{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T15:42:30Z","timestamp":1740152550725,"version":"3.37.3"},"reference-count":61,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T00:00:00Z","timestamp":1581984000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Council of Sciences and Technology (CONACYT), Mexico","award":["CB-256769, CB-258068 and PN-2016-4107."]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"Flying robots have gained great interest because of their numerous applications. For this reason, the control of Unmanned Aerial Vehicles (UAVs) is one of the most important challenges in mobile robotics. These kinds of robots are commonly controlled with Proportional-Integral-Derivative (PID) controllers; however, traditional linear controllers have limitations when controlling highly nonlinear and uncertain systems such as UAVs. In this paper, a control scheme for the pose of a quadrotor is presented. The scheme presented has the behavior of a PD controller and it is based on a Multilayer Perceptron trained with an Extended Kalman Filter. The Neural Network is trained online in order to ensure adaptation to changes in the presence of dynamics and uncertainties. The control scheme is tested in real time experiments in order to show its effectiveness.<\/jats:p>","DOI":"10.3390\/a13020040","type":"journal-article","created":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T15:10:25Z","timestamp":1582038625000},"page":"40","source":"Crossref","is-referenced-by-count":7,"title":["Neural PD Controller for an Unmanned Aerial Vehicle Trained with Extended Kalman Filter"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9724-1729","authenticated-orcid":false,"given":"Javier","family":"Gomez-Avila","sequence":"first","affiliation":[{"name":"Centro Universitario de Ciencias Exactas e Ingenier\u00edas, Universidad de Guadalajara, Blvd Marcelino Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44430, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0802-0121","authenticated-orcid":false,"given":"Carlos","family":"Villase\u00f1or","sequence":"additional","affiliation":[{"name":"Centro Universitario de Ciencias Exactas e Ingenier\u00edas, Universidad de Guadalajara, Blvd Marcelino Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44430, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7518-1668","authenticated-orcid":false,"given":"Jesus","family":"Hernandez-Barragan","sequence":"additional","affiliation":[{"name":"Centro Universitario de Ciencias Exactas e Ingenier\u00edas, Universidad de Guadalajara, Blvd Marcelino Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44430, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8803-9502","authenticated-orcid":false,"given":"Nancy","family":"Arana-Daniel","sequence":"additional","affiliation":[{"name":"Centro Universitario de Ciencias Exactas e Ingenier\u00edas, Universidad de Guadalajara, Blvd Marcelino Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44430, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9600-779X","authenticated-orcid":false,"given":"Alma Y.","family":"Alanis","sequence":"additional","affiliation":[{"name":"Centro Universitario de Ciencias Exactas e Ingenier\u00edas, Universidad de Guadalajara, Blvd Marcelino Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44430, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8122-3799","authenticated-orcid":false,"given":"Carlos","family":"Lopez-Franco","sequence":"additional","affiliation":[{"name":"Centro Universitario de Ciencias Exactas e Ingenier\u00edas, Universidad de Guadalajara, Blvd Marcelino Garc\u00eda Barrag\u00e1n 1421, Guadalajara 44430, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,18]]},"reference":[{"key":"ref_1","first-page":"1193","article-title":"A light-weight multispectral sensor for micro UAV\u2014Opportunities for very high resolution airborne remote sensing","volume":"37","author":"Nebiker","year":"2008","journal-title":"Int. Arch. Photogramme. Remote Sens. Spat. Inf. Sci."},{"key":"ref_2","first-page":"54","article-title":"Unmanned aerial vehicles: An overview","volume":"3","author":"Bento","year":"2008","journal-title":"Inside GNSS"},{"key":"ref_3","first-page":"1229","article-title":"UAV-based augmented monitoring-real-time georeferencing and integration of video imagery with virtual globes","volume":"37","author":"Eugster","year":"2008","journal-title":"IAPRSSIS"},{"key":"ref_4","unstructured":"Bouabdallah, S., Murrieri, P., and Siegwart, R. (May, January 26). Design and control of an indoor micro quadrotor. Proceedings of the IEEE International Conference on Robotics and Automation, New Orleans, LA, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10846-010-9492-x","article-title":"Towards autonomous micro uav swarms","volume":"61","author":"Segor","year":"2011","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_6","unstructured":"Engel, J., Sturm, J., and Cremers, D. (2012). Accurate figure flying with a quadrocopter using onboard visual and inertial sensing. Imu, 320."},{"key":"ref_7","first-page":"262","article-title":"PID based on a single artificial neural network algorithm for intelligent sensors","volume":"10","year":"2012","journal-title":"J. Appl. Res. Technol."},{"key":"ref_8","first-page":"2368","article-title":"The PID Controller Based on the Artificial Neural Network and the Differential Evolution Algorithm","volume":"7","author":"Lu","year":"2012","journal-title":"JCP"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1630","DOI":"10.1109\/TSMCB.2004.826827","article-title":"Adaptive neural network control for a class of MIMO nonlinear systems with disturbances in discrete-time","volume":"34","author":"Ge","year":"2004","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_11","unstructured":"S\u00e1nchez Camperos, E., and Alan\u00eds Garc\u00eda, A. (2006). Redes Neuronales: Conceptos fundamentales y aplicaciones a control autom\u00e1tico, Pearson Prentice Hall."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1109\/78.134446","article-title":"The complex backpropagation algorithm","volume":"39","author":"Leung","year":"1991","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1109\/34.141559","article-title":"Comparative analysis of backpropagation and the extended Kalman filter for training multilayer perceptrons","volume":"14","author":"Ruck","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1162\/089976600300015655","article-title":"Hierarchical Bayesian models for regularization in sequential learning","volume":"12","author":"Niranjan","year":"2000","journal-title":"Neural Comput."},{"key":"ref_15","unstructured":"Singhal, S., and Wu, L. (1989, January 23\u201326). Training feed-forward networks with the extended Kalman algorithm. Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Glasgow, UK."},{"key":"ref_16","unstructured":"Williams, R.J. (1992). Some Observations on the Use of the Extended Kalman Filter as A Recurrent Network Learning Algorithm, Citeseer."},{"key":"ref_17","unstructured":"Latt, Z.K.K., Si, H., and Kaneko, O. (2019, January 7\u20139). Controller Parameter Tuning of a Hexacopter with Fictitious Reference Iterative Tuning. Proceedings of the 2019 SICE International Symposium on Control Systems (SICE ISCS), Kumamoto, Japan."},{"key":"ref_18","first-page":"325","article-title":"Meta-heuristic algorithms for the control tuning of omnidirectional mobile robots","volume":"52","year":"2019","journal-title":"Eng. Optim."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bari, S., Hamdani, S.S.Z., Khan, H.U., ur Rehman, M., and Khan, H. (2019, January 21\u201322). Artificial Neural Network Based Self-Tuned PID Controller for Flight Control of Quadcopter. Proceedings of the 2019 International Conference on Engineering and Emerging Technologies (ICEET), Lahore, Pakistan.","DOI":"10.1109\/CEET1.2019.8711864"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Radiansyah, S., Kusrini, M., and Prasetyo, L. (2017). Quadcopter Applications for Wildlife Monitoring, IOP Publishing.","DOI":"10.1088\/1755-1315\/54\/1\/012066"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.ifacol.2018.07.337","article-title":"Real-time integral backstepping with sliding mode control for a quadrotor UAV","volume":"51","author":"Sanchez","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, H., Zhang, Y., Yi, Y., Xin, J., and Liu, D. (2016, January 28\u201330). Nonlinear tracking control methods applied to qball-x4 quadrotor uav against actuator faults. Proceedings of the 2016 Chinese Control and Decision Conference (CCDC), Yinchuan, China.","DOI":"10.1109\/CCDC.2016.7531584"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Reyes-Valeria, E., Enriquez-Caldera, R., Camacho-Lara, S., and Guichard, J. (2013, January 11\u201313). LQR control for a quadrotor using unit quaternions: Modeling and simulation. Proceedings of the CONIELECOMP 2013, 23rd International Conference on Electronics, Communications and Computing, Cholula, Mexico.","DOI":"10.1109\/CONIELECOMP.2013.6525781"},{"key":"ref_24","unstructured":"Cowling, I.D., Whidborne, J.F., and Cooke, A.K. (2006, January 2). Optimal trajectory planning and LQR control for a quadrotor UAV. Proceedings of the International Conference on Control, Glasgow, UK."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Khatoon, S., Gupta, D., and Das, L. (2014, January 24\u201327). PID & LQR control for a quadrotor: Modeling and simulation. Proceedings of the 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI), New Delhi, India.","DOI":"10.1109\/ICACCI.2014.6968232"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lin, Q., Cai, Z., Wang, Y., Yang, J., and Chen, L. (2013, January 21\u201323). Adaptive flight control design for quadrotor UAV based on dynamic inversion and neural networks. Proceedings of the 2013 Third International Conference on Instrumentation, Measurement, Computer, Communication and Control, Shenyang, China.","DOI":"10.1109\/IMCCC.2013.326"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bouabdallah, S., and Siegwart, R. (November, January 29). Full control of a quadrotor. Proceedings of the 2007 IEEE\/RSJ International Conference on Intelligent Robots and Systems, San Diego, CA, USA.","DOI":"10.1109\/IROS.2007.4399042"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Madani, T., and Benallegue, A. (2006, January 6\u201310). Backstepping sliding mode control applied to a miniature quadrotor flying robot. Proceedings of the IECON 2006\u201432nd Annual Conference on IEEE Industrial Electronics, Paris, France.","DOI":"10.1109\/IECON.2006.347236"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/j.ifacol.2016.03.117","article-title":"A simplified adaptive backstepping control of aircraft lateral directional dynamics","volume":"49","author":"Swarnkar","year":"2016","journal-title":"IFAC PapersOnLine"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0005-1098(84)90069-4","article-title":"Application of nonlinear transformations to automatic flight control","volume":"20","author":"Meyer","year":"1984","journal-title":"Automatica"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/0005-1098(88)90092-1","article-title":"Flight control design using non-linear inverse dynamics","volume":"24","author":"Lane","year":"1988","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"903","DOI":"10.2514\/3.20730","article-title":"Design of restructurable flight control systems using feedback linearization","volume":"14","author":"Ochi","year":"1991","journal-title":"J. Guid. Control Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Raffo, G.V., Ortega, M.G., and Rubio, F.R. (2008, January 11\u201313). Backstepping\/nonlinear Hinf control for path tracking of a quadrotor unmanned aerial vehicle. Proceedings of the 2008 American Control Conference, Seattle, WA, USA.","DOI":"10.1109\/ACC.2008.4587010"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, Y., and Chamseddine, A. (2012). Fault tolerant flight control techniques with application to a quadrotor UAV testbed. Automatic Flight Control Systems-Latest Developments, IntechOpen.","DOI":"10.5772\/38918"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.3182\/20120829-3-MX-2028.00056","article-title":"Nonlinear fault-tolerant control of a quadrotor uav based on sliding mode control technique","volume":"45","author":"Li","year":"2012","journal-title":"IFAC Proc. Vol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1109\/TCST.2011.2121907","article-title":"Command filtered adaptive backstepping","volume":"20","author":"Dong","year":"2011","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_37","first-page":"461","article-title":"Neural network control for a semi-active vehicle suspension with a magnetorheological damper","volume":"10","author":"Guo","year":"2004","journal-title":"Modal Anal."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1109\/72.883478","article-title":"A robust neural controller for underwater robot manipulators","volume":"11","author":"Lee","year":"2000","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1109\/48.107144","article-title":"A neural net controller for underwater robotic vehicles","volume":"15","author":"Yuh","year":"1990","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Freddi, A., Longhi, S., Monteri\u00f9, A., and Prist, M. (2014, January 10\u201312). Actuator fault detection and isolation system for an hexacopter. Proceedings of the 2014 IEEE\/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications (MESA), Senigallia, Italy.","DOI":"10.1109\/MESA.2014.6935563"},{"key":"ref_41","unstructured":"Sheng, Q., Xianyi, Z., Changhong, W., Gao, X., and Zilong, L. (2002, January 10\u201314). Design and implementation of an adaptive PID controller using single neuron learning algorithm. Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, China."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Grzonka, S., Grisetti, G., and Burgard, W. (2009, January 12\u201317). Towards a navigation system for autonomous indoor flying. Proceedings of the 2009 IEEE international conference on Robotics and Automation, Kobe, Japan.","DOI":"10.1109\/ROBOT.2009.5152446"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"733219","DOI":"10.1117\/12.819082","article-title":"Stereo vision and laser odometry for autonomous helicopters in GPS-denied indoor environments","volume":"Volume 7332","author":"Achtelik","year":"2009","journal-title":"Unmanned Systems Technology XI"},{"key":"ref_44","unstructured":"Strydom, R., Thurrowgood, S., and Srinivasan, M.V. (2014, January 2\u20134). Visual odometry: Autonomous uav navigation using optic flow and stereo. Proceedings of the Australasian Conference on Robotics and Automation, Melbourne, Australia."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Huang, A.S., Bachrach, A., Henry, P., Krainin, M., Maturana, D., Fox, D., and Roy, N. (2017). Visual odometry and mapping for autonomous flight using an RGB-D camera. Robotics Research, Springer.","DOI":"10.1007\/978-3-319-29363-9_14"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Whelan, T., Johannsson, H., Kaess, M., Leonard, J.J., and McDonald, J. (2013, January 6\u201310). Robust real-time visual odometry for dense RGB-D mapping. Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6631400"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Dryanovski, I., Valenti, R.G., and Xiao, J. (2013, January 6\u201310). Fast visual odometry and mapping from RGB-D data. Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6630889"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Bl\u00f6sch, M., Weiss, S., Scaramuzza, D., and Siegwart, R. (2010, January 3\u20137). Vision based MAV navigation in unknown and unstructured environments. Proceedings of the 2010 IEEE International Conference on Robotics and Automation, Anchorage, AK, USA.","DOI":"10.1109\/ROBOT.2010.5509920"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Achtelik, M., Achtelik, M., Weiss, S., and Siegwart, R. (2011, January 9\u201313). Onboard IMU and monocular vision based control for MAVs in unknown in-and outdoor environments. Proceedings of the 2011 IEEE International Conference on Robotics and Automation, Shanghai, China.","DOI":"10.1109\/ICRA.2011.5980343"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Forster, C., Pizzoli, M., and Scaramuzza, D. (June, January 31). SVO: Fast semi-direct monocular visual odometry. Proceedings of the 2014 IEEE international conference on robotics and automation (ICRA), Hong Kong, China.","DOI":"10.1109\/ICRA.2014.6906584"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Engel, J., Sturm, J., and Cremers, D. (2012, January 7\u201312). Camera-based navigation of a low-cost quadrocopter. Proceedings of the 2012 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Portugal.","DOI":"10.1109\/IROS.2012.6385458"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1646","DOI":"10.1016\/j.robot.2014.03.012","article-title":"Scale-aware navigation of a low-cost quadrocopter with a monocular camera","volume":"62","author":"Engel","year":"2014","journal-title":"Robot. Auton. Syst."},{"key":"ref_53","unstructured":"Schmidt, M.D. (2011). Simulation and Control of a Quadrotor Unmanned Aerial Vehicle. [Master \u2019s Thesis, University of Kentucky]."},{"key":"ref_54","unstructured":"Haykin, S. (1994). Neural Networks: A Comprehensive Foundation, Prentice Hall PTR."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Puskorius, G.V., and Feldkamp, L.A. (2001). Parameter-based Kalman filter training: Theory and implementation. Kalman Filter. Neural Netw., 23.","DOI":"10.1002\/0471221546.ch2"},{"key":"ref_56","unstructured":"Williams, R.J. (1992, January 7\u201311). Training recurrent networks using the extended Kalman filter. Proceedings of the IJCNN International Joint Conference on Neural Networks, Baltimore, MD, USA."},{"key":"ref_57","unstructured":"Haykin, S. (2004). Kalman Filtering and Neural Networks, John Wiley & Sons."},{"key":"ref_58","unstructured":"Alanis, A.Y., and Sanchez, E.N. (2017). Discrete-Time Neural Observers: Analysis and Applications, Academic Press."},{"key":"ref_59","unstructured":"Camperos, E.N.S., and Garc\u00eda, A.Y.A. (2006). Redes neuronales: conceptos fundamentales y aplicaciones a control autom\u00e1tico, Pearson Educaci\u00f3n."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Klein, G., and Murray, D. (2007, January 13\u201316). Parallel tracking and mapping for small AR workspaces. Proceedings of the 2007 6th IEEE and ACM International Symposium on Mixed and Augmented Reality, Nara, Japan.","DOI":"10.1109\/ISMAR.2007.4538852"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Engel, J. (2011). Autonomous Camera-Based Navigation of a Quadrocopter. [Master\u2019s Thesis, TUM University].","DOI":"10.1109\/IROS.2012.6385458"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/2\/40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T13:38:05Z","timestamp":1719236285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/2\/40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,18]]},"references-count":61,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["a13020040"],"URL":"https:\/\/doi.org\/10.3390\/a13020040","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2020,2,18]]}}}