{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T11:03:39Z","timestamp":1775819019583,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,3,23]],"date-time":"2015-03-23T00:00:00Z","timestamp":1427068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"STRANDS","award":["600623"],"award-info":[{"award-number":["600623"]}]},{"DOI":"10.13039\/100010269","name":"Wellcome Trust","doi-asserted-by":"publisher","award":["WT089367AIA"],"award-info":[{"award-number":["WT089367AIA"]}],"id":[{"id":"10.13039\/100010269","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>In this paper we propose a probabilistic sequential model of Human-Robot Spatial Interaction (HRSI) using a well-established Qualitative Trajectory Calculus (QTC) to encode HRSI between a human and a mobile robot in a meaningful, tractable, and systematic manner. Our key contribution is to utilise QTC as a state descriptor and model HRSI as a probabilistic sequence of such states. Apart from the sole direction of movements of human and robot modelled by QTC, attributes of HRSI like proxemics and velocity profiles play vital roles for the modelling and generation of HRSI behaviour. In this paper, we particularly present how the concept of proxemics can be embedded in QTC to facilitate richer models. To facilitate reasoning on HRSI with qualitative representations, we show how we can combine the representational power of QTC with the concept of proxemics in a concise framework, enriching our probabilistic representation by implicitly modelling distances. We show the appropriateness of our sequential model of QTC by encoding different HRSI behaviours observed in two spatial interaction experiments. We classify these encounters, creating a comparative measurement, showing the representational capabilities of the model.<\/jats:p>","DOI":"10.3390\/robotics4010063","type":"journal-article","created":{"date-parts":[[2015,3,23]],"date-time":"2015-03-23T12:17:00Z","timestamp":1427113020000},"page":"63-102","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["A Computational Model of Human-Robot Spatial Interactions Based on a Qualitative Trajectory Calculus"],"prefix":"10.3390","volume":"4","author":[{"given":"Christian","family":"Dondrup","sequence":"first","affiliation":[{"name":"School of Computer Science, University of Lincoln, Brayford Pool, LN6 7TS Lincoln, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola","family":"Bellotto","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Lincoln, Brayford Pool, LN6 7TS Lincoln, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc","family":"Hanheide","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Lincoln, Brayford Pool, LN6 7TS Lincoln, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kerstin","family":"Eder","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Clifton, BS8 1UB Bristol, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ute","family":"Leonards","sequence":"additional","affiliation":[{"name":"School of Experimental Psychology, University of Bristol, 12A Priory Road, Clifton, BS8 1TU Bristol, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Steinfeld, A., Fong, T., Kaber, D., Lewis, M., Scholtz, J., Schultz, A.C., and Goodrich, M. (2006, January 2\u20133). Common metrics for human-robot interaction. Proceeding of the 1st ACM SIGCHI\/SIGART Conference on Human-Robot Interaction-HRI \u201906, Salt Lake City, UT, USA.","DOI":"10.1145\/1121241.1121249"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/21.44033","article-title":"Real-time obstacle avoidance for fast mobile robots","volume":"19","author":"Borenstein","year":"1989","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_3","unstructured":"Simmons, R. (1996, January 22\u201328). The curvature-velocity method for local obstacle avoidance. Proceeding of the IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1109\/TRO.2007.904911","article-title":"A Human Aware Mobile Robot Motion Planner","volume":"23","author":"Sisbot","year":"2007","journal-title":"IEEE Trans. Robot."},{"key":"ref_5","unstructured":"Yoda, M., and Shiota, Y. (1996, January 11\u201314). Analysis of human avoidance motion for application to robot. Proceeding of the 5th IEEE International Workshop on Robot and Human Communication, RO-MAN\u201996, Tsukuba, Japan."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Feil-Seifer, D.J., and Matari\u0107, M.J. (2011, January 24\u201327). People-Aware Navigation For Goal-Oriented Behavior Involving a Human Partner. Proceedings of the International Conference on Development and Learning, Frankfurt am Main, Germany.","DOI":"10.1109\/DEVLRN.2011.6037331"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.neulet.2005.06.052","article-title":"Timing and distance characteristics of interpersonal coordination during locomotion","volume":"389","author":"Ducourant","year":"2005","journal-title":"Neurosci. Lett."},{"key":"ref_8","unstructured":"Hall, E.T. (1969). The Hidden Dimension, Anchor Books."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1726","DOI":"10.1016\/j.robot.2013.05.007","article-title":"Human-aware robot navigation: A survey","volume":"61","author":"Kruse","year":"2013","journal-title":"Robot. Auton. Syst."},{"key":"ref_10","unstructured":"Peters, A. (2011, January 6\u20139). Small movements as communicational cues in HRI. Proceeding of the 6th ACM SIGCHI\/SIGART Conference on Human-Robot Interaction-HRI \u201911, Lausanne, Switzerland."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hanheide, M., Peters, A., and Bellotto, N. (2012, January 9\u201313). Analysis of human-robot Spatial behaviour applying a qualitative trajectory calculus. Proceeding of the RO-MAN, Paris, France.","DOI":"10.1109\/ROMAN.2012.6343831"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bellotto, N., Hanheide, M., and van de Weghe, N. (2013, January 27\u201329). Qualitative Design and Implementation of Human-Robot Spatial Interactions. Proceeding of the International Conference on Social Robotics (ICSR), Bristol, UK.","DOI":"10.1007\/978-3-319-02675-6_33"},{"key":"ref_13","unstructured":"Dondrup, C., Bellotto, N., and Hanheide, M. (2014, January 24\u201326). A Probabilistic Model of Human-Robot Spatial Interaction using a Qualitative Trajectory Calculus. Proceeding of the 2014 AAAI Spring Symposium Series, Palo Alto, CA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Dondrup, C., Bellotto, N., and Hanheide, M. (2014, January 25\u201329). Social distance augmented qualitative trajectory calculus for Human-Robot Spatial Interaction. Proceeding of the 23rd IEEE International Symposium on Robot and Human Interactive Communication, 2014 RO-MAN, Edinburgh, UK.","DOI":"10.1109\/ROMAN.2014.6926305"},{"key":"ref_15","unstructured":"Van de Weghe, N. (2004). Representing and Reasoning about Moving Objects: A Qualitative Approach. [Ph.D. Thesis, Ghent University]."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pacchierotti, E., Christensen, H.I., and Jensfelt, P. (2006, January 6\u20138). Evaluation of Passing Distance for Social Robots. Proceeding of the 15th IEEE International Symposium on Robot and Human Interactive Communication, RO-MAN 2006, Hafield, UK.","DOI":"10.1109\/ROMAN.2006.314436"},{"key":"ref_17","unstructured":"Lichtenth\u00e4ler, C., Peters, A., Griffiths, S., and Kirsch, A. (2013). Social Robotics, Springer International Publishing."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/S1574-6526(07)03013-1","article-title":"Chapter 13 Qualitative Spatial Representation and Reasoning","volume":"Volume 3","author":"Lifschitz","year":"2008","journal-title":"Handbook of Knowledge Representation"},{"key":"ref_19","unstructured":"Torta, E., Cuijpers, R.H., Juola, J.F., and van der Pol, D. (2011). Social Robotics, Springer."},{"key":"ref_20","unstructured":"Aldebaran Robotics NAO robot: intelligent and friendly companion. Available online: https:\/\/www.aldebaran.com\/en\/humanoid-robot\/nao-robot."},{"key":"ref_21","unstructured":"Walters, M.L., Oskoei, M.A., Syrdal, D.S., and Dautenhahn, K. (August, January 31). A Long-Term Human-Robot Proxemic Study. Proceeding of the 20th IEEE International Symposium on Robot and Human Interactive Communication, Atlanta, GA, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Tranberg Hansen, S., Svenstrup, M., Andersen, H.J., and Bak, T. (October, January 27). Adaptive human aware navigation based on motion pattern analysis. Proceeding of the 18th IEEE International Symposium on Robot and Human Interactive Communication, RO-MAN 2009, Toyama, Japan.","DOI":"10.1109\/ROMAN.2009.5326212"},{"key":"ref_23","unstructured":"Kirby, R., Simmons, R., and Forlizzi, J. (October, January 27). COMPANION: A Constraint-Optimizing Method for Person-Acceptable Navigation. Proceeding of the 18th IEEE International Symposium on Robot and Human Interactive Communication, Toyama, Japan."},{"key":"ref_24","unstructured":"Lu, D.V., Allan, D.B., and Smart, W.D. (2013). Social Robotics, Springer International Publishing."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Scandolo, L., and Fraichard, T. (2011, January 9\u201313). An anthropomorphic navigation scheme for dynamic scenarios. Proceeding of the 2011 IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China.","DOI":"10.1109\/ICRA.2011.5979772"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Svenstrup, M., Bak, T., and Andersen, H.J. (2010, January 18\u201322). Trajectory planning for robots in dynamic human environments. Proceeding of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5651531"},{"key":"ref_27","unstructured":"Martinez-Garcia, E.A., Akihisa, O., and Yuta, S. (2005, January 12\u201315). Crowding and guiding groups of humans by teams of mobile robots. Proceeding of the 2005 IEEE Workshop on Advanced Robotics and its Social Impacts, Nagoya, Japan."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Tamura, Y., Dai Le, P., Hitomi, K., Chandrasiri, N.P., Bando, T., Yamashita, A., and Asama, H. (2012, January 7\u201312). Development of pedestrian behavior model taking account of intention. Proceeding of the 2012 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vilamoura, Algarve, Portugal.","DOI":"10.1109\/IROS.2012.6385599"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Feil-Seifer, D., and Mataric, M. (2011, January 24\u201327). People-aware navigation for goal-oriented behavior involving a human partner. Proceeding of the 2011 IEEE International Conference on Development and Learning (ICDL), Frankfurt am Main, Germany.","DOI":"10.1109\/DEVLRN.2011.6037331"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Garrido, J., and Yu, W. (2014, January 25\u201329). Trajectory generation in joint space using modified hidden Markov model. Proceedingof the 23rd IEEE International Symposium on Robot and Human Interactive Communication, Edinburgh, UK.","DOI":"10.1109\/ROMAN.2014.6926290"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Avrunin, E., and Simmons, R. (2014, January 25\u201329). Socially-appropriate approach paths using human data. Proceeding of the 23rd IEEE International Symposium on Robot and Human Interactive Communication, Edinburgh, UK.","DOI":"10.1109\/ROMAN.2014.6926389"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kushleyev, A., and Likhachev, M. (2009, January 12\u201317). Time-bounded lattice for efficient planning in dynamic environments. Proceeding of the IEEE International Conference on Robotics and Automation, ICRA\u201909, Kobe, Japan.","DOI":"10.1109\/ROBOT.2009.5152860"},{"key":"ref_33","unstructured":"Tadokoro, S., Hayashi, M., Manabe, Y., Nakami, Y., and Takamori, T. (1995, January 5\u20139). On motion planning of mobile robots which coexist and cooperate with human. Proceeding of the 1995 IEEE\/RSJ International Conference on Intelligent Robots and Systems 95. Human Robot Interaction and Cooperative Robots, Pittsburgh, PA, USA."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ohki, T., Nagatani, K., and Yoshida, K. (2010, January 18\u201322). Collision avoidance method for mobile robot considering motion and personal spaces of evacuees. Proceeding of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5653217"},{"key":"ref_35","unstructured":"Bennewitz, M. (2004). Mobile robot navigation in dynamic environments. [Ph.D. Thesis, University of Freiburg]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1177\/0278364904048962","article-title":"Learning motion patterns of people for compliant robot motion","volume":"24","author":"Bennewitz","year":"2005","journal-title":"Int. J. Robot. Res."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Ziebart, B.D., Ratliff, N., Gallagher, G., Mertz, C., Peterson, K., Bagnell, J.A., Hebert, M., Dey, A.K., and Srinivasa, S. (2009, January 11\u201315). Planning-based prediction for pedestrians. Proceeding of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, IROS 2009, St. Louis, MO, USA.","DOI":"10.1109\/IROS.2009.5354147"},{"key":"ref_38","unstructured":"Chung, S.Y., and Huang, H.P. (2010, January 18\u201322). A mobile robot that understands pedestrian spatial behaviors. Proceeding of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan."},{"key":"ref_39","unstructured":"Randell, D.A., Cui, Z., and Cohn, A.G. (, January 25\u201329,). A spatial logic based on regions and connection. Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR\u201992), Cambridge, MA."},{"key":"ref_40","unstructured":"Strands EU FP7 Project, No. 600623. Available online: https:\/\/github.com\/strands-project\/strands_qsr_lib."},{"key":"ref_41","unstructured":"Delafontaine, M. (2011). Modelling and Analysing Moving Objects and Travelling Subjects: Bridging Theory and Practice. [Ph.D. Thesis, Department of Geography, Ghent University]."},{"key":"ref_42","unstructured":"Fink, G.A. (2008). Markov Models for Pattern Recognition, Springer-Verlag."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Dondrup, C., Lichtenth\u00e4ler, C., and Hanheide, M. (2014, January 3\u20136). Hesitation signals in human-robot head-on encounters: A pilot study. Proceedings of the 2014 ACM\/IEEE International Conference on Human-Robot Interaction, ACM, Bielefeld, Germany.","DOI":"10.1145\/2559636.2559817"},{"key":"ref_44","unstructured":"Lincoln Centre for Autonomous Systems Research Raw Study Data. Available online: https:\/\/github.com\/LCAS\/data."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/100.580977","article-title":"The dynamic window approach to collision avoidance","volume":"4","author":"Fox","year":"1997","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_46","unstructured":"Thrun, S., Burgard, W., and Fox, D. (2005). Probabilistic Robotics, MIT Press."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"De Boor, C. (1978). A Practical Guide to Splines, Springer.","DOI":"10.1007\/978-1-4612-6333-3"},{"key":"ref_48","unstructured":"Strands EU FP7 Project, No. 600623. Available online: http:\/\/strands-project.eu."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/4\/1\/63\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:43:51Z","timestamp":1760215431000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/4\/1\/63"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,23]]},"references-count":48,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["robotics4010063"],"URL":"https:\/\/doi.org\/10.3390\/robotics4010063","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,23]]}}}