{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T21:05:32Z","timestamp":1761599132579,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2014,8,4]],"date-time":"2014-08-04T00:00:00Z","timestamp":1407110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The minimum time search in uncertain domains is a searching task, which appears in real world problems such as natural disasters and sea rescue operations, where a target has to be found, as soon as possible, by a set of sensor-equipped searchers. The automation of this task, where the time to detect the target is critical, can be achieved by new probabilistic techniques that directly minimize the Expected Time (ET) to detect a dynamic target using the observation probability models and actual observations collected by the sensors on board the searchers. The selected technique, described in algorithmic form in this paper for completeness, has only been previously partially tested with an ideal binary detection model, in spite of being designed to deal with complex non-linear\/non-differential sensorial models. This paper covers the gap, testing its performance and applicability over different searching tasks with searchers equipped with different complex sensors. The sensorial models under test vary from stepped detection probabilities to continuous\/discontinuous differentiable\/non-differentiable detection probabilities dependent on distance, orientation, and structured maps. The analysis of the simulated results of several static and dynamic scenarios performed in this paper validates the applicability of the technique with different types of sensor models.<\/jats:p>","DOI":"10.3390\/s140814131","type":"journal-article","created":{"date-parts":[[2014,8,5]],"date-time":"2014-08-05T10:59:37Z","timestamp":1407236377000},"page":"14131-14179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms"],"prefix":"10.3390","volume":"14","author":[{"given":"Pablo","family":"Lanillos","sequence":"first","affiliation":[{"name":"Mobile Robotics Lab, Institute of Systems and Robotics, University of Coimbra, Pinhal de Marrocos, Plo II, 3030-290 Coimbra, Portugal"}]},{"given":"Eva","family":"Besada-Portas","sequence":"additional","affiliation":[{"name":"Departamento de Arquitectura de Computadores y Automatica, Universidad Complutense de Madrid, Av. Complutense s\/n, 28040 Madrid, Spain"}]},{"given":"Jose","family":"Lopez-Orozco","sequence":"additional","affiliation":[{"name":"Departamento de Arquitectura de Computadores y Automatica, Universidad Complutense de Madrid, Av. Complutense s\/n, 28040 Madrid, Spain"}]},{"given":"Jesus","family":"De la Cruz","sequence":"additional","affiliation":[{"name":"Departamento de Arquitectura de Computadores y Automatica, Universidad Complutense de Madrid, Av. Complutense s\/n, 28040 Madrid, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2014,8,4]]},"reference":[{"key":"ref_1","unstructured":"Stone, L.D. (1975). Theory of Optimal Search, Academic Press."},{"key":"ref_2","unstructured":"Koopman, B. (1980). Search and Screening: General Principles with Historical Applications, Pergamon Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1287\/opre.21.5.1071","article-title":"The Optimal Control of Partially Observable Markov Processes over a Finite Horizon","volume":"21","author":"Smallwood","year":"1973","journal-title":"Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0004-3702(98)00023-X","article-title":"Planning and acting in partially observable stochastic domains","volume":"101","author":"Kaelbling","year":"1998","journal-title":"Artif. Intell."},{"key":"ref_5","first-page":"874","article-title":"Dual control theory I\u2013II","volume":"21","author":"Feldbaum","year":"1961","journal-title":"Automn Remote Control"},{"key":"ref_6","first-page":"1033","article-title":"Dual control theory III\u2013IV","volume":"22","author":"Feldbaum","year":"1961","journal-title":"Automn Remote Control"},{"key":"ref_7","unstructured":"Grocholsky, B., Makarenko, A., and Durrant-Whyte, H. (2003, January 14\u201319). Information-theoretic coordinated control of multiple sensor platforms. Taipei, Taiwan."},{"key":"ref_8","unstructured":"Bourgault, F., Furukawa, T., and Durrant-Whyte, H.F. (October, January 28). Decentralized Bayesian Negotiation for Cooperative Search. Sendai, Japan."},{"key":"ref_9","unstructured":"Furukawa, T., Bourgault, F., Lavis, B., and Durrant-Whyte, H.F. (2006, January 15\u201319). Recursive Bayesian search-and-tracking using coordinated UAVs for lost targets. Orlando, FL, USA."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bessire, P., Laugier, C., and Siegwart, R. (2008). Probabilistic Reasoning and Decision Making in Sensory-Motor Systems, Springer. [1st ed.].","DOI":"10.1007\/978-3-540-79007-5"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yang, Y., Minai, A., and Polycarpou, M. (2002, January 5). Decentralized cooperative search in UAV's using opportunistic learning. Montery, CA, USA.","DOI":"10.2514\/6.2002-4590"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lanillos, P., Besada-Portas, E., Pajares, G., and Ruz, J.J. (2012, January 7\u201312). Minimum time search for lost targets using cross entropy optimization. Vilamoura, Portugal.","DOI":"10.1109\/IROS.2012.6385510"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lanillos, P., Ya\u00f1ez Zuluaga, J., Ruz, J.J., and Besada-Portas, E. (2013, January 6\u201310). A Bayesian Approach for Constrained Multi-Agent Minimum Time Search in Uncertain Dynamic Domains. Amsterdam, The Netherlands.","DOI":"10.1145\/2463372.2463417"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.automatica.2005.12.018","article-title":"Optimal sensor placement and motion coordination for target tracking","volume":"42","author":"Martinez","year":"2006","journal-title":"Automatica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/TAC.2009.2034206","article-title":"Mobile Sensor Networks Control Using Mutual Information Methods and Particle Filters","volume":"55","author":"Hoffmann","year":"2012","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MRA.2006.1678135","article-title":"Cooperative air and ground surveillance","volume":"13","author":"Grocholsky","year":"2006","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1287\/opre.32.5.1107","article-title":"The Optimal Search for a Moving Target When the Search Path is Constrained","volume":"32","author":"Eagle","year":"1984","journal-title":"Oper. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1287\/opre.38.1.110","article-title":"An Optimal Branch-and-Bound Procedure for the Constrained Path, Moving Target Search Problem","volume":"38","author":"Eagle","year":"1990","journal-title":"Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1002\/(SICI)1520-6750(199606)43:4<463::AID-NAV1>3.0.CO;2-5","article-title":"Using Multiple Searchers in Constrained-Path, Moving-Target Search Problems","volume":"43","author":"Dell","year":"1996","journal-title":"Nav. Res. Logist."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1002\/nav.3800270214","article-title":"On a Search for a Moving Target","volume":"27","author":"Washburn","year":"1980","journal-title":"Nav. Res. Logist."},{"key":"ref_21","unstructured":"Bourgault, F., Furukawa, T., and Durrant-Whyte, H.F. (2003). Field and Service Robotics, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mathews, G., Durrant-Whyte, H., and Prokopenko, M. (2007, January 12\u201314). Asynchronous gradient-based optimisation for team decision making. New Orleans, LA, USA.","DOI":"10.1109\/CDC.2007.4434301"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.ejor.2007.06.043","article-title":"Discounted mean bound for the optimal searcher path problem with non-uniform travel times","volume":"180","author":"Lau","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Gan, S.K., and Sukkarieh, S. (2010, January 3\u20138). Multi-UAV Target Search using Explicit Decentralized Gradient-Based Negotiation. Anchorage, AK, USA.","DOI":"10.1109\/ICRA.2011.5979704"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1163\/016918609X12496339799170","article-title":"An Efficient Motion Strategy to Compute Expected-Time Locally Optimal Continuous Search Paths in Known Environments","volume":"23","author":"Sarmiento","year":"2009","journal-title":"Adv. Robot."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1002\/nav.20411","article-title":"Path optimization for the resource-constrained searcher","volume":"57","author":"Sato","year":"2010","journal-title":"Nav. Res. Logist."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, S., and Guo, Y. (2012, January 14\u201318). Distributed source seeking by cooperative robots: All-to-all and limited communications. Saint Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6224713"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2308","DOI":"10.1109\/TAC.2012.2186927","article-title":"Stochastic Source Seeking by Mobile Robots","volume":"57","author":"Azuma","year":"2012","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s10846-013-9897-4","article-title":"Multiple UAV Formations for Cooperative Source Seeking and Contour Mapping of a Radiative Signal Field","volume":"74","author":"Han","year":"2014","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_30","unstructured":"Rubinstein, R.Y., and Kroese, D.P. (2004). The Cross Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning, Springer."},{"key":"ref_31","unstructured":"Ferreira, J.F., and Dias, J. (2014). Springer Tracts in Advanced Robotics, Springer."},{"key":"ref_32","unstructured":"Mathews, G. (2008). Asynchronous Decision Making for Decentralised Autonomous Systems. [Ph.D. Thesis, The University of Sydney]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1287\/opre.34.2.324","article-title":"The Complexity of the Optimal Searcher Path Problem","volume":"34","author":"Trummel","year":"1986","journal-title":"Oper. Res."},{"key":"ref_34","first-page":"335","article-title":"Anytime point-based approximations for large POMDPs","volume":"27","author":"Pineau","year":"2006","journal-title":"J. Artif. Int. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s10458-009-9103-z","article-title":"Optimizing Fixed-Size Stochastic Controllers for POMDPs and Decentralized POMDPs","volume":"21","author":"Amato","year":"2010","journal-title":"Auton. Agents Multi-Agent Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10458-012-9200-2","article-title":"A survey of point-based POMDP solvers","volume":"27","author":"Shani","year":"2012","journal-title":"Auton. Agents Multi-Agent Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Vlassis, N., and Toussaint, M. (2009, January 14\u201318). Model free reinforcement learning as mixture learning. Montreal, QC, Canada.","DOI":"10.1145\/1553374.1553512"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hsu, D., Lee, W., and Rong, N. (2008, January 19\u201323). A Point-Based POMDP Planner for Target Tracking. Pasadena, CA, USA.","DOI":"10.1109\/ROBOT.2008.4543611"},{"key":"ref_39","first-page":"724597","article-title":"A POMDP Framework for Coordinated Guidance of Autonomous UAVs for Multitarget Tracking","volume":"2009","author":"Miller","year":"2009","journal-title":"J. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1109\/TAES.2013.6621824","article-title":"UAV Path Planning in a Dynamic Environment via Partially Observable Markov Decision Process","volume":"49","author":"Ragi","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_41","unstructured":"Chanel, C.P.C., Teichteil-Knigsbuch, F., and Lesire, C. (2013, January 14\u201318). Multi-Target Detection and Recognition by UAVs Using Online POMDPs. Bellevue, WA, USA."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Deisenroth, M.P., Neumann, G., and Peters, J. (2011). A Survey on Policy Search for Robotics. Found. Trends Robot., 2.","DOI":"10.1561\/9781601987037"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4891","DOI":"10.1016\/j.cnsns.2012.05.024","article-title":"Model-free control of Lorenz chaos using an approximate optimal control strategy","volume":"17","author":"Li","year":"2012","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Powell, W.B. (2007). Approximate Dynamic Programming: Solving the Curses of Dimensionality, John Wiley & Sons.","DOI":"10.1002\/9780470182963"},{"key":"ref_45","unstructured":"Neapolitan, R.E. (2003). Learning Bayesian Networks, Prentince Hall."},{"key":"ref_46","unstructured":"Budge, M. Introduction to Radar Systems. Available online: http:\/\/www.ece.uah.edu\/courses\/material\/EE619-2011\/."},{"key":"ref_47","first-page":"269","article-title":"Probability of Detection for Fluctuating Targets","volume":"IT-6","author":"Swerling","year":"1960","journal-title":"IRE Trans."},{"key":"ref_48","unstructured":"Skolnik, M. (1990). Radar Handbook, McGraw-Hill."},{"key":"ref_49","unstructured":"Burden, R., Faires, J., and Reynolds, A.C. (1985). Numerical Analysis, Prindle, Weber & Schmidt."},{"key":"ref_50","unstructured":"Thrun, S., Burgard, W., and Fox, D. (2005). Probabilistic Robotics, MIT Press Cambridge."},{"key":"ref_51","unstructured":"Luenberger, D. (1984). Linear and Nonlinear Programming, Addison Wesley."},{"key":"ref_52","unstructured":"Bertsekas, D. (1998). Constraint Optimization and Lagrange Multiplier Methods, Athena Scientific."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neucom.2012.01.034","article-title":"Decentralized kinematic control of a class of collaborative redundant manipulators via recurrent neural networks","volume":"91","author":"Li","year":"2012","journal-title":"Neurocomputing"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1080\/02331939508844053","article-title":"Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993","volume":"32","author":"Boukari","year":"1995","journal-title":"Optimization"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1016\/j.asoc.2010.04.001","article-title":"Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm","volume":"10","author":"Ghosieri","year":"2010","journal-title":"Appl. Soft Comput."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Furukawa, T., Lavis, B., and Durrant-Whyte, H. (2010, January 3\u20138). Parallel grid-based recursive Bayesian estimation using GPU por real-time autonomous navigation. Anchorage, AK, USA.","DOI":"10.1109\/ROBOT.2010.5509396"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s11554-010-0156-7","article-title":"Bayesian real-time perception algorithms on GPU","volume":"6","author":"Ferreira","year":"2011","journal-title":"J. Real-Time Image Process."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Larra\u00f1aga, P., and Lozano, J.A. (2001). Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, Kluwer Academic.","DOI":"10.1007\/978-1-4615-1539-5"},{"key":"ref_59","unstructured":"Lanillos, P. (2013). Minimum Time Search of Mobile Targets in Uncertain Environments. [Ph.D. Thesis, University Complutense of Madrid]."},{"key":"ref_60","unstructured":"Papoulis, A., and Pillai, S. (1991). Probability, Random Variables, and Stochastic Processes, McGraw-Hill. McGraw-Hill Electrical and Electronic Engineering Series."},{"key":"ref_61","unstructured":"Feller, W. (1971). An Introduction to Probability Theory and Its Applications, John Wiley and Sons."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/8\/14131\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:14:21Z","timestamp":1760217261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/8\/14131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,4]]},"references-count":61,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2014,8]]}},"alternative-id":["s140814131"],"URL":"https:\/\/doi.org\/10.3390\/s140814131","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2014,8,4]]}}}