{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:46:56Z","timestamp":1760237216462,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,22]],"date-time":"2020-03-22T00:00:00Z","timestamp":1584835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This article presents the possibility of helping navigators direct the movement of an object, while safely passing through other objects, using an artificial neural network and optimization methods. It has been shown that the best trajectory of an object in terms of optimality and security, from among many possible options, can be determined by the method of dynamic programming with the simultaneous use of an artificial neural network, by depicting the encountered objects as moving in forbidden domains. Analytical considerations are illustrated with examples of simulation studies of the developed calculation program on real navigational situations at sea. This research took into account both the number of objects encountered and the different shapes of domains assigned to the objects encountered. Finally, the optimal value of the safe object trajectory time was compared on the setpoint value of the safe passing distance of objects in given visibility conditions at sea, and the degree of discretization of calculations was determined by the density of the location of nodes along the route of objects.<\/jats:p>","DOI":"10.3390\/rs12061020","type":"journal-article","created":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T07:16:08Z","timestamp":1585034168000},"page":"1020","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multistage Dynamic Optimization with Different Forms of Neural-State Constraints to Avoid Many Object Collisions Based on Radar Remote Sensing"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9281-376X","authenticated-orcid":false,"given":"J\u00f3zef","family":"Lisowski","sequence":"first","affiliation":[{"name":"Faculty of Marine Electrical Engineering, Gdynia Maritime University, 81-225 Gdynia, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Graziano, M.D., D\u2019Errico, M., and Rufino, G. (2016). Wake Component Detection in X-Band SAR Images for Ship Heading and Velocity Estimation. Remote Sens., 8.","DOI":"10.3390\/rs8060498"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7695","DOI":"10.3390\/rs70607695","article-title":"Automatic Ship Detection in SAR Images Using Multi-Scale Heterogeneities and an a Contrario Decision","volume":"7","author":"Huang","year":"2015","journal-title":"Remote Sens."},{"key":"ref_3","unstructured":"Bist, D.S. (2000). Safety and Security at Sea, Butterworth Heinemann."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.oceaneng.2016.11.044","article-title":"A method of determining and visualizing safe motion parameters of a ships navigating in restricted waters","volume":"129","author":"Szlapczynski","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lyu, H., and Yin, Y. (2018). Fast Path Planning for Autonomous Ships in Restricted Waters. Appl. Sci., 8.","DOI":"10.3390\/app8122592"},{"key":"ref_6","unstructured":"Deng, W., Gan, L., Zhou, C., Zheng, Y., Liu, M., and Zhang, L. (2017, January 25\u201330). Study on Path Planning of Ship Collision Avoidance in Restricted Water base on AFS Algorithm. Proceedings of the 27th Int. Ocean and Polar Engineering Conf., San Francisco, CA, USA. ID: ISOPE-I-17-280."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lebkowski, A. (2015, January 17\u201319). Evolutionary methods in the management of vessel traffic. Proceedings of the Int. Conf. on Marine Navigation and Safety of Sea Transportation, Gdynia, Poland.","DOI":"10.1201\/b18514-41"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lazarowska, A. (2015). Safe Ship Trajectory Planning Based on the Ant Algorithm\u2014The Development of the Method. Activities in Navigation: Marine Navigation and Safety of Sea Transportation, CRC Press.","DOI":"10.1201\/b18513-25"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.procs.2014.08.087","article-title":"Ant Colony Optimization Algorithm Applied to Ship Steering Control","volume":"35","author":"Tomera","year":"2014","journal-title":"Procedia Comput. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"294","DOI":"10.5391\/IJFIS.2017.17.4.294","article-title":"Study on the Construction of Stage Discrimination Model and Consecutive Waypoints Generation Method for Ship\u2019s Automatic Avoiding Action","volume":"17","author":"Dinh","year":"2017","journal-title":"Int. J. Fuzzy Log. Intell. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1017\/S0373463318000796","article-title":"COLREGS-Constrained Real-time Path Planning for Autonomous Ships Using Modified Artificial Potential Fields","volume":"72","author":"Lyu","year":"2019","journal-title":"J. Navig."},{"key":"ref_12","unstructured":"Rocha, A.F. Neural Nets - Theory of Brain a Machines, Springer."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hwang, J.I., Chae, S.H., Kim, D., and Jung, H.S. (2017). Application of Artificial Neural Networks to Ship Detection from X-Band Kompsat-5 Imagery. Appl. Sci., 7.","DOI":"10.3390\/app7090961"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kang, M., Ji, K., Leng, X., and Lin, Z. (2017). Contextual Region-Based Convolutional Neural Network with Multilayer Fusion for SAR Ship Detection. Remote Sens., 9.","DOI":"10.3390\/rs9080860"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2134","DOI":"10.3390\/rs6032134","article-title":"Artificial Neural Network Modeling of High Arctic Phytomass Using Synthetic Aperture Radar and Multispectral Data","volume":"6","author":"Collingwood","year":"2014","journal-title":"Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1017\/S0373463315000223","article-title":"Analysis of Collision Threat Parameters and Criteria","volume":"68","author":"Lenart","year":"2015","journal-title":"J. Navig."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Borkowski, P. (2017). The Ship Movement Trajectory Prediction Algorithm Using Navigational Data Fusion. Sensors, 17.","DOI":"10.3390\/s17061432"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106175","DOI":"10.1016\/j.oceaneng.2019.106175","article-title":"A Cooperative Game Approach for Assessing the Collision Risk in Multi-Vessel Encountering","volume":"187","author":"Liu","year":"2019","journal-title":"Ocean Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4028\/www.scientific.net\/SSP.210.215","article-title":"Optimization-supported decision-making in the marine game environment","volume":"210","author":"Lisowski","year":"2014","journal-title":"Solid State Phenomena"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1017\/S0373463300025030","article-title":"Manoeuvring Times, Domains and Arenas","volume":"36","author":"Colley","year":"1983","journal-title":"J. Navig."},{"key":"ref_21","unstructured":"Cross, S.J. (1994, January 11\u201313). Objective Assessment of Maritime Simulator Training. Proceedings of the International Conference the Development and Implementation of International Maritime Training Standards, Malmo, Sweden."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/S0373463300035220","article-title":"A computer simulation of marine traffic using domains and areas","volume":"33","author":"Davis","year":"1980","journal-title":"J. Navig."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1017\/S0373463300041230","article-title":"Statistical study of ship domains","volume":"28","author":"Goodvin","year":"1975","journal-title":"J. Navig."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Guenin, B., Konemann, J., and Tuncel, L.A. (2014). Gentle Introduction to Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9781107282094"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Speyer, J.L., and Jacobson, D.H. (2010). Primer on Optimal Control Theory, SIAM.","DOI":"10.1137\/1.9780898718560"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yong, J. (2018). Optimization Theory\u2013A Concise Introduction, World Sc.","DOI":"10.1142\/10923"},{"key":"ref_27","unstructured":"Bellman, R.E. (2003). Dynamic Programming, Dover Publication."},{"key":"ref_28","unstructured":"Lew, A., and Mauch, H. (2007). Dynamic Programming\u2013A Computational Tool, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Geng, X., Wang, Y., Wang, P., and Zhang, B. (2019). Motion of maritime autonomous surface ships by dynamic programming for collision avoidance and speed optimization. Sensors, 19.","DOI":"10.3390\/s19020434"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.oceaneng.2018.05.061","article-title":"Adaptive Dynamic Control Allocation for Dynamic Positioning of Marine Vessel Based on Backstepping Method and Sequential Quadratic Program","volume":"163","author":"Witkowska","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_31","unstructured":"Stateczny, A. (2011, January 19\u201321). Neural Manoeuvre Detection of the Tracked Target in ARPA Systems. Proceedings of the IFAC Conference on Control Applications in Marine Systems, Glasgow, Scotland."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wlodarczyk-Sielicka, M., Lubczonek, J., and Stateczny, A. (2016, January 10\u201312). Comparison of selected clustering algorithms of raw data obtained by interferometric methods using artificial neural networks. Proceedings of the 17th Int. Radar Symp., Krakow, Poland.","DOI":"10.1109\/IRS.2016.7497290"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Hertz, J., Krogh, A., and Palmer, R.G. (2018). Introduction to the Theory of Neural Computation, CRC Press.","DOI":"10.1201\/9780429499661"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hunt, K.J., Irwin, G.R., and Warwick, K. (1995). Neural Network Engineering in Dynamic Control Systems, Springer.","DOI":"10.1007\/978-1-4471-3066-6"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Leondes, C.T. (1998). Control and Dynamic Systems, Neural Network Systems Techniques and Applications, Academic Press.","DOI":"10.4324\/9780203304143"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1111\/j.1934-6093.2001.tb00052.x","article-title":"Neural Network Based Algorithm for Dynamic System Optimization","volume":"3","author":"Francelin","year":"2001","journal-title":"Asian J. 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