{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:08:40Z","timestamp":1760148520893,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T00:00:00Z","timestamp":1683072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Council of the University of Patras"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work, we address the single robot navigation problem within a planar and arbitrarily connected workspace. In particular, we present an algorithm that transforms any static, compact, planar workspace of arbitrary connectedness and shape to a disk, where the navigation problem can be easily solved. Our solution benefits from the fact that it only requires a fine representation of the workspace boundary (i.e., a set of points), which is easily obtained in practice via SLAM. The proposed transformation, combined with a workspace decomposition strategy that reduces the computational complexity, has been exhaustively tested and has shown excellent performance in complex workspaces. A motion control scheme is also provided for the class of non-holonomic robots with unicycle kinematics, which are commonly used in most industrial applications. Moreover, the tuning of the underlying control parameters is rather straightforward as it affects only the shape of the resulted trajectories and not the critical specifications of collision avoidance and convergence to the goal position. Finally, we validate the efficacy of the proposed navigation strategy via extensive simulations and experimental studies.<\/jats:p>","DOI":"10.3390\/s23094464","type":"journal-article","created":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T02:03:18Z","timestamp":1683165798000},"page":"4464","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Robot Navigation in Complex Workspaces Employing Harmonic Maps and Adaptive Artificial Potential Fields"],"prefix":"10.3390","volume":"23","author":[{"given":"Panagiotis","family":"Vlantis","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9850-2540","authenticated-orcid":false,"given":"Charalampos P.","family":"Bechlioulis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1229-3029","authenticated-orcid":false,"given":"Kostas J.","family":"Kyriakopoulos","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, National Technical University of Athens, 15780 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Canny, J. 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Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1109\/70.508439","article-title":"Probabilistic roadmaps for path planning in high-dimensional configuration spaces","volume":"12","author":"Kavraki","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102196","DOI":"10.1016\/j.rcim.2021.102196","article-title":"Path planning for manipulators based on an improved probabilistic roadmap method","volume":"72","author":"Chen","year":"2021","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/TASE.2014.2331983","article-title":"On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages","volume":"12","author":"Salzman","year":"2015","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1146\/annurev-control-060117-105226","article-title":"Sampling-Based Methods for Motion Planning with Constraints","volume":"1","author":"Kingston","year":"2018","journal-title":"Annu. Rev. Control Robot. Auton. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/TRO.2004.838008","article-title":"A convergent dynamic window approach to obstacle avoidance","volume":"21","author":"Ogren","year":"2005","journal-title":"IEEE Trans. Robot."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2762","DOI":"10.1109\/TASE.2021.3128521","article-title":"E3MoP: Efficient Motion Planning Based on Heuristic-Guided Motion Primitives Pruning and Path Optimization With Sparse-Banded Structure","volume":"19","author":"Wen","year":"2021","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10472-018-9596-8","article-title":"Path Homotopy Invariants and their Application to Optimal Trajectory Planning","volume":"84","author":"Bhattacharya","year":"2018","journal-title":"Ann. Math. Artif. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1109\/TASE.2016.2638208","article-title":"Homotopy Path Planning for Terrestrial Robots Using Spherical Algorithm","volume":"15","author":"Pascual","year":"2018","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_13","unstructured":"Khatib, O. (1985, January 25\u201328). Real-time obstacle avoidance for manipulators and mobile robots. Proceedings of the IEEE International Conference on Robotics and Automation, St. Louis, MO, USA."},{"key":"ref_14","unstructured":"Koditschek, D. (April, January 31). Exact robot navigation by means of potential functions: Some topological considerations. Proceedings of the IEEE International Conference on Robotics and Automation, Raleigh, NC, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/70.163777","article-title":"Exact Robot Navigation Using Artificial Potential Functions","volume":"8","author":"Rimon","year":"1992","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1109\/TAC.2008.917745","article-title":"Density Functions for Navigation-Function-Based Systems","volume":"53","author":"Loizou","year":"2008","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Filippidis, I., and Kyriakopoulos, K.J. (2011, January 12\u201315). Adjustable navigation functions for unknown sphere worlds. Proceedings of the IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6161176"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Filippidis, I.F., and Kyriakopoulos, K.J. (2012, January 14\u201318). Navigation Functions for everywhere partially sufficiently curved worlds. Proceedings of the IEEE International Conference on Robotics and Automation, St Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6225105"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2944","DOI":"10.1109\/TAC.2017.2775046","article-title":"Navigation Functions for Convex Potentials in a Space With Convex Obstacles","volume":"63","author":"Paternain","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1177\/0278364918796267","article-title":"Sensor-based reactive navigation in unknown convex sphere worlds","volume":"38","author":"Arslan","year":"2019","journal-title":"Int. J. Robot. Res."},{"key":"ref_21","unstructured":"Connolly, C., B Burns, J., and Weiss, R. (1990, January 13\u201318). Path Planning Using Laplace\u2019s Equation. Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, OH, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s10846-010-9394-y","article-title":"Path Planning for Autonomous Mobile Robots Using the Boundary Integral Equation Method","volume":"59","author":"Mantegh","year":"2010","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1109\/LRA.2017.2665682","article-title":"Online Robot Navigation Using Continuously Updated Artificial Temperature Gradients","volume":"2","author":"Golan","year":"2017","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1109\/70.143352","article-title":"Real-time obstacle avoidance using harmonic potential functions","volume":"8","author":"Kim","year":"1992","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2556","DOI":"10.1109\/TMECH.2016.2580303","article-title":"Implementation Studies of Robot Swarm Navigation Using Potential Functions and Panel Methods","volume":"21","author":"Merheb","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1007\/s12555-019-0009-5","article-title":"Mobile Robot Motion Framework Based on Enhanced Robust Panel Method","volume":"18","year":"2020","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_27","unstructured":"Feder, H.J.S., and Slotine, J.J.E. (1997, January 20\u201325). Real-time path planning using harmonic potentials in dynamic environments. Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"104156","DOI":"10.1016\/j.robot.2022.104156","article-title":"A local reactive steering law for 2D collision avoidance with curvature constraints and constant speed","volume":"155","author":"Marchidan","year":"2022","journal-title":"Robot. Auton. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0921-8890(02)00209-9","article-title":"Exploration Method Using Harmonic Functions","volume":"40","author":"Engel","year":"2002","journal-title":"Robot. Auton. Syst."},{"key":"ref_30","unstructured":"Maffei, R., Souza, M.P., Mantelli, M., Pittol, D., Kolberg, M., and Jorge, V.A.M. (August, January 31). Exploration of 3D terrains using potential fields with elevation-based local distortions. Proceedings of the IEEE International Conference on Robotics and Automation, Paris, France."},{"key":"ref_31","unstructured":"Voruganti, H., Dasgupta, B., and Hommel, U. (2006, January 13). A novel potential field based domain mapping method. Proceedings of the 10th WSEAS Conference on Computers (ICCOMPP06), Athens, Greece."},{"key":"ref_32","unstructured":"Gautam Pradeepkumar, B., Gondegaon, S., and Voruganti, H.K. (2014, January 29\u201331). Domain Mapping for Path Planning and Mesh Generation. Proceedings of the International Conference on Theoretical, Applied, Computational and Experimental Mechanics, Kharagpur, India."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Loizou, S.G. (2011, January 12\u201315). Closed form Navigation Functions based on harmonic potentials. Proceedings of the IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA.","DOI":"10.1109\/CDC.2011.6161438"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1516","DOI":"10.1109\/TRO.2017.2725323","article-title":"The Navigation Transformation","volume":"33","author":"Loizou","year":"2017","journal-title":"IEEE Trans. Robot."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Loizou, S.G. (2012, January 27\u201329). Navigation functions in topologically complex 3-D workspaces. Proceedings of the American Control Conference, Montreal, QC, Canada.","DOI":"10.1109\/ACC.2012.6315464"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Loizou, S.G. (2014, January 14\u201316). The Multi-Agent Navigation Transformation: Tuning-Free Multi-Robot Navigation. Proceedings of the Robotics: Science and Systems, Berkeley, CA, USA.","DOI":"10.15607\/RSS.2014.X.017"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Vlantis, P., Vrohidis, C., Bechlioulis, C.P., and Kyriakopoulos, K.J. (2018, January 21\u201325). Robot Navigation in Complex Workspaces Using Harmonic Maps. Proceedings of the IEEE International Conference on Robotics and Automation, Brisbane, Australia.","DOI":"10.1109\/ICRA.2018.8460695"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"201","DOI":"10.2140\/pjm.1997.180.201","article-title":"Harmonic mappings of multiply connected domains","volume":"180","author":"Duren","year":"1997","journal-title":"Pac. J. Math."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Biringen, S., and Chow, C.Y. (2011). An Introduction to Computational Fluid Mechanics by Example, John Wiley & Sons, Inc.","DOI":"10.1002\/9780470549162"},{"key":"ref_40","unstructured":"Kuethe, A.M., Chow, C.Y., and Fung, Y.C. (1997). Foundations of Aerodynamics: Bases of Aerodynamics Design, John Wiley & Sons, Inc.. [5th ed.]."},{"key":"ref_41","unstructured":"Khalil, H.K. (1996). Nonlinear Systems, Prentice-Hall."},{"key":"ref_42","unstructured":"Panageas, I., and Piliouras, G. (2016). Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions. arXiv."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/9\/4464\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:28:49Z","timestamp":1760124529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/9\/4464"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,3]]},"references-count":42,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["s23094464"],"URL":"https:\/\/doi.org\/10.3390\/s23094464","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,5,3]]}}}