.: Neural network-based approaches for mobile robot navigation in static and moving obstacles environments. Intel. Serv. Robot. 12(1), 55\u201367 (2019)","journal-title":"Intel. Serv. Robot."},{"key":"2318_CR42","doi-asserted-by":"crossref","unstructured":"Xie, Z., Xin, P., Dames, P.: Towards safe navigation through crowded dynamic environments. In: 2021 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp.\u00a04934\u20134940. IEEE (2021)","DOI":"10.1109\/IROS51168.2021.9636102"},{"key":"2318_CR43","doi-asserted-by":"crossref","unstructured":"Chen, Y.\u00a0F. , Liu, M., Everett, M., How, J.\u00a0P.: Decentralized non-communicating multiagent collision avoidance with deep reinforcement learning. In: 2017 IEEE international conference on robotics and automation (ICRA), pp.\u00a0285\u2013292. IEEE (2017)","DOI":"10.1109\/ICRA.2017.7989037"},{"key":"2318_CR44","doi-asserted-by":"crossref","unstructured":"Chen, C., Liu, Y., Kreiss, S., Alahi, A.: Crowd-robot interaction: crowd-aware robot navigation with attention-based deep reinforcement learning. In: 2019 international conference on robotics and automation (ICRA), pp.\u00a06015\u20136022. IEEE (2019)","DOI":"10.1109\/ICRA.2019.8794134"},{"key":"2318_CR45","unstructured":"Yildirim, Y., Ugur, E.: Learning social navigation from demonstrations with deep neural networks. arXiv preprint (2024)"},{"key":"2318_CR46","doi-asserted-by":"crossref","unstructured":"Ram\u00edrez, O.\u00a0A.\u00a0I. , Khambhaita, H., Chatila, R., Chetouani, M., Alami, R.: Robots learning how and where to approach people. In: 2016 25th IEEE international symposium on robot and human interactive communication (RO-MAN), pp.\u00a0347\u2013353. IEEE (2016)","DOI":"10.1109\/ROMAN.2016.7745154"},{"issue":"13","key":"2318_CR47","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1080\/01691864.2020.1753569","volume":"34","author":"S Sun","year":"2020","unstructured":"Sun, S., Zhao, X., Li, Q., Tan, M.: Inverse reinforcement learning-based time-dependent a* planner for human-aware robot navigation with local vision. Adv. Robot. 34(13), 888\u2013901 (2020)","journal-title":"Adv. Robot."},{"key":"2318_CR48","doi-asserted-by":"crossref","unstructured":"Johora, F.\u00a0T., M\u00fcller, J.\u00a0P.: Modeling interactions of multimodal road users in shared spaces. In: 2018 21st International Conference on Intelligent Transportation Systems (ITSC), pp.\u00a03568\u20133574. IEEE (2018)","DOI":"10.1109\/ITSC.2018.8569687"},{"issue":"3","key":"2318_CR49","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1002\/oca.727","volume":"24","author":"S Hoogendoorn","year":"2003","unstructured":"Hoogendoorn, S., Bovy, P.H.L.: Simulation of pedestrian flows by optimal control and differential games. Optim. Control Appl. Methods 24(3), 153\u2013172 (2003)","journal-title":"Optim. Control Appl. Methods"},{"issue":"3","key":"2318_CR50","doi-asserted-by":"publisher","first-page":"032312","DOI":"10.1103\/PhysRevE.98.032312","volume":"98","author":"Y Rahmati","year":"2018","unstructured":"Rahmati, Y., Talebpour, A.: Learning-based game theoretical framework for modeling pedestrian motion. Phys. Rev. E 98(3), 032312 (2018)","journal-title":"Phys. Rev. E"},{"issue":"2","key":"2318_CR51","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1109\/LRA.2020.2965416","volume":"5","author":"A Rudenko","year":"2020","unstructured":"Rudenko, A., Kucner, T.P., Swaminathan, C.S., Chadalavada, R.T., Arras, K.O., Lilienthal, A.J.: Th\u00f6r: human-robot navigation data collection and accurate motion trajectories dataset. IEEE Robot. Autom. Lett. 5(2), 676\u2013682 (2020)","journal-title":"IEEE Robot. Autom. Lett."},{"issue":"6","key":"2318_CR52","doi-asserted-by":"publisher","first-page":"68005","DOI":"10.1209\/0295-5075\/93\/68005","volume":"93","author":"F Zanlungo","year":"2011","unstructured":"Zanlungo, F., Ikeda, T., Kanda, T.: Social force model with explicit collision prediction. Europhys. Lett. 93(6), 68005 (2011)","journal-title":"Europhys. Lett."},{"key":"2318_CR53","doi-asserted-by":"crossref","unstructured":"Ferrer, G., Garrell, A., Sanfeliu, A.: Robot companion: a social-force based approach with human awareness-navigation in crowded environments. In: 2013 IEEE\/RSJ international conference on intelligent robots and systems, pp.\u00a01688\u20131694. IEEE (2013)","DOI":"10.1109\/IROS.2013.6696576"},{"issue":"1","key":"2318_CR54","doi-asserted-by":"publisher","first-page":"e0169734","DOI":"10.1371\/journal.pone.0169734","volume":"12","author":"F Farina","year":"2017","unstructured":"Farina, F., Fontanelli, D., Garulli, A., Giannitrapani, A., Prattichizzo, D.: Walking ahead: the headed social force model. PLoS ONE 12(1), e0169734 (2017)","journal-title":"PLoS ONE"},{"issue":"2","key":"2318_CR55","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s12369-014-0251-1","volume":"7","author":"J Rios-Martinez","year":"2015","unstructured":"Rios-Martinez, J., Spalanzani, A., Laugier, C.: From proxemics theory to socially-aware navigation: a survey. Int. J. Soc. Robot. 7(2), 137\u2013153 (2015)","journal-title":"Int. J. Soc. Robot."},{"key":"2318_CR56","volume-title":"The hidden dimension","author":"ET Hall","year":"1966","unstructured":"Hall, E.T.: The hidden dimension, vol. 609. Doubleday, Garden City, NY (1966)"},{"issue":"5","key":"2318_CR57","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1002\/ajhb.10067","volume":"14","author":"Alexander R McNeill","year":"2002","unstructured":"McNeill, Alexander R.: Energetics and optimization of human walking and running: the 2000 Raymond pearl memorial lecture. Am. J Hum. Biol. 14(5), 641\u2013648 (2002)","journal-title":"Am. J Hum. Biol."},{"issue":"3","key":"2318_CR58","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s10589-017-9927-4","volume":"68","author":"S Sagratella","year":"2017","unstructured":"Sagratella, S.: Algorithms for generalized potential games with mixed-integer variables. Comput. Optim. Appl. 68(3), 689\u2013717 (2017)","journal-title":"Comput. Optim. Appl."},{"issue":"6","key":"2318_CR59","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1109\/TEVC.2006.873220","volume":"10","author":"PP Menon","year":"2006","unstructured":"Menon, P.P., Kim, J., Bates, D.G., Postlethwaite, I.: Clearance of nonlinear flight control laws using hybrid evolutionary optimization. IEEE Trans. Evol. Comput. 10(6), 689\u2013699 (2006)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"4","key":"2318_CR60","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/j.robot.2008.05.005","volume":"57","author":"L Moreno","year":"2009","unstructured":"Moreno, L., Garrido, S., Blanco, D., Munoz, M.L.: Differential evolution solution to the slam problem. Robot. Auton. Syst. 57(4), 441\u2013450 (2009)","journal-title":"Robot. Auton. Syst."},{"key":"2318_CR61","doi-asserted-by":"crossref","unstructured":"Aydin, S., Temeltas, H.: Fuzzy-differential evolution algorithm for planning time-optimal trajectories of a unicycle mobile robot on a predefined path. Adv. Robot. 18(7), 725\u2013748 (2004)","DOI":"10.1163\/1568553041719456"},{"key":"2318_CR62","doi-asserted-by":"crossref","unstructured":"Johansson, A., Helbing, D., Shukla, P.K.: Specification of the social force pedestrian model by evolutionary adjustment to video tracking data. Adv. Complex Syst. 10(supp02), 271\u2013288 (2007)","DOI":"10.1142\/S0219525907001355"},{"key":"2318_CR63","unstructured":"Tensorflow. https:\/\/www.tensorflow.org\/~overview?hl=it. Accessed on 23 Aug 2023"},{"issue":"7","key":"2318_CR64","doi-asserted-by":"publisher","first-page":"1517","DOI":"10.1007\/s12369-020-00667-4","volume":"13","author":"N Spatola","year":"2021","unstructured":"Spatola, N., K\u00fchnlenz, B., Cheng, G.: Perception and evaluation in human-robot interaction: the human-robot interaction evaluation scale (hries)\u2014a multicomponent approach of anthropomorphism. Int. J. Soc. Robot. 13(7), 1517\u20131539 (2021)","journal-title":"Int. J. Soc. Robot."},{"issue":"4","key":"2318_CR65","doi-asserted-by":"publisher","first-page":"1743","DOI":"10.1109\/TASE.2017.2731371","volume":"14","author":"X-T Truong","year":"2017","unstructured":"Truong, X.-T., Ngo, T.D.: Toward socially aware robot navigation in dynamic and crowded environments: a proactive social motion model. IEEE Trans. Autom. Sci. Eng. 14(4), 1743\u20131760 (2017)","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"issue":"3","key":"2318_CR66","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3476413","volume":"11","author":"A Biswas","year":"2022","unstructured":"Biswas, A., Wang, A., Silvera, G., Steinfeld, A., Admoni, H.: Socnavbench: a grounded simulation testing framework for evaluating social navigation. ACM Transactions on Human-Robot Interaction (THRI) 11(3), 1\u201324 (2022)","journal-title":"ACM Transactions on Human-Robot Interaction (THRI)"},{"key":"2318_CR67","doi-asserted-by":"publisher","first-page":"721317","DOI":"10.3389\/frobt.2021.721317","volume":"8","author":"Y Gao","year":"2022","unstructured":"Gao, Y., Huang, C.-M.: Evaluation of socially-aware robot navigation. Front. Robot. AI 8, 721317 (2022)","journal-title":"Front. Robot. AI"},{"key":"2318_CR68","doi-asserted-by":"crossref","unstructured":"Neggers, M.\u00a0M. , Cuijpers, R.\u00a0H. , Ruijten, P.\u00a0A., IJsselsteijn, W.\u00a0A.: The effect of robot speed on comfortable passing distances. Front. Robot. AI 9:915972 (2022)","DOI":"10.3389\/frobt.2022.915972"},{"issue":"7","key":"2318_CR69","first-page":"10","volume":"16","author":"B Prajapati","year":"2010","unstructured":"Prajapati, B., Dunne, M., Armstrong, R.: Sample size estimation and statistical power analyses. Optom. Today 16(7), 10\u201318 (2010)","journal-title":"Optom. Today"},{"issue":"1","key":"2318_CR70","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3758\/BF03203630","volume":"28","author":"E Erdfelder","year":"1996","unstructured":"Erdfelder, E., Faul, F., Buchner, A.: Gpower: a general power analysis program. Behav. Res. Methods. Instrum. Comput. 28(1), 1\u201311 (1996)","journal-title":"Behav. Res. Methods. Instrum. Comput."},{"key":"2318_CR71","doi-asserted-by":"crossref","unstructured":"Chin, R., Lee, B.\u00a0Y.: Principles and practice of clinical trial medicine. Elsevier (2008)","DOI":"10.1016\/B978-0-12-373695-6.00001-6"},{"issue":"2065","key":"2318_CR72","first-page":"20150202","volume":"374","author":"IT Jolliffe","year":"2016","unstructured":"Jolliffe, I.T., Cadima, J.: Principal component analysis: a review and recent developments. Philos. Trans. A Math. Phys. Eng. Sci. 374(2065), 20150202 (2016)","journal-title":"Philos. Trans. A Math. Phys. Eng. Sci."},{"key":"2318_CR73","unstructured":"Preferred walking speed. https:\/\/en.wikipedia.org\/~wiki\/~Preferred_walking_speed. Accessed: 2023"},{"key":"2318_CR74","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s12369-013-0191-1","volume":"5","author":"M Joosse","year":"2013","unstructured":"Joosse, M., Sardar, A., Lohse, M., Evers, V.: Behave-ii: the revised set of measures to assess users\u2019 attitudinal and behavioral responses to a social robot. Int. J. Soc. Robot. 5, 379\u2013388 (2013)","journal-title":"Int. J. Soc. Robot."},{"key":"2318_CR75","doi-asserted-by":"crossref","unstructured":"Carpinella, C.\u00a0M., Wyman, A.\u00a0B., Perez, M.\u00a0A., Stroessner, S.\u00a0J., The robotic social attributes scale (rosas) development and validation. In: Proceedings of the 2017 ACM\/IEEE International Conference on human-robot interaction, pp.\u00a0254\u2013262. (2017)","DOI":"10.1145\/2909824.3020208"},{"issue":"12","key":"2318_CR76","doi-asserted-by":"publisher","first-page":"1476","DOI":"10.1016\/j.robot.2013.07.007","volume":"61","author":"MM De Graaf","year":"2013","unstructured":"De Graaf, M.M., Allouch, S.B.: Exploring influencing variables for the acceptance of social robots. Robot. Auton. Syst. 61(12), 1476\u20131486 (2013)","journal-title":"Robot. Auton. Syst."},{"key":"2318_CR77","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.ijhcs.2016.02.004","volume":"90","author":"\u00c1 Castro-Gonz\u00e1lez","year":"2016","unstructured":"Castro-Gonz\u00e1lez, \u00c1., Admoni, H., Scassellati, B.: Effects of form and motion on judgments of social robots\u2019 animacy, likability, trustworthiness and unpleasantness. Int. J. Hum Comput Stud. 90, 27\u201338 (2016)","journal-title":"Int. J. Hum Comput Stud."},{"key":"2318_CR78","unstructured":"Average human height by country. https:\/\/en.wikipedia.org\/~wiki\/~Average_human_height_by_country. Accessed: 2023"},{"issue":"2","key":"2318_CR79","doi-asserted-by":"publisher","first-page":"e12629","DOI":"10.2196\/12629","volume":"6","author":"CR Crowell","year":"2019","unstructured":"Crowell, C.R., Deska, J.C., Villano, M., Zenk, J., Roddy, J.T.: Anthropomorphism of robots: study of appearance and agency. JMIR Hum. Factors 6(2), e12629 (2019)","journal-title":"JMIR Hum. Factors"}],"container-title":["Journal of Intelligent &amp; Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-025-02318-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-025-02318-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-025-02318-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T09:02:04Z","timestamp":1768035724000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-025-02318-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,7]]},"references-count":79,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["2318"],"URL":"https:\/\/doi.org\/10.1007\/s10846-025-02318-0","relation":{},"ISSN":["1573-0409"],"issn-type":[{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,7]]},"assertion":[{"value":"16 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Alessandro Rizzo is a Senior Editor at Large of the Journal of Intelligent and Robotic Systems. The authors declare no additional conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"The experiment protocol received ethical approval (protocol number: 90584\/2023) from the Politecnico di Torino\u2019s ethics committee.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"The authors affirm that human research participants provided informed consent for publication of the image in Figure 3.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to publish"}}],"article-number":"110"}}