Mathematical Modelling and Identification of a Quadrotor

Motivated by the important growth of VTOL vehicles research such as quadrotors and to a small extent autonomous flight, a quadrotor dynamical model is presented in this work. The purpose of this study is to get a better understanding of its flight dynamics. It is an underactuated system. So, a simpl...

Full description

Autores:
Cárdenas R., César A.
COLLAZOS MORALES, CARLOS ANDRES
P. Ospina, Juan
Sánchez, Joaquín F.
Caro-Ruiz, Claudia
Hugo Grisales, Victor
Ariza Colpas, Paola Patricia
De-La-Hoz-Franco, Emiro
R. González, Ramón E.
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/7355
Acceso en línea:
https://hdl.handle.net/11323/7355
https://doi.org/10.1007/978-3-030-58799-4_19
https://repositorio.cuc.edu.co/
Palabra clave:
Quadrotor
VTOL
Flight dynamics
UAV
Rights
openAccess
License
Attribution-NonCommercial-NoDerivatives 4.0 International
id RCUC2_bce304ea529d4e1ba49e859c9976184a
oai_identifier_str oai:repositorio.cuc.edu.co:11323/7355
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.spa.fl_str_mv Mathematical Modelling and Identification of a Quadrotor
title Mathematical Modelling and Identification of a Quadrotor
spellingShingle Mathematical Modelling and Identification of a Quadrotor
Quadrotor
VTOL
Flight dynamics
UAV
title_short Mathematical Modelling and Identification of a Quadrotor
title_full Mathematical Modelling and Identification of a Quadrotor
title_fullStr Mathematical Modelling and Identification of a Quadrotor
title_full_unstemmed Mathematical Modelling and Identification of a Quadrotor
title_sort Mathematical Modelling and Identification of a Quadrotor
dc.creator.fl_str_mv Cárdenas R., César A.
COLLAZOS MORALES, CARLOS ANDRES
P. Ospina, Juan
Sánchez, Joaquín F.
Caro-Ruiz, Claudia
Hugo Grisales, Victor
Ariza Colpas, Paola Patricia
De-La-Hoz-Franco, Emiro
R. González, Ramón E.
dc.contributor.author.spa.fl_str_mv Cárdenas R., César A.
COLLAZOS MORALES, CARLOS ANDRES
P. Ospina, Juan
Sánchez, Joaquín F.
Caro-Ruiz, Claudia
Hugo Grisales, Victor
Ariza Colpas, Paola Patricia
De-La-Hoz-Franco, Emiro
R. González, Ramón E.
dc.subject.spa.fl_str_mv Quadrotor
VTOL
Flight dynamics
UAV
topic Quadrotor
VTOL
Flight dynamics
UAV
description Motivated by the important growth of VTOL vehicles research such as quadrotors and to a small extent autonomous flight, a quadrotor dynamical model is presented in this work. The purpose of this study is to get a better understanding of its flight dynamics. It is an underactuated system. So, a simplified and clear model is needed to implement controllers on these kind of unmanned aerial systems. In addition, a computational tool is used for validation purposes. For future works embedded or intelligent control systems can be developed to control them. Gyroscopic and some aerodynamics effects are neglected.
publishDate 2020
dc.date.accessioned.none.fl_str_mv 2020-11-19T14:37:57Z
dc.date.available.none.fl_str_mv 2020-11-19T14:37:57Z
dc.date.issued.none.fl_str_mv 2020
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
format http://purl.org/coar/resource_type/c_6501
status_str acceptedVersion
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/7355
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.1007/978-3-030-58799-4_19
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
url https://hdl.handle.net/11323/7355
https://doi.org/10.1007/978-3-030-58799-4_19
https://repositorio.cuc.edu.co/
identifier_str_mv Corporación Universidad de la Costa
REDICUC - Repositorio CUC
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartof.spa.fl_str_mv https://link.springer.com/bookseries/558
dc.relation.references.spa.fl_str_mv 1. Bresciani, T.: Modelling, identification and control of a quadrotor helicopter. MSc theses (2008)
2. Cárdenas Ruiz, C.A.: Performance study of the flight control and path planning for a UAV type Quadrotor. Ingeniería Mecatrónica (2018)
3. Collazos, C., et al.: State estimation of a dehydration process by interval analysis. In: Figueroa-García, J.C., López-Santana, E.R., Rodriguez-Molano, J.I. (eds.) WEA 2018. CCIS, vol. 915, pp. 66–77. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00350-0_6
4. Cook, M.V.: Flight Dynamics Prıncıples. Elsevıer (2007)
5. Cork, L.R.: Aircraft dynamic navigation for unmanned aerial vehicles. Ph.D. thesis. Queensland University of Technology (2014)
6. Cowling, I.: Towards autonomy of a Quadrotor UAV (2008)
7. Habib, M.K., Abdelaal, W.G.A., Saad, M.S., et al.: Dynamic modeling and control of a Quadrotor using linear and nonlinear approaches (2014)
8. Huang, H., et al.: Aerodynamics and control of autonomous Quadrotor helicopters in aggressive maneuvering. In: IEEE International Conference on Robotics and Automation, ICRA 2009, pp. 3277–3282. IEEE (2009)
9. Ireland, M.L.: Investigations in multi-resolution modelling of the Quadrotor micro air vehicle. Ph.D. thesis. University of Glasgow (2014)
10. Jiménez-Cabas, J., et al.: Robust control of an evaporator through algebraic Riccati equations and d-K iteration. In: Misra, S., et al. (eds.) ICCSA 2019. LNCS, vol. 11620, pp. 731–742. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-24296-1_58
11. Leishman, G.J.: Principles of Helicopter Aerodynamics with CD Extra. Cambridge University Press, Cambridge (2006)
12. Lugo-Cárdenas, I., et al.: Dubins path generation for a fixed wing UAV. In: 2014 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 339–346. IEEE (2014)
13. Malang, Y.: Design and Control of a Vertical Takeo and Landing Fixed-wing Unmanned Aerial Vehicle. Ph.D. thesis (2016)
14. Mulder, S.: Flight Dynamics (2007)
15. Swartling, J.O.: Circumnavigation with a group of Quadrotor helicopters (2014)
16. Pharpatara, P.: Trajectory planning for aerial vehicles with constraints. Theses. Université Paris-Saclay; Université d’Evry-Val-d’Essonne, September 2015. https://tel.archives-ouvertes.fr/tel-01206423
17. Poyi, G.T.: A novel approach to the control of quad-rotor helicopters using fuzzy-neural networks (2014)
18. Sabatino, F.: Quadrotor control: modeling, nonlinear control design, and simulation (2015)
19. Voos, H.: Nonlinear control of a Quadrotor micro-UAV using feedback linearization. In: International Conference on Mechatronics, ICM 2009, pp. 1–6. IEEE (2009)
dc.rights.spa.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Corporación Universidad de la Costa
dc.source.spa.fl_str_mv International Conference on Computational Science and Its Applications
institution Corporación Universidad de la Costa
dc.source.url.spa.fl_str_mv https://link.springer.com/chapter/10.1007/978-3-030-58799-4_19
bitstream.url.fl_str_mv https://repositorio.cuc.edu.co/bitstreams/a1d6dace-a033-47a9-9149-e650537ec96d/download
https://repositorio.cuc.edu.co/bitstreams/7c5f19c3-17a7-4a2d-9c6c-f1382445e253/download
https://repositorio.cuc.edu.co/bitstreams/4054b093-b708-4449-9b2e-360c5e858d7a/download
https://repositorio.cuc.edu.co/bitstreams/5456aaf8-beb6-4c25-b165-8a48d12971de/download
https://repositorio.cuc.edu.co/bitstreams/c7a6252d-c546-439c-b3d6-d01462735d88/download
bitstream.checksum.fl_str_mv 0ad0e83fb0c4c40ee38d9c6079b279df
4460e5956bc1d1639be9ae6146a50347
e30e9215131d99561d40d6b0abbe9bad
7bb3e7e82bbf230d6b890867546001ba
b08f705026bdde88ff04cc31a9eba5b0
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio de la Universidad de la Costa CUC
repository.mail.fl_str_mv repdigital@cuc.edu.co
_version_ 1828166816853131264
spelling Cárdenas R., César A.COLLAZOS MORALES, CARLOS ANDRESP. Ospina, JuanSánchez, Joaquín F.Caro-Ruiz, ClaudiaHugo Grisales, VictorAriza Colpas, Paola PatriciaDe-La-Hoz-Franco, EmiroR. González, Ramón E.2020-11-19T14:37:57Z2020-11-19T14:37:57Z2020https://hdl.handle.net/11323/7355https://doi.org/10.1007/978-3-030-58799-4_19Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Motivated by the important growth of VTOL vehicles research such as quadrotors and to a small extent autonomous flight, a quadrotor dynamical model is presented in this work. The purpose of this study is to get a better understanding of its flight dynamics. It is an underactuated system. So, a simplified and clear model is needed to implement controllers on these kind of unmanned aerial systems. In addition, a computational tool is used for validation purposes. For future works embedded or intelligent control systems can be developed to control them. Gyroscopic and some aerodynamics effects are neglected.Cárdenas R., César A.COLLAZOS MORALES, CARLOS ANDRES-will be generated-orcid-0000-0002-1996-1384-600P. Ospina, JuanSánchez, Joaquín F.Caro-Ruiz, ClaudiaHugo Grisales, VictorAriza Colpas, Paola Patricia-will be generated-orcid-0000-0003-4503-5461-600De-La-Hoz-Franco, Emiro-will be generated-orcid-0000-0002-4926-7414-600R. González, Ramón E.application/pdfengCorporación Universidad de la Costahttps://link.springer.com/bookseries/5581. Bresciani, T.: Modelling, identification and control of a quadrotor helicopter. MSc theses (2008)2. Cárdenas Ruiz, C.A.: Performance study of the flight control and path planning for a UAV type Quadrotor. Ingeniería Mecatrónica (2018)3. Collazos, C., et al.: State estimation of a dehydration process by interval analysis. In: Figueroa-García, J.C., López-Santana, E.R., Rodriguez-Molano, J.I. (eds.) WEA 2018. CCIS, vol. 915, pp. 66–77. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00350-0_64. Cook, M.V.: Flight Dynamics Prıncıples. Elsevıer (2007)5. Cork, L.R.: Aircraft dynamic navigation for unmanned aerial vehicles. Ph.D. thesis. Queensland University of Technology (2014)6. Cowling, I.: Towards autonomy of a Quadrotor UAV (2008)7. Habib, M.K., Abdelaal, W.G.A., Saad, M.S., et al.: Dynamic modeling and control of a Quadrotor using linear and nonlinear approaches (2014)8. Huang, H., et al.: Aerodynamics and control of autonomous Quadrotor helicopters in aggressive maneuvering. In: IEEE International Conference on Robotics and Automation, ICRA 2009, pp. 3277–3282. IEEE (2009)9. Ireland, M.L.: Investigations in multi-resolution modelling of the Quadrotor micro air vehicle. Ph.D. thesis. University of Glasgow (2014)10. Jiménez-Cabas, J., et al.: Robust control of an evaporator through algebraic Riccati equations and d-K iteration. In: Misra, S., et al. (eds.) ICCSA 2019. LNCS, vol. 11620, pp. 731–742. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-24296-1_5811. Leishman, G.J.: Principles of Helicopter Aerodynamics with CD Extra. Cambridge University Press, Cambridge (2006)12. Lugo-Cárdenas, I., et al.: Dubins path generation for a fixed wing UAV. In: 2014 International Conference on Unmanned Aircraft Systems (ICUAS), pp. 339–346. IEEE (2014)13. Malang, Y.: Design and Control of a Vertical Takeo and Landing Fixed-wing Unmanned Aerial Vehicle. Ph.D. thesis (2016)14. Mulder, S.: Flight Dynamics (2007)15. Swartling, J.O.: Circumnavigation with a group of Quadrotor helicopters (2014)16. Pharpatara, P.: Trajectory planning for aerial vehicles with constraints. Theses. Université Paris-Saclay; Université d’Evry-Val-d’Essonne, September 2015. https://tel.archives-ouvertes.fr/tel-0120642317. Poyi, G.T.: A novel approach to the control of quad-rotor helicopters using fuzzy-neural networks (2014)18. Sabatino, F.: Quadrotor control: modeling, nonlinear control design, and simulation (2015)19. Voos, H.: Nonlinear control of a Quadrotor micro-UAV using feedback linearization. In: International Conference on Mechatronics, ICM 2009, pp. 1–6. IEEE (2009)Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2International Conference on Computational Science and Its Applicationshttps://link.springer.com/chapter/10.1007/978-3-030-58799-4_19QuadrotorVTOLFlight dynamicsUAVMathematical Modelling and Identification of a QuadrotorArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionPublicationORIGINALMathematical Modelling and Identification of a Quadrotor.pdfMathematical Modelling and Identification of a Quadrotor.pdfapplication/pdf80079https://repositorio.cuc.edu.co/bitstreams/a1d6dace-a033-47a9-9149-e650537ec96d/download0ad0e83fb0c4c40ee38d9c6079b279dfMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.cuc.edu.co/bitstreams/7c5f19c3-17a7-4a2d-9c6c-f1382445e253/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/4054b093-b708-4449-9b2e-360c5e858d7a/downloade30e9215131d99561d40d6b0abbe9badMD53THUMBNAILMathematical Modelling and Identification of a Quadrotor.pdf.jpgMathematical Modelling and Identification of a Quadrotor.pdf.jpgimage/jpeg29961https://repositorio.cuc.edu.co/bitstreams/5456aaf8-beb6-4c25-b165-8a48d12971de/download7bb3e7e82bbf230d6b890867546001baMD54TEXTMathematical Modelling and Identification of a Quadrotor.pdf.txtMathematical Modelling and Identification of a Quadrotor.pdf.txttext/plain957https://repositorio.cuc.edu.co/bitstreams/c7a6252d-c546-439c-b3d6-d01462735d88/downloadb08f705026bdde88ff04cc31a9eba5b0MD5511323/7355oai:repositorio.cuc.edu.co:11323/73552024-09-17 14:13:28.642http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.coQXV0b3Jpem8gKGF1dG9yaXphbW9zKSBhIGxhIEJpYmxpb3RlY2EgZGUgbGEgSW5zdGl0dWNpw7NuIHBhcmEgcXVlIGluY2x1eWEgdW5hIGNvcGlhLCBpbmRleGUgeSBkaXZ1bGd1ZSBlbiBlbCBSZXBvc2l0b3JpbyBJbnN0aXR1Y2lvbmFsLCBsYSBvYnJhIG1lbmNpb25hZGEgY29uIGVsIGZpbiBkZSBmYWNpbGl0YXIgbG9zIHByb2Nlc29zIGRlIHZpc2liaWxpZGFkIGUgaW1wYWN0byBkZSBsYSBtaXNtYSwgY29uZm9ybWUgYSBsb3MgZGVyZWNob3MgcGF0cmltb25pYWxlcyBxdWUgbWUobm9zKSBjb3JyZXNwb25kZShuKSB5IHF1ZSBpbmNsdXllbjogbGEgcmVwcm9kdWNjacOzbiwgY29tdW5pY2FjacOzbiBww7pibGljYSwgZGlzdHJpYnVjacOzbiBhbCBww7pibGljbywgdHJhbnNmb3JtYWNpw7NuLCBkZSBjb25mb3JtaWRhZCBjb24gbGEgbm9ybWF0aXZpZGFkIHZpZ2VudGUgc29icmUgZGVyZWNob3MgZGUgYXV0b3IgeSBkZXJlY2hvcyBjb25leG9zIHJlZmVyaWRvcyBlbiBhcnQuIDIsIDEyLCAzMCAobW9kaWZpY2FkbyBwb3IgZWwgYXJ0IDUgZGUgbGEgbGV5IDE1MjAvMjAxMiksIHkgNzIgZGUgbGEgbGV5IDIzIGRlIGRlIDE5ODIsIExleSA0NCBkZSAxOTkzLCBhcnQuIDQgeSAxMSBEZWNpc2nDs24gQW5kaW5hIDM1MSBkZSAxOTkzIGFydC4gMTEsIERlY3JldG8gNDYwIGRlIDE5OTUsIENpcmN1bGFyIE5vIDA2LzIwMDIgZGUgbGEgRGlyZWNjacOzbiBOYWNpb25hbCBkZSBEZXJlY2hvcyBkZSBhdXRvciwgYXJ0LiAxNSBMZXkgMTUyMCBkZSAyMDEyLCBsYSBMZXkgMTkxNSBkZSAyMDE4IHkgZGVtw6FzIG5vcm1hcyBzb2JyZSBsYSBtYXRlcmlhLg0KDQpBbCByZXNwZWN0byBjb21vIEF1dG9yKGVzKSBtYW5pZmVzdGFtb3MgY29ub2NlciBxdWU6DQoNCi0gTGEgYXV0b3JpemFjacOzbiBlcyBkZSBjYXLDoWN0ZXIgbm8gZXhjbHVzaXZhIHkgbGltaXRhZGEsIGVzdG8gaW1wbGljYSBxdWUgbGEgbGljZW5jaWEgdGllbmUgdW5hIHZpZ2VuY2lhLCBxdWUgbm8gZXMgcGVycGV0dWEgeSBxdWUgZWwgYXV0b3IgcHVlZGUgcHVibGljYXIgbyBkaWZ1bmRpciBzdSBvYnJhIGVuIGN1YWxxdWllciBvdHJvIG1lZGlvLCBhc8OtIGNvbW8gbGxldmFyIGEgY2FibyBjdWFscXVpZXIgdGlwbyBkZSBhY2Npw7NuIHNvYnJlIGVsIGRvY3VtZW50by4NCg0KLSBMYSBhdXRvcml6YWNpw7NuIHRlbmRyw6EgdW5hIHZpZ2VuY2lhIGRlIGNpbmNvIGHDsW9zIGEgcGFydGlyIGRlbCBtb21lbnRvIGRlIGxhIGluY2x1c2nDs24gZGUgbGEgb2JyYSBlbiBlbCByZXBvc2l0b3JpbywgcHJvcnJvZ2FibGUgaW5kZWZpbmlkYW1lbnRlIHBvciBlbCB0aWVtcG8gZGUgZHVyYWNpw7NuIGRlIGxvcyBkZXJlY2hvcyBwYXRyaW1vbmlhbGVzIGRlbCBhdXRvciB5IHBvZHLDoSBkYXJzZSBwb3IgdGVybWluYWRhIHVuYSB2ZXogZWwgYXV0b3IgbG8gbWFuaWZpZXN0ZSBwb3IgZXNjcml0byBhIGxhIGluc3RpdHVjacOzbiwgY29uIGxhIHNhbHZlZGFkIGRlIHF1ZSBsYSBvYnJhIGVzIGRpZnVuZGlkYSBnbG9iYWxtZW50ZSB5IGNvc2VjaGFkYSBwb3IgZGlmZXJlbnRlcyBidXNjYWRvcmVzIHkvbyByZXBvc2l0b3Jpb3MgZW4gSW50ZXJuZXQgbG8gcXVlIG5vIGdhcmFudGl6YSBxdWUgbGEgb2JyYSBwdWVkYSBzZXIgcmV0aXJhZGEgZGUgbWFuZXJhIGlubWVkaWF0YSBkZSBvdHJvcyBzaXN0ZW1hcyBkZSBpbmZvcm1hY2nDs24gZW4gbG9zIHF1ZSBzZSBoYXlhIGluZGV4YWRvLCBkaWZlcmVudGVzIGFsIHJlcG9zaXRvcmlvIGluc3RpdHVjaW9uYWwgZGUgbGEgSW5zdGl0dWNpw7NuLCBkZSBtYW5lcmEgcXVlIGVsIGF1dG9yKHJlcykgdGVuZHLDoW4gcXVlIHNvbGljaXRhciBsYSByZXRpcmFkYSBkZSBzdSBvYnJhIGRpcmVjdGFtZW50ZSBhIG90cm9zIHNpc3RlbWFzIGRlIGluZm9ybWFjacOzbiBkaXN0aW50b3MgYWwgZGUgbGEgSW5zdGl0dWNpw7NuIHNpIGRlc2VhIHF1ZSBzdSBvYnJhIHNlYSByZXRpcmFkYSBkZSBpbm1lZGlhdG8uDQoNCi0gTGEgYXV0b3JpemFjacOzbiBkZSBwdWJsaWNhY2nDs24gY29tcHJlbmRlIGVsIGZvcm1hdG8gb3JpZ2luYWwgZGUgbGEgb2JyYSB5IHRvZG9zIGxvcyBkZW3DoXMgcXVlIHNlIHJlcXVpZXJhIHBhcmEgc3UgcHVibGljYWNpw7NuIGVuIGVsIHJlcG9zaXRvcmlvLiBJZ3VhbG1lbnRlLCBsYSBhdXRvcml6YWNpw7NuIHBlcm1pdGUgYSBsYSBpbnN0aXR1Y2nDs24gZWwgY2FtYmlvIGRlIHNvcG9ydGUgZGUgbGEgb2JyYSBjb24gZmluZXMgZGUgcHJlc2VydmFjacOzbiAoaW1wcmVzbywgZWxlY3Ryw7NuaWNvLCBkaWdpdGFsLCBJbnRlcm5ldCwgaW50cmFuZXQsIG8gY3VhbHF1aWVyIG90cm8gZm9ybWF0byBjb25vY2lkbyBvIHBvciBjb25vY2VyKS4NCg0KLSBMYSBhdXRvcml6YWNpw7NuIGVzIGdyYXR1aXRhIHkgc2UgcmVudW5jaWEgYSByZWNpYmlyIGN1YWxxdWllciByZW11bmVyYWNpw7NuIHBvciBsb3MgdXNvcyBkZSBsYSBvYnJhLCBkZSBhY3VlcmRvIGNvbiBsYSBsaWNlbmNpYSBlc3RhYmxlY2lkYSBlbiBlc3RhIGF1dG9yaXphY2nDs24uDQoNCi0gQWwgZmlybWFyIGVzdGEgYXV0b3JpemFjacOzbiwgc2UgbWFuaWZpZXN0YSBxdWUgbGEgb2JyYSBlcyBvcmlnaW5hbCB5IG5vIGV4aXN0ZSBlbiBlbGxhIG5pbmd1bmEgdmlvbGFjacOzbiBhIGxvcyBkZXJlY2hvcyBkZSBhdXRvciBkZSB0ZXJjZXJvcy4gRW4gY2FzbyBkZSBxdWUgZWwgdHJhYmFqbyBoYXlhIHNpZG8gZmluYW5jaWFkbyBwb3IgdGVyY2Vyb3MgZWwgbyBsb3MgYXV0b3JlcyBhc3VtZW4gbGEgcmVzcG9uc2FiaWxpZGFkIGRlbCBjdW1wbGltaWVudG8gZGUgbG9zIGFjdWVyZG9zIGVzdGFibGVjaWRvcyBzb2JyZSBsb3MgZGVyZWNob3MgcGF0cmltb25pYWxlcyBkZSBsYSBvYnJhIGNvbiBkaWNobyB0ZXJjZXJvLg0KDQotIEZyZW50ZSBhIGN1YWxxdWllciByZWNsYW1hY2nDs24gcG9yIHRlcmNlcm9zLCBlbCBvIGxvcyBhdXRvcmVzIHNlcsOhbiByZXNwb25zYWJsZXMsIGVuIG5pbmfDum4gY2FzbyBsYSByZXNwb25zYWJpbGlkYWQgc2Vyw6EgYXN1bWlkYSBwb3IgbGEgaW5zdGl0dWNpw7NuLg0KDQotIENvbiBsYSBhdXRvcml6YWNpw7NuLCBsYSBpbnN0aXR1Y2nDs24gcHVlZGUgZGlmdW5kaXIgbGEgb2JyYSBlbiDDrW5kaWNlcywgYnVzY2Fkb3JlcyB5IG90cm9zIHNpc3RlbWFzIGRlIGluZm9ybWFjacOzbiBxdWUgZmF2b3JlemNhbiBzdSB2aXNpYmlsaWRhZA==