{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T19:12:30Z","timestamp":1775934750122,"version":"3.50.1"},"reference-count":74,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T00:00:00Z","timestamp":1745107200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T00:00:00Z","timestamp":1745107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2046955"],"award-info":[{"award-number":["2046955"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1937957"],"award-info":[{"award-number":["1937957"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1937957"],"award-info":[{"award-number":["1937957"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2019844"],"award-info":[{"award-number":["2019844"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2046955"],"award-info":[{"award-number":["2046955"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-18-2243"],"award-info":[{"award-number":["N00014-18-2243"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["E2061621"],"award-info":[{"award-number":["E2061621"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Auton Robot"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We present an approach to ensure safe and deadlock-free navigation for decentralized multi-robot systems operating in constrained environments, including doorways and intersections. Although many solutions have been proposed that ensure safety and resolve deadlocks, optimally preventing deadlocks in a minimally invasive and decentralized fashion remains an open problem. We first formalize the objective as a non-cooperative, non-communicative, partially observable multi-robot navigation problem in constrained spaces with multiple conflicting agents, which we term as social mini-games. Formally, we solve a discrete-time optimal receding horizon control problem leveraging control barrier functions for safe long-horizon planning. Our approach to ensuring liveness rests on the insight that\n                    <jats:italic>there exists barrier certificates that allow each robot to preemptively perturb their state in a minimally-invasive fashion onto liveness sets i.e. states where robots are deadlock-free<\/jats:italic>\n                    . We evaluate our approach in simulation as well on physical robots using F1\/10 robots, a Clearpath Jackal, as well as a Boston Dynamics Spot in a doorway, hallway, and corridor intersection scenario. Compared to both fully decentralized and centralized approaches with and without deadlock resolution capabilities, we demonstrate that our approach results in safer, more efficient, and smoother navigation, based on a comprehensive set of metrics including success rate, collision rate, stop time, change in velocity, path deviation, time-to-goal, and flow rate.\n                  <\/jats:p>","DOI":"10.1007\/s10514-025-10194-8","type":"journal-article","created":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T00:12:42Z","timestamp":1745107962000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Deadlock-free, safe, and decentralized multi-robot navigation in social mini-games via discrete-time control barrier functions"],"prefix":"10.1007","volume":"49","author":[{"given":"Rohan","family":"Chandra","sequence":"first","affiliation":[]},{"given":"Vrushabh","family":"Zinage","sequence":"additional","affiliation":[]},{"given":"Efstathios","family":"Bakolas","sequence":"additional","affiliation":[]},{"given":"Peter","family":"Stone","sequence":"additional","affiliation":[]},{"given":"Joydeep","family":"Biswas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,20]]},"reference":[{"key":"10194_CR1","doi-asserted-by":"crossref","unstructured":"Long, P., Fan, T., Liao, X., Liu, W., Zhang, H., & Pan, J. (2018). \u201cTowards optimally decentralized multi-robot collision avoidance via deep reinforcement learning,\u201d in 2018 IEEE international conference on robotics and automation (ICRA), pp.\u00a06252\u20136259, IEEE.","DOI":"10.1109\/ICRA.2018.8461113"},{"key":"10194_CR2","doi-asserted-by":"crossref","unstructured":"Chen, Y.\u00a0F., Liu, M., Everett, M., & How, J.\u00a0P. (2017). \u201cDecentralized non-communicating multiagent collision avoidance with deep reinforcement learning,\u201d in 2017 IEEE international conference on robotics and automation (ICRA), pp.\u00a0285\u2013292, IEEE.","DOI":"10.1109\/ICRA.2017.7989037"},{"key":"10194_CR3","doi-asserted-by":"publisher","first-page":"10357","DOI":"10.1109\/ACCESS.2021.3050338","volume":"9","author":"M Everett","year":"2021","unstructured":"Everett, M., Chen, Y. F., & How, J. P. (2021). Collision avoidance in pedestrian-rich environments with deep reinforcement learning. IEEE Access, 9, 10357\u201310377.","journal-title":"IEEE Access"},{"key":"10194_CR4","doi-asserted-by":"crossref","unstructured":"Everett, M., Chen, Y.\u00a0F., & How, J.\u00a0P., (2018). \u201cMotion planning among dynamic, decision-making agents with deep reinforcement learning,\u201d in 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp.\u00a03052\u20133059, IEEE.","DOI":"10.1109\/IROS.2018.8593871"},{"key":"10194_CR5","doi-asserted-by":"crossref","unstructured":"Dergachev, S., & Yakovlev, K., (2021). \u201cDistributed multi-agent navigation based on reciprocal collision avoidance and locally confined multi-agent path finding,\u201d in 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE), pp.\u00a01489\u20131494, IEEE.","DOI":"10.1109\/CASE49439.2021.9551564"},{"key":"10194_CR6","doi-asserted-by":"crossref","unstructured":"Kamenev, A., Wang, L., Bohan, O.\u00a0B., Kulkarni, I., Kartal, B., Molchanov, A., Birchfield, S., Nist\u00e9r, D., & Smolyanskiy, N. (2022). \u201cPredictionnet: Real-time joint probabilistic traffic prediction for planning, control, and simulation,\u201d in 2022 International Conference on Robotics and Automation (ICRA), pp.\u00a08936\u20138942, IEEE.","DOI":"10.1109\/ICRA46639.2022.9812223"},{"issue":"1","key":"10194_CR7","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s10514-021-10024-7","volume":"46","author":"S Le Cleac\u2019h","year":"2022","unstructured":"Le Cleac\u2019h, S., Schwager, M., & Manchester, Z. (2022). Algames: a fast augmented lagrangian solver for constrained dynamic games. Autonomous Robots, 46(1), 201\u2013215.","journal-title":"Autonomous Robots"},{"key":"10194_CR8","doi-asserted-by":"crossref","unstructured":"Davis, B., Karamouzas, I., & Guy, S.\u00a0J. (2019). \u201cNh-ttc: A gradient-based framework for generalized anticipatory collision avoidance,\u201d arXiv preprint arXiv:1907.05945.","DOI":"10.15607\/RSS.2020.XVI.078"},{"key":"10194_CR9","unstructured":"Chandra, R., Menon, R., Sprague, Z., Anantula, A., & Biswas, J. (2023). \u201cDecentralized social navigation with non-cooperative robots via bi-level optimization,\u201d arXiv preprint arXiv:2306.08815."},{"key":"10194_CR10","unstructured":"Chen, Y., Guo, M., & Li, Z. (2022). \u201cRecursive feasibility and deadlock resolution in mpc-based multi-robot trajectory generation,\u201d arXiv preprint arXiv:2202.06071."},{"key":"10194_CR11","doi-asserted-by":"crossref","unstructured":"Alonso-Mora, J., Breitenmoser, A., Rufli, M., Beardsley, P., & Siegwart, R. (2013). \u201cOptimal reciprocal collision avoidance for multiple non-holonomic robots,\u201d in Distributed Autonomous Robotic Systems: The 10th International Symposium, pp.\u00a0203\u2013216, Springer.","DOI":"10.1007\/978-3-642-32723-0_15"},{"issue":"3","key":"10194_CR12","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1109\/TRO.2017.2659727","volume":"33","author":"L Wang","year":"2017","unstructured":"Wang, L., Ames, A. D., & Egerstedt, M. (2017). Safety barrier certificates for collisions-free multirobot systems. IEEE Trans Robotics, 33(3), 661\u2013674.","journal-title":"IEEE Trans Robotics"},{"key":"10194_CR13","unstructured":"Grover, J., Liu, C., & Sycara, K. (2016). \u201cThe before, during, and after of multi-robot deadlock,\u201d The International Journal of Robotics Research, p.\u00a002783649221074718."},{"key":"10194_CR14","doi-asserted-by":"crossref","unstructured":"Arul, S.\u00a0H., Park, J.\u00a0J., & Manocha, D. (2023). \u201cDs-mpepc: Safe and deadlock-avoiding robot navigation in cluttered dynamic scenes,\u201d arXiv preprint arXiv:2303.10133.","DOI":"10.1109\/IROS55552.2023.10341869"},{"key":"10194_CR15","doi-asserted-by":"crossref","unstructured":"\u015eenba\u015flar, B., H\u00f6nig, W., & Ayanian, N. (2023).\u201cRlss: real-time, decentralized, cooperative, networkless multi-robot trajectory planning using linear spatial separations,\u201d Autonomous Robots, pp.\u00a01\u201326.","DOI":"10.1007\/s10514-023-10104-w"},{"key":"10194_CR16","unstructured":"Yang, Y., & Wang, J. (2020). \u201cAn overview of multi-agent reinforcement learning from game theoretical perspective,\u201d arXiv preprint arXiv:2011.00583."},{"key":"10194_CR17","doi-asserted-by":"crossref","unstructured":"Chandra, R., Maligi, R., Anantula, A., & Biswas, J. (2022). \u201cSocialmapf: Optimal and efficient multi-agent path finding with strategic agents for social navigation,\u201d arXiv preprint arXiv:2210.08390.","DOI":"10.1109\/LRA.2023.3265169"},{"key":"10194_CR18","doi-asserted-by":"crossref","unstructured":"Van Den\u00a0Berg, J., Guy, S.\u00a0J., Lin, M., & Manocha, D. (2011). \u201cReciprocal n-body collision avoidance,\u201d in Robotics Research: The 14th International Symposium ISRR, pp.\u00a03\u201319, Springer.","DOI":"10.1007\/978-3-642-19457-3_1"},{"issue":"2","key":"10194_CR19","doi-asserted-by":"publisher","first-page":"9746","DOI":"10.1016\/j.ifacol.2020.12.2644","volume":"53","author":"J Grover","year":"2020","unstructured":"Grover, J., Liu, C., & Sycara, K. (2020). Why does symmetry cause deadlocks? IFAC-PapersOnLine, 53(2), 9746\u20139753.","journal-title":"IFAC-PapersOnLine"},{"issue":"2","key":"10194_CR20","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1109\/LRA.2017.2656241","volume":"2","author":"D Zhou","year":"2017","unstructured":"Zhou, D., Wang, Z., Bandyopadhyay, S., & Schwager, M. (2017). Fast, on-line collision avoidance for dynamic vehicles using buffered voronoi cells. IEEE Robotics and Automation Letters, 2(2), 1047\u20131054.","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"2","key":"10194_CR21","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1109\/MITS.2020.3014074","volume":"13","author":"Z Zhong","year":"2020","unstructured":"Zhong, Z., Nejad, M., & Lee, E. E. (2020). Autonomous and semiautonomous intersection management: A survey. IEEE Intelligent Transportation Systems Magazine, 13(2), 53\u201370.","journal-title":"IEEE Intelligent Transportation Systems Magazine"},{"key":"10194_CR22","unstructured":"Au, T.-C., Zhang, S., & Stone, P. (2015). \u201cAutonomous intersection management for semi-autonomous vehicles,\u201d in The Routledge handbook of transportation, pp.\u00a088\u2013104, Routledge."},{"key":"10194_CR23","doi-asserted-by":"crossref","unstructured":"Carlino, D., Boyles, S.\u00a0D., & Stone, P. (2013). \u201cAuction-based autonomous intersection management,\u201d in 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), pp.\u00a0529\u2013534, IEEE.","DOI":"10.1109\/ITSC.2013.6728285"},{"key":"10194_CR24","doi-asserted-by":"crossref","unstructured":"Suriyarachchi, N., Chandra, R., Baras, J.\u00a0S., & Manocha, D. (2022). \u201cGameopt: Optimal real-time multi-agent planning and control for dynamic intersections,\u201d in 2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC), pp.\u00a02599\u20132606, IEEE.","DOI":"10.1109\/ITSC55140.2022.9921968"},{"key":"10194_CR25","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1613\/jair.2502","volume":"31","author":"K Dresner","year":"2008","unstructured":"Dresner, K., & Stone, P. (2008). A multiagent approach to autonomous intersection management. J Artificial Intelligence Res, 31, 591\u2013656.","journal-title":"J Artificial Intelligence Res"},{"issue":"5","key":"10194_CR26","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1007\/s10514-022-10039-8","volume":"46","author":"X Xiao","year":"2022","unstructured":"Xiao, X., Liu, B., Warnell, G., & Stone, P. (2022). Motion planning and control for mobile robot navigation using machine learning: a survey. Autonomous Robots, 46(5), 569\u2013597.","journal-title":"Autonomous Robots"},{"key":"10194_CR27","unstructured":"Ross, S., Gordon, G.\u00a0J., & Bagnell, J.\u00a0A. (2011). \u201cA reduction of imitation learning and structured prediction to no-regret online learning\u201d."},{"key":"10194_CR28","unstructured":"Ross, S., Gordon, G.\u00a0J., & Bagnell, J.\u00a0A. (2011). \u201cA reduction of imitation learning and structured prediction to no-regret online learning\u201d."},{"key":"10194_CR29","doi-asserted-by":"crossref","unstructured":"Daftry, S., Bagnell, J.\u00a0A., & Hebert, M. (2016). \u201cLearning transferable policies for monocular reactive mav control\u201d.","DOI":"10.1007\/978-3-319-50115-4_1"},{"key":"10194_CR30","unstructured":"Ziebart, B.\u00a0D., Maas, A.\u00a0L., Bagnell, J.\u00a0A., Dey, A.\u00a0K. et\u00a0al. (2008). \u201cMaximum entropy inverse reinforcement learning.,\u201d in Aaai, vol.\u00a08, pp.\u00a01433\u20131438, Chicago, IL, USA."},{"key":"10194_CR31","doi-asserted-by":"crossref","unstructured":"Mehr, N., Wang, M., Bhatt, M., & Schwager, M. (2023). \u201cMaximum-entropy multi-agent dynamic games: Forward and inverse solutions,\u201d IEEE Transactions on Robotics.","DOI":"10.1109\/TRO.2022.3232300"},{"key":"10194_CR32","doi-asserted-by":"crossref","unstructured":"Gonon, D., & Billard, A. (2023). \u201cInverse reinforcement learning of pedestrian\u2013robot coordination,\u201d IEEE Robotics and Automation Letters.","DOI":"10.1109\/LRA.2023.3289770"},{"key":"10194_CR33","unstructured":"Sutton, R.\u00a0S., & Barto, A.\u00a0G. (2018). Reinforcement Learning: An Introduction. MIT Press."},{"key":"10194_CR34","unstructured":"Ho, J., & Ermon, S. (2016). \u201cGenerative adversarial imitation learning,\u201d in  Proceedings of the 30th International Conference on Neural Information Processing Systems, pp.\u00a04572\u20134580."},{"key":"10194_CR35","unstructured":"Kostrikov, I., Nachum, O., & Tompson, J. (2019). \u201cImitation learning via off-policy distribution matching\u201d."},{"key":"10194_CR36","unstructured":"Dadashi, R., Hussenot, L., Geist, M., & Pietquin, O. (2020). \u201cPrimal wasserstein imitation learning,\u201d CoRR, vol. arxiv:2006.04678."},{"key":"10194_CR37","first-page":"1","volume":"99","author":"B Zheng","year":"2022","unstructured":"Zheng, B., Verma, S., Zhou, J., Tsang, I. W., & Chen, F. (2022). Imitation learning: Progress, taxonomies and challenges. IEEE Transactions on Neural Networks and Learning Systems, 99, 1\u201316.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"10194_CR38","doi-asserted-by":"crossref","unstructured":"Torabi, F., Warnell, G., & Stone, P. (2018). \u201cBehavioral cloning from observation,\u201d arXiv preprint arXiv:1805.01954.","DOI":"10.24963\/ijcai.2018\/687"},{"key":"10194_CR39","doi-asserted-by":"crossref","unstructured":"Karnan, H., Torabi, F., Warnell, G., & Stone, P. (2022). \u201cAdversarial imitation learning from video using a state observer,\u201d in 2022 International Conference on Robotics and Automation (ICRA), pp.\u00a02452\u20132458, IEEE.","DOI":"10.1109\/ICRA46639.2022.9811570"},{"issue":"4","key":"10194_CR40","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.1109\/TRO.2020.3047521","volume":"37","author":"M Wang","year":"2021","unstructured":"Wang, M., Wang, Z., Talbot, J., Gerdes, J. C., & Schwager, M. (2021). Game-theoretic planning for self-driving cars in multivehicle competitive scenarios. IEEE Transactions on Robotics, 37(4), 1313\u20131325.","journal-title":"IEEE Transactions on Robotics"},{"key":"10194_CR41","doi-asserted-by":"crossref","unstructured":"Britzelmeier, A., Dreves, A., & Gerdts, M. (2019). \u201cNumerical solution of potential games arising in the control of cooperative automatic vehicles,\u201d in  2019 Proceedings of the conference on control and its applications, pp.\u00a038\u201345, SIAM.","DOI":"10.1137\/1.9781611975758.7"},{"key":"10194_CR42","doi-asserted-by":"crossref","unstructured":"Fisac, J.\u00a0F., Bronstein, E., Stefansson, E., Sadigh, D., Sastry, S.\u00a0S., & Dragan, A.\u00a0D. (2019). \u201cHierarchical game-theoretic planning for autonomous vehicles,\u201d in 2019 International conference on robotics and automation (ICRA), pp.\u00a09590\u20139596, IEEE.","DOI":"10.1109\/ICRA.2019.8794007"},{"key":"10194_CR43","doi-asserted-by":"crossref","unstructured":"Schwarting, W., Pierson, A., Karaman, S., & Rus, D. (2021). \u201cStochastic dynamic games in belief space,\u201d IEEE Transactions on Robotics, pp.\u00a01\u201316.","DOI":"10.1109\/TRO.2021.3075376"},{"key":"10194_CR44","doi-asserted-by":"crossref","unstructured":"Sun, W., Theodorou, E.\u00a0A., & Tsiotras, P. (2015). \u201cGame theoretic continuous time differential dynamic programming,\u201d in 2015 American Control Conference (ACC), pp.\u00a05593\u20135598, IEEE.","DOI":"10.1109\/ACC.2015.7172215"},{"key":"10194_CR45","doi-asserted-by":"crossref","unstructured":"Sun, W., Theodorou, E.\u00a0A., & Tsiotras, P. (2016). \u201cStochastic game theoretic trajectory optimization in continuous time,\u201d in 2016 IEEE 55th Conference on Decision and Control (CDC), pp.\u00a06167\u20136172, IEEE.","DOI":"10.1109\/CDC.2016.7799217"},{"key":"10194_CR46","unstructured":"Morimoto, J., & Atkeson, C.\u00a0G. (2003). \u201cMinimax differential dynamic programming: An application to robust biped walking,\u201d in Advances in neural information processing systems, pp.\u00a01563\u20131570."},{"key":"10194_CR47","doi-asserted-by":"crossref","unstructured":"Fridovich-Keil, D., Ratner, E., Peters, L., Dragan, A.\u00a0D., & Tomlin, C.\u00a0J. (2020). \u201cEfficient iterative linear-quadratic approximations for nonlinear multi-player general-sum differential games,\u201d in 2020 IEEE international conference on robotics and automation (ICRA), pp.\u00a01475\u20131481, IEEE.","DOI":"10.1109\/ICRA40945.2020.9197129"},{"key":"10194_CR48","unstructured":"Di, B., & Lamperski, A. (2018). \u201cDifferential dynamic programming for nonlinear dynamic games,\u201d arXiv preprint arXiv:1809.08302."},{"key":"10194_CR49","doi-asserted-by":"crossref","unstructured":"Di, B., & Lamperski, A. (2019). \u201cNewton\u2019s method and differential dynamic programming for unconstrained nonlinear dynamic games,\u201d in 2019 IEEE 58th Conference on Decision and Control (CDC), pp.\u00a04073\u20134078, IEEE.","DOI":"10.1109\/CDC40024.2019.9029237"},{"key":"10194_CR50","doi-asserted-by":"crossref","unstructured":"Di, B., & Lamperski, A. (2020). \u201cFirst-order algorithms for constrained nonlinear dynamic games,\u201d arXiv preprint arXiv:2001.01826.","DOI":"10.23919\/ACC45564.2020.9147602"},{"key":"10194_CR51","first-page":"709","volume":"4","author":"EA Hansen","year":"2004","unstructured":"Hansen, E. A., Bernstein, D. S., & Zilberstein, S. (2004). Dynamic programming for partially observable stochastic games. AAAI, 4, 709\u2013715.","journal-title":"AAAI"},{"key":"10194_CR52","doi-asserted-by":"crossref","unstructured":"Laumond, J.-P., Sekhavat, S., & Lamiraux, F. (2005). \u201cGuidelines in nonholonomic motion planning for mobile robots,\u201d Robot motion planning and control, pp.\u00a01\u201353.","DOI":"10.1007\/BFb0036070"},{"issue":"5","key":"10194_CR53","doi-asserted-by":"publisher","first-page":"625","DOI":"10.3182\/20100705-3-BE-2011.00104","volume":"43","author":"X Chen","year":"2010","unstructured":"Chen, X., Liu, J., de la Pena, D. M., & Christofides, P. D. (2010). Sequential and iterative distributed model predictive control of nonlinear process systems subject to asynchronous measurements. IFAC Proceedings Volumes, 43(5), 625\u2013630.","journal-title":"IFAC Proceedings Volumes"},{"key":"10194_CR54","doi-asserted-by":"crossref","unstructured":"Ames, A.\u00a0D., Coogan, S., Egerstedt, M., Notomista, G., Sreenath, K., & Tabuada, P. (2019). \u201cControl barrier functions: Theory and applications,\u201d in 2019 18th European control conference (ECC), pp.\u00a03420\u20133431, IEEE.","DOI":"10.23919\/ECC.2019.8796030"},{"key":"10194_CR55","doi-asserted-by":"crossref","unstructured":"Zeng, J., Zhang, B., & Sreenath, K. (2021). \u201cSafety-critical model predictive control with discrete-time control barrier function,\u201d in 2021 American Control Conference (ACC), pp.\u00a03882\u20133889, IEEE.","DOI":"10.23919\/ACC50511.2021.9483029"},{"key":"10194_CR56","unstructured":"Tedrake, R., (2023). Underactuated Robotics."},{"key":"10194_CR57","doi-asserted-by":"crossref","unstructured":"Robey, A., Hu, H., Lindemann, L., Zhang, H., Dimarogonas, D.\u00a0V., Tu, S., & Matni, N. (2020). \u201cLearning control barrier functions from expert demonstrations,\u201d in 2020 59th IEEE Conference on Decision and Control (CDC), pp.\u00a03717\u20133724, IEEE.","DOI":"10.1109\/CDC42340.2020.9303785"},{"key":"10194_CR58","doi-asserted-by":"crossref","unstructured":"Jagtap, P., Pappas, G.\u00a0J., & Zamani, M. (2020). \u201cControl barrier functions for unknown nonlinear systems using gaussian processes,\u201d in 2020 59th IEEE Conference on Decision and Control (CDC), pp.\u00a03699\u20133704, IEEE.","DOI":"10.1109\/CDC42340.2020.9303847"},{"issue":"8","key":"10194_CR59","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.1016\/j.automatica.2014.04.021","volume":"50","author":"JW Grizzle","year":"2014","unstructured":"Grizzle, J. W., Chevallereau, C., Sinnet, R. W., & Ames, A. D. (2014). Models, feedback control, and open problems of 3d bipedal robotic walking. Automatica, 50(8), 1955\u20131988.","journal-title":"Automatica"},{"key":"10194_CR60","doi-asserted-by":"crossref","unstructured":"Roughgarden, T. (2016). Twenty lectures on algorithmic game theory. Cambridge University Press.","DOI":"10.1017\/CBO9781316779309"},{"issue":"2","key":"10194_CR61","doi-asserted-by":"publisher","first-page":"2676","DOI":"10.1109\/LRA.2022.3144516","volume":"7","author":"R Chandra","year":"2022","unstructured":"Chandra, R., & Manocha, D. (2022). Gameplan: Game-theoretic multi-agent planning with human drivers at intersections, roundabouts, and merging. IEEE Robotics and Automation Letters, 7(2), 2676\u20132683.","journal-title":"IEEE Robotics and Automation Letters"},{"key":"10194_CR62","doi-asserted-by":"crossref","unstructured":"Alan, A., Molnar, T.\u00a0G., Ames, A.\u00a0D., & Orosz, G. (2023). \u201cParameterized barrier functions to guarantee safety under uncertainty,\u201d IEEE Control Systems Letters.","DOI":"10.1109\/LCSYS.2023.3285188"},{"key":"10194_CR63","doi-asserted-by":"crossref","unstructured":"Zinage, V., Chandra, R., & Bakolas, E. (2024). \u201cDisturbance observer-based robust integral control barrier functions for nonlinear systems with high relative degree,\u201d in 2024 American Control Conference (ACC), pp.\u00a02470\u20132475, IEEE.","DOI":"10.23919\/ACC60939.2024.10644578"},{"issue":"3","key":"10194_CR64","doi-asserted-by":"publisher","first-page":"887","DOI":"10.1109\/LCSYS.2020.3006764","volume":"5","author":"AD Ames","year":"2020","unstructured":"Ames, A. D., Notomista, G., Wardi, Y., & Egerstedt, M. (2020). Integral control barrier functions for dynamically defined control laws. IEEE control systems letters, 5(3), 887\u2013892.","journal-title":"IEEE control systems letters"},{"key":"10194_CR65","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., & Biegler, L. T. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical programming, 106, 25\u201357.","journal-title":"Mathematical programming"},{"key":"10194_CR66","doi-asserted-by":"crossref","unstructured":"Chen, Y.\u00a0F., Everett, M., Liu, M., & How, J.\u00a0P. (2017). \u201cSocially aware motion planning with deep reinforcement learning,\u201d in 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp.\u00a01343\u20131350, IEEE.","DOI":"10.1109\/IROS.2017.8202312"},{"issue":"4","key":"10194_CR67","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2016\/04\/043402","volume":"2016","author":"A Garcimart\u00edn","year":"2016","unstructured":"Garcimart\u00edn, A., Parisi, D. R., Pastor, J. M., Mart\u00edn-G\u00f3mez, C., & Zuriguel, I. (2016). Flow of pedestrians through narrow doors with different competitiveness. Journal of Statistical Mechanics: Theory and Experiment, 2016(4), 043402.","journal-title":"Journal of Statistical Mechanics: Theory and Experiment"},{"issue":"10","key":"10194_CR68","doi-asserted-by":"publisher","first-page":"P10014","DOI":"10.1088\/1742-5468\/2006\/10\/P10014","volume":"2006","author":"T Kretz","year":"2006","unstructured":"Kretz, T., Gr\u00fcnebohm, A., & Schreckenberg, M. (2006). Experimental study of pedestrian flow through a bottleneck. Journal of Statistical Mechanics: Theory and Experiment, 2006(10), P10014.","journal-title":"Journal of Statistical Mechanics: Theory and Experiment"},{"issue":"2","key":"10194_CR69","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1109\/LRA.2022.3227858","volume":"8","author":"A Patwardhan","year":"2022","unstructured":"Patwardhan, A., Murai, R., & Davison, A. J. (2022). Distributing collaborative multi-robot planning with gaussian belief propagation. IEEE Robotics and Automation Letters, 8(2), 552\u2013559.","journal-title":"IEEE Robotics and Automation Letters"},{"key":"10194_CR70","unstructured":"Zhang, S., Garg, K., & Fan, C. (2023). \u201cNeural graph control barrier functions guided distributed collision-avoidance multi-agent control,\u201d in Conference on robot learning, pp.\u00a02373\u20132392, PMLR."},{"key":"10194_CR71","unstructured":"Qin, Z., Zhang, K., Chen, Y., Chen, J., & Fan, C. (2021). \u201cLearning safe multi-agent control with decentralized neural barrier certificates,\u201d arXiv preprint arXiv:2101.05436."},{"key":"10194_CR72","first-page":"24611","volume":"35","author":"C Yu","year":"2022","unstructured":"Yu, C., Velu, A., Vinitsky, E., Gao, J., Wang, Y., Bayen, A., & Wu, Y. (2022). The surprising effectiveness of ppo in cooperative multi-agent games. Adv Neural Information Processing Systems, 35, 24611\u201324624.","journal-title":"Adv Neural Information Processing Systems"},{"key":"10194_CR73","unstructured":"Liu, I.-J., Yeh, R.A., & Schwing, A.G, (2020). \u201cPic: permutation invariant critic for multi-agent deep reinforcement learning,\u201d in Conference on Robot Learning, pp.\u00a0590\u2013602, PMLR."},{"key":"10194_CR74","unstructured":"Zinage, V., Jha, A., Chandra, R., & Bakolas, E., (2024). \u201cDecentralized safe and scalable multi-agent control under limited actuation,\u201d arXiv preprint arXiv:2409.09573."}],"container-title":["Autonomous Robots"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10514-025-10194-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10514-025-10194-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10514-025-10194-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,28]],"date-time":"2025-06-28T01:32:02Z","timestamp":1751074322000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10514-025-10194-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,20]]},"references-count":74,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["10194"],"URL":"https:\/\/doi.org\/10.1007\/s10514-025-10194-8","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3979309\/v1","asserted-by":"object"}]},"ISSN":["0929-5593","1573-7527"],"issn-type":[{"value":"0929-5593","type":"print"},{"value":"1573-7527","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,20]]},"assertion":[{"value":"22 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 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":"This work was conducted in full accordance with the principles highlighted in the Committee on Publication Ethics. Our experiments involving cameras, lidars and any other sensors did not capture or record identifiable information of other humans. Lastly, the authors declare that there are no financial or personal Conflict of interest regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Considerations and Conflict of interest"}}],"article-number":"12"}}