{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:48:41Z","timestamp":1760230121174,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T00:00:00Z","timestamp":1657497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon 2020 Research and Innovation Program PATHOCERT\u2014Pathogen Contamination Emergency Response Technologies","award":["883484"],"award-info":[{"award-number":["883484"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work, we develop a reactive algorithm for autonomous exploration of indoor, unknown environments for multiple autonomous multi-rotor robots. The novelty of our approach rests on a two-level control architecture comprised of an Artificial-Harmonic Potential Field (AHPF) for navigation and a low-level tracking controller. Owing to the AHPF properties, the field is provably safe while guaranteeing workspace exploration. At the same time, the low-level controller ensures safe tracking of the field through velocity commands to the drone\u2019s attitude controller, which handles the challenging non-linear dynamics. This architecture leads to a robust framework for autonomous exploration, which is extended to a multi-agent approach for collaborative navigation. The integration of approximate techniques for AHPF acquisition further improves the computational complexity of the proposed solution. The control scheme and the technical results are validated through high-fidelity simulations, where all aspects, from sensing and dynamics to control, are incorporated, demonstrating the capacity of our method in successfully tackling the multi-agent exploration task.<\/jats:p>","DOI":"10.3390\/s22145194","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T03:50:36Z","timestamp":1657597836000},"page":"5194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Indoor Visual Exploration with Multi-Rotor Aerial Robotic Vehicles"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4669-3204","authenticated-orcid":false,"given":"Panagiotis","family":"Rousseas","sequence":"first","affiliation":[{"name":"Control Systems Laboratory, National Technical University of Athens, 15772 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4045-4715","authenticated-orcid":false,"given":"George C.","family":"Karras","sequence":"additional","affiliation":[{"name":"Control Systems Laboratory, National Technical University of Athens, 15772 Athens, Greece"},{"name":"Department of Informatics and Telecommunications, University of Thessaly, 35100 Lamia, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9850-2540","authenticated-orcid":false,"given":"Charalampos P.","family":"Bechlioulis","sequence":"additional","affiliation":[{"name":"Control Systems Laboratory, National Technical University of Athens, 15772 Athens, Greece"},{"name":"Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1229-3029","authenticated-orcid":false,"given":"Kostas J.","family":"Kyriakopoulos","sequence":"additional","affiliation":[{"name":"Control Systems Laboratory, National Technical University of Athens, 15772 Athens, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,11]]},"reference":[{"key":"ref_1","unstructured":"Stanford Artificial Intelligence Laboratory (2022). Robotic Operating System, Stanford Artificial Intelligence Laboratory."},{"key":"ref_2","unstructured":"Thrun, S., Burgard, W., and Fox, D. (2005). Probabilistic Robotics (Intelligent Robotics and Autonomous Agents), The MIT Press."},{"key":"ref_3","unstructured":"Yamauchi, B. (1997, January 10\u201311). A frontier-based approach for autonomous exploration. Proceedings of the 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA\u201997. Towards New Computational Principles for Robotics and Automation, Monterey, CA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lu, L., Redondo, C., and Campoy, P. (2020). Optimal Frontier-Based Autonomous Exploration in Unconstructed Environment Using RGB-D Sensor. Sensors, 20.","DOI":"10.3390\/s20226507"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Stachniss, C., Grisetti, G., and Burgard, W. (2005). Information Gain-based Exploration Using Rao-Blackwellized Particle Filters. Proceeding of the Robotics: Science and Systems I, Cambridge, MA, USA, 8\u201311 June 2005, The MIT Press.","DOI":"10.15607\/RSS.2005.I.009"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Carrillo, H., Dames, P., Kumar, V., and Castellanos, J.A. (2015, January 26\u201330). Autonomous robotic exploration using occupancy grid maps and graph SLAM based on Shannon and R\u00e9nyi Entropy. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139224"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Charrow, B., Liu, S., Kumar, V., and Michael, N. (2015, January 26\u201330). Information-theoretic mapping using Cauchy-Schwarz Quadratic Mutual Information. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139865"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bai, S., Wang, J., Chen, F., and Englot, B. (2016, January 9\u201314). Information-theoretic exploration with Bayesian optimization. Proceedings of the 2016 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Korea.","DOI":"10.1109\/IROS.2016.7759289"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhao, L., Yan, L., Hu, X., Yuan, J., and Liu, Z. (2021). Efficient and High Path Quality Autonomous Exploration and Trajectory Planning of UAV in an Unknown Environment. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10100631"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liu, S., Li, S., Pang, L., Hu, J., Chen, H., and Zhang, X. (2020). Autonomous Exploration and Map Construction of a Mobile Robot Based on the TGHM Algorithm. Sensors, 20.","DOI":"10.3390\/s20020490"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Shi, C., Zhu, P., Zeng, Z., and Zhang, H. (2021). Autonomous Exploration of Mobile Robots via Deep Reinforcement Learning Based on Spatiotemporal Information on Graph. Appl. Sci., 11.","DOI":"10.3390\/app11188299"},{"key":"ref_12","unstructured":"Prestes, E., Idiart, M., Engel, P., and Trevisan, M. (November, January 29). Exploration technique using potential fields calculated from relaxation methods. Proceedings of the 2001 IEEE\/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180), Maui, HI, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Maffei, R., Jorge, V.A.M., Prestes, E., and Kolberg, M. (June, January 31). Integrated exploration using time-based potential rails. Proceedings of the 2014 IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China.","DOI":"10.1109\/ICRA.2014.6907394"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Shade, R., and Newman, P. (2011, January 9\u201313). Choosing where to go: Complete 3D exploration with stereo. Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980121"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jorge, V.A.M., Maffei, R., Franco, G.S., Daltrozo, J., Giambastiani, M., Kolberg, M., and Prestes, E. (2015, January 26\u201330). Ouroboros: Using potential field in unexplored regions to close loops. Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA.","DOI":"10.1109\/ICRA.2015.7139479"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Silveira, R., Prestes, E., and Nedel, L. (2010, January 18\u201322). Fast path planning using multi-resolution boundary value problems. Proceedings of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5650673"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wurm, K.M., Stachniss, C., and Burgard, W. (2008, January 22\u201326). Coordinated multi-robot exploration using a segmentation of the environment. Proceedings of the 2008 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Nice, France.","DOI":"10.1109\/IROS.2008.4650734"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cipolleschi, R., Giusto, M., Li, A.Q., and Amigoni, F. (2013, January 25\u201327). Semantically-informed coordinated multirobot exploration of relevant areas in search and rescue settings. Proceedings of the 2013 European Conference on Mobile Robots, Barcelona, Catalonia, Spain.","DOI":"10.1109\/ECMR.2013.6698845"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s10514-011-9249-9","article-title":"Exploration strategies based on multi-criteria decision making for searching environments in rescue operations","volume":"31","author":"Basilico","year":"2011","journal-title":"Auton. Robot."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rekleitis, I. (2013, January 12\u201314). Multi-robot simultaneous localization and uncertainty reduction on maps (MR-SLURM). Proceedings of the 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenzhen, China.","DOI":"10.1109\/ROBIO.2013.6739630"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s10514-012-9298-8","article-title":"A comparison of path planning strategies for autonomous exploration and mapping of unknown environments","volume":"33","author":"Gil","year":"2012","journal-title":"Auton. Robot."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mukhija, P., Krishna, K.M., and Krishna, V. (2010, January 18\u201322). A two phase recursive tree propagation based multi-robotic exploration framework with fixed base station constraint. Proceedings of the 2010 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5649864"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.conengprac.2006.08.007","article-title":"Multi-robot exploration under the constraints of wireless networking","volume":"15","author":"Rooker","year":"2007","journal-title":"Control. Eng. Pract."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1109\/JSAC.2012.120609","article-title":"Connectivity Maintenance in Mobile Wireless Networks via Constrained Mobility","volume":"30","author":"Reich","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1109\/TRO.2012.2190178","article-title":"Multirobot Coordination With Periodic Connectivity: Theory and Experiments","volume":"28","author":"Hollinger","year":"2012","journal-title":"IEEE Trans. Robot."},{"key":"ref_26","unstructured":"Visser, A., and Slamet, B.A. (April, January 31). Including communication success in the estimation of information gain for multi-robot exploration. Proceedings of the 6th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops, Berlin, Germany."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"de Hoog, J., Cameron, S., and Visser, A. (2009, January 15\u201320). Role-Based Autonomous Multi-robot Exploration. Proceedings of the 2009 Computation World: Future Computing, Service Computation, Cognitive, Adaptive, Content, Patterns, Athens, Greece.","DOI":"10.1109\/ComputationWorld.2009.14"},{"key":"ref_28","unstructured":"Arkin, R., and Diaz, J. (2002, January 3\u20135). Line-of-sight constrained exploration for reactive multiagent robotic teams. Proceedings of the 7th International Workshop on Advanced Motion Control. Proceedings (Cat. No.02TH8623), Maribor, Slovenia."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Jensen, E.A., Lowmanstone, L., Gini, M., Kolling, A., Berman, S., Frazzoli, E., Martinoli, A., Matsuno, F., and Gauci, M. (2018). Communication-Restricted Exploration for Search Teams. Distributed Autonomous Robotic Systems: The 13th International Symposium, Tokyo, Japan, 12\u201314 November 2018, Springer.","DOI":"10.1007\/978-3-319-73008-0_2"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.adhoc.2012.06.009","article-title":"An incremental deployment algorithm for wireless sensor networks using one or multiple autonomous agents","volume":"11","author":"Lin","year":"2013","journal-title":"Ad Hoc Netw."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Stump, E., Michael, N., Kumar, V., and Isler, V. (2011, January 6\u20138). Visibility-based deployment of robot formations for communication maintenance. Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Wellington, New Zealand.","DOI":"10.1109\/ICRA.2011.5980179"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1002\/wcm.1145","article-title":"Connectivity and bandwidth-aware real-time exploration in mobile robot networks","volume":"13","author":"Pei","year":"2013","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1109\/LRA.2020.2970640","article-title":"Computationally Efficient Harmonic-Based Reactive Exploration","volume":"5","author":"Grontas","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_34","unstructured":"Chunyu, J., Qu, Z., Pollak, E., and Falash, M. (July, January 30). Reactive target-tracking control with obstacle avoidance of unicycle-type mobile robots in a dynamic environment. Proceedings of the American Control Conference, ACC 2010, Baltimore, MD, USA."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Loizou, S.G. (2011, January 12\u201315). Closed form Navigation Functions based on harmonic potentials. Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6161438"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Karras, G.C., Bechlioulis, C.P., Fourlas, G.K., and Kyriakopoulos, K.J. (2020, January 1\u20134). Target Tracking with Multi-rotor Aerial Vehicles based on a Robust Visual Servo Controller with Prescribed Performance. Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS), Athens, Greece.","DOI":"10.1109\/ICUAS48674.2020.9213893"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MRA.2012.2206474","article-title":"Multirotor Aerial Vehicles: Modeling, Estimation, and Control of Quadrotor","volume":"19","author":"Mahony","year":"2012","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kohlbrecher, S., Meyer, J., von Stryk, O., and Klingauf, U. (2011, January 1\u20135). A Flexible and Scalable SLAM System with Full 3D Motion Estimation. Proceedings of the IEEE International Symposium on Safety, Security and Rescue Robotics (SSRR), Kyoto, Japan.","DOI":"10.1109\/SSRR.2011.6106777"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Solomon, C., and Breckon, T. (2010). Front Matter. Fundamentals of Digital Image Processing, John Wiley and Sons, Ltd.","DOI":"10.1002\/9780470689776"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"959","DOI":"10.3390\/ijgi2040959","article-title":"Simplified Occupancy Grid Indoor Mapping Optimized for Low-Cost Robots","volume":"2","author":"Sanchez","year":"2013","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/0907058","article-title":"GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems","volume":"7","author":"Saad","year":"1986","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"ref_42","unstructured":"Yu, Y., Yang, S., Wang, M., Li, C., and Li, Z. (2015, January 26\u201330). High performance full attitude control of a quadrotor on SO(3). Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA."},{"key":"ref_43","first-page":"V001T01A004","article-title":"Position and Attitude Control of Underactuated Drones Using the Adaptive Function Approximation Technique","volume":"Volume 1","author":"Shamshirgaran","year":"2020","journal-title":"Proceedings of the Dynamic Systems and Control Conference 2020"},{"key":"ref_44","unstructured":"Fenwick, J., Newman, P., and Leonard, J. (2002, January 11\u201315). Cooperative concurrent mapping and localization. Proceedings of the 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), Washington, DC, USA."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1177\/0278364906072250","article-title":"Multi-robot Simultaneous Localization and Mapping using Particle Filters","volume":"25","author":"Howard","year":"2006","journal-title":"Int. J. Robot. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1177\/02783640122067435","article-title":"A Probabilistic On-Line Mapping Algorithm for Teams of Mobile Robots","volume":"20","author":"Thrun","year":"2001","journal-title":"Int. J. Robot. Res."},{"key":"ref_47","unstructured":"H\u00f6rner, J. (2016). Map-Merging for Multi-Robot System. [Bachelor\u2019s Thesis, Faculty of Mathematics and Physics, Charles University in Prague]."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Citroni, R., Di Paolo, F., and Livreri, P. (2019). A Novel Energy Harvester for Powering Small UAVs: Performance Analysis, Model Validation and Flight Results. Sensors, 19.","DOI":"10.3390\/s19081771"},{"key":"ref_49","unstructured":"Liu, X., and Gong, D. (2011, January 16\u201318). A comparative study of A-star algorithms for search and rescue in perfect maze. Proceedings of the International Conference on Electric Information and Control Engineering, Yichang, China."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1109\/LRA.2022.3143308","article-title":"Trajectory Planning in Unknown 2D Workspaces: A Smooth, Reactive, Harmonics-Based Approach","volume":"7","author":"Rousseas","year":"2022","journal-title":"IEEE Robot. Autom. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/14\/5194\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:48:20Z","timestamp":1760140100000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/14\/5194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,11]]},"references-count":50,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["s22145194"],"URL":"https:\/\/doi.org\/10.3390\/s22145194","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,7,11]]}}}