Categories
Aircraft Flight Control Aircraft Flight Dynamics Aircraft Flight Mechanics Control Theory Embedded Systems Fault Tolerant Control Intelligent Control Systems Real-time Control Systems Remotely Operated Vehicles Robotics ROV UAV Unmanned Aerial Vehicles

Research

Fault Tolerant Air Data System

Fault tolerant air data system for pitot failure simulation results

An integrated fault detection, identification, isolation, and accommodation scheme is proposed for an Air Data System with airspeed and angle of attack sensors. The system uses information from the inertial measurement unit, available air data sensors, and an aircraft digital twin model that provides virtual measurements of its aerodynamic and propulsion forces to feed a nonlinear estimator capable of detecting air sensor failure and suppressing sensor fault effects on the aircraft air data prediction.

UAV for research in Flight Mechanics and Control

UAV for research in flight mechanics and control

A UAV was developed for research in Flight Mechanics and Flight Controls. The project involves integrating sensors with an embedded processor in a small fixed-wing aircraft and creating a flexible software infrastructure for implementing and testing flight control algorithms. The sensor suite consists of an IMU, a magnetometer, a GPS, a pitot tube with a differential pressure sensor, alpha and beta vanes, control surface position sensors, and a sensor for engine RPM. An actuator interface and RF communication link are also included for telecommand and telemetry.

Flight Data Recorder for acquisition of flight test data in a ultra light aircraft

Flight data recorder for acquisition of flight test data

A flight data recording system was developed for an ultralight aircraft. The aircraft was instrumented for recording data from certification flight tests and mathematical aircraft modeling.

Structure Manager, a software infrastructure for the implementation of Real Time Control Systems

Structure manager software in a Eclipse IDE

A software infrastructure for implementing real-time control systems has been developed in C language. The infrastructure, combined with a sound programming methodology (object-oriented), enables some powerful features in the real-time application, accelerating the production cycle of the software. The Structure Manager comprises a library that implements all the infrastructure functionality and a tool to automatically generate code at compilation time that connects the infrastructure with the application.

Andean Condor UAV

Andean Condor UAV

The Andean Condor unmanned aerial system is a tactical UAV for surveillance, exploration, reconnaissance, and intelligence. Possible applications in photogrammetry and precision agriculture are also considered. This development resulted from the project “Development of a fixed-wing unmanned aerial system for short-range missions – Aura Jr” (2007-2009).

Software for modeling, analysis and design of a fixed wing aircraft

Software for modeling, analysis and design of a fixed wing aircraft

The software has been developed to model, analyze, and design a fixed-wing aircraft. The software comprises a set of functions written in the Matlab® language and is fully compatible with Octave and a collection of simulation models developed in Simulink® that include the simulation of the nonlinear aircraft model with the flight control system. Several versions of the simulation model are more refined than others.

VISOR 3 ROV

Visor 3 ROV

VISOR 3 is an ROV developed by the Excuela Naval Almirante Padilla (ENAP) and Universidad Pontificia Bolivariana (UPB), through the research groups in Naval Engineering (GIIN), Automation and Design A+D and the Institute of Energy and Thermodynamics (IET), with the support of Colciencias. The ROV is an underwater robotic platform for inspecting port structures and hulls of transport vessels to comply with the ISPS code.

Aura Jr UAV

Aura Jr UAV

Aura Jr was a small UAV for short-range missions, the first UAV developed at the Universidad Pontificia Bolivariana. The prototype was a technology demonstrator for the project “Research and Design of an Automatic Remote Inspection System for Electric Power Transmission Lines” (2004-2005) sponsored by Interconectado Eléctrica SA (ISA), Colciencias and Universidad Pontificia Bolivariana. It led to another project, “Development of a fixed-wing unmanned aerial system for short-range missions – Aura Jr” (2007-2009).

Preliminary design of Aura UAV for monitoring of Power Transmission Lines

Aura UAV

The Aura UAV’s preliminary design resulted from the project “Research and Design of an Automatic Remote Inspection System for Electric Power Transmission Lines” (2004-2005). Its primary objective was to investigate and design an autonomous inspection system prototype for high and extra-high-voltage transmission lines.

Adaptive Mode Transition Control Architecture With an Application to Unmanned Aerial Vehicles

GTmax, Georgia Tech UAV testbed

A new approach to unmanned aerial vehicles’ adaptive mode transition control was proposed. The proposed architecture consists of three levels: mission planning routines are at the highest level, where the information about waypoints the vehicle must follow is processed; the mid-level controller uses a trajectory-planning component to coordinate the task execution and provides set points for low-level stabilizing controllers. The adaptive mode-transitioning control algorithm resides at the lowest level of the hierarchy consisting of a mode-transitioning controller and the accompanying adaptation mechanism. A flight demonstration was done as part of a Software Enabled Control research program (sponsored by DARPA) to validate the control algorithms using the GTmax, the Georgia Tech UAV testbed.

VISOR 2 ROV

Visor 2 ROV

VISOR 2 was an ROV developed as an underwater vehicle with dual control (1998-2000). Julio Cesar Correa Rodríguez, Luis Benigno Gutiérrez Zea, and Laszlo Jurko led the project.

Neural Network Control of a Flexible Link

Neural network control of a flexible link

A neural network (NN) tracking controller was implemented on a single flexible link, and the performance results of the neural network controller were compared to that of proportional derivative (PD) and proportional integral derivative (PID) standard controllers. The NN controller comprises an outer PD tracking loop, a singular perturbation inner loop to stabilize the fast flexible-mode dynamics, and an NN inner loop to feedback linearize the slow pointing dynamics. It is shown that the tracking performance of the NN controller is far better than that of the PD or PID standard controllers. No offline training or learning was needed for the NN. An extra friction term was added to the tests to demonstrate the ability of the NN to learn unmodeled nonlinear dynamics.

Categories
Control Theory Intelligent Control Systems Robotics

Neural Network Control of a Flexible Link

Neural network control of a flexible link

Summary

A neural network (NN) tracking controller was implemented on a single flexible link and the performance results of the neural network controller were compared to that of proportional derivative (PD) and proportional integral derivative (PID) standard controllers. The NN controller is composed of an outer PD tracking loop, a singular perturbation inner loop for stabilization of the fast flexible-mode dynamics, and an NN inner loop used to feedback linearize the slow pointing dynamics. No off-line training or learning is needed for the NN. It is shown that the tracking performance of the NN controller is far better than that of the PD or PID standard controllers. An extra friction term was added in the tests to demonstrate the ability of the NN to learn unmodeled nonlinear dynamics.

Gallery

Presentation

Related publications

[1] L. B. Gutiérrez, F. L. Lewis, and J. A. Lowe, “Implementation of a neural network tracking controller for a single flexible link: comparison with PD and PID controllers,” IEEE Transactions on Industrial Electronics, vol. 45, pp. 307–318, April 1998. Available: https://ieeexplore.ieee.org/document/681230, ISSN: 1557-9948, doi: https://doi.org/10.1109/41.681230. pdf

[2] L. B. Gutiérrez and F. L. Lewis, “Implementation of a neural net tracking controller for a single flexible link: comparison with PD and PID controllers,” in Proc. 1997 American Control Conference, (Albuquerque, NM, USA), pp. 657–661, IEEE, June 6, 1997. Available: https://ieeexplore.ieee.org/document/611882, ISBN:0-7803-3832-4, ISSN: 0743-1619, doi: https://doi.org/10.1109/ACC.1997.611882. pdf

[3] L. B. Gutiérrez and F. L. Lewis, “Implementación de un controlador de seguimiento con redes neuronales para un brazo flexible sencillo: comparación con controladores PD y PID,” in 2o Congreso de la Asociacion Colombiana de Automatica, (Bucaramanga, Colombia), pp. 200-216, Asociación Colombiana de Automática, Marzo 19-22, 1997. pdf

[4] L. B. Gutiérrez, “Implementation of a neural network tracking controller for a single flexible link: comparison with PD and PID controllers,” Master’s thesis, The University of Texas at Arlington, Department of Electrical Engineering, Arlington, TX, USA, August 1996. pdf

Categories
Aircraft Flight Control Control Theory Embedded Systems Intelligent Control Systems Real-time Control Systems Robotics UAV Unmanned Aerial Vehicles

Adaptive Mode Transition Control Architecture With an Application to Unmanned Aerial Vehicles

GTmax, Georgia Tech UAV testbed

Summary

A new approach to the adaptive mode transition control of unmanned aerial vehicles was proposed. The proposed architecture consists of three levels: the highest level is occupied by mission planning routines where information about way points the vehicle must follow is processed, The mid-level controller uses a trajectory-planning component to coordinate the task execution and provides set points for low-level stabilizing controllers. The adaptive mode transitioning control algorithm resides at the lowest level of the hierarchy consisting of a mode transitioning controller and the accompanying adaptation mechanism. A flight demonstration was done as part of a DARPA sponsored research program to validate the control algorithms using the GTmax, the Georgia Tech UAV testbed.

Adaptive Mode Transition Control

Unmanned Aerial Vehicles (UAVs) are required to possess levels of autonomy in order to execute complex missions robustly and reliably. Intelligent/hierarchical control techniques have been suggested as a means to address critical autonomy issues. The objective of this research is to develop a hierarchical/intelligent control architecture for an UAV. The architecture consists of three levels: high level, middle level, and low level. Mission planning routines occupy the highest level. At this level, information about waypoints that the vehicle must follow is used to generate the sequence of actions that should be performed to go through those waypoints while maintaining some physical constraints. These actions are split into a sequence of tasks; each of them containing target position, target speed, target heading, heading mode, and target direction of the flight path. The tasks are then stored in a task queue and sent in an orderly manner to the middle level. The middle-level controller coordinates task execution while a trajectory generation component receives the task information from the high-level module and provides set points for low-level stabilizing controllers whose function is to maintain the vehicle in a stable state and follow accurately the commanded trajectory. An adaptive mode transitioning control algorithm resides at the lowest level of the hierarchy consisting of two components: a mode transitioning controller and the accompanying adaptation mechanism. The mode transition controller is composed of a mode transition manager, a set of local controllers, and a set of active control models. Local controllers operate in local modes and active control models operate in transitions between two local modes. The mode transition manager determines the actual mode of operation of the vehicle based on a set of mode membership functions and activates a local controller or an active control model accordingly. The adaptation mechanism uses an indirect adaptive control methodology to adapt the active control models. For this purpose, a set of plant models is trained based on input/output information from the vehicle and used to compute the linearized models required by the adaptation algorithms. The core of the adaptation mechanism is a finite horizon optimal control algorithm, which determines the optimal control signal that in turn is used to train the active control models. The adaptation routine may be turned on only when needed. The transitioning algorithm operates in real-time while adapting on-line to disturbances and other external inputs. This intelligent/hierarchical architecture has been implemented using a novel software infrastructure called Open Control Platform (OCP), which facilitates interoperability, plug-and-play and other functionalities. Simulation and flight test results validate the proposed scheme.

The main contributions of this research are:

  • Development of a hierarchical architecture for the implementation of the adaptive mode transition control, flexible enough to be able to accommodate future enhancements and more intelligent at the highest level of the hierarchy.
  • Development of a new approach to the adaptive mode transition control problem addressing main concerns from previous accomplishments in this area.
  • Exploitation of new software technologies including the OCP and hybrid controls API to show how they enable the implementation of advanced control algorithms for UAVs.

Presentation

Related Publications

[1] G. Vachtsevanos, L. Tang, G. Drozeski, and L. Gutiérrez, “From mission planning to flight control of unmanned aerial vehicles: Strategies and implementation tools,” Annual Reviews in Control, vol. 29, no. 1, pp. 101–115, 2005. Available: https://www.sciencedirect.com/science/article/pii/S136757880500009X, ISSN: 1367-5788, doi: https://doi.org/10.1016/j.arcontrol.2004.11.002. pdf

[2] G. Vachtsevanos, L. Tang, G. Drozeski, and L. Gutiérrez, “Intelligent control of unmanned aerial vehicles for improved autonomy and reliability,” in IFAC/EURON Symposium on Intelligent Autonomous Vehicles, (Lisbon, Portugal), pp. 852–861, International Federation of Automatic Control, IFAC, July 5-7, 2004. Available: https://www.sciencedirect.com/science/article/pii/S1474667017320876, ISSN: 1474-6670, doi: https://doi.org/10.1016/S1474-6670(17)32087-6. pdf

[3] L. B. Gutiérrez, G. Vachtsevanos, and B. Heck, “A hierarchical architecture for the adaptive mode transition control of unmanned aerial vehicles,” in Proc. AIAA Guidance, Navigation, and Control Conference and Exhibit, (Austin, Texas, USA), American Institute of Aeronautics and Astronautics, AIAA, August 11-14, 2003. Available: https://arc.aiaa.org/doi/10.2514/6.2003-5740, eISBN: 978-1-62410-090-1, doi: https://doi.org/10.2514/6.2003-5740. pdf

[4] L. B. Gutiérrez, “Vehículos aéreos autónomos,” in Memorias del V Congreso de la Asociación Colombiana de Automática, (Medellı́n, Colombia), Asociación Colombiana de Automática, ACA, Julio 17-19, 2003. ISBN: 9588173515. Presentation

[5] L. B. Gutiérrez, G. Vachtsevanos, and B. Heck, “A hierarchical/intelligent control architecture for unmanned aerial vehicles,” in Proc. of the 11th Mediterranean Conference on Control and Automation MED’03, (Rhodes, Greece), Mediterranean Control Association, June 18-20, 2003. Available: http://med-control.org/medproceedings/MED11-2003.zip. pdf

[6] L. B. Gutiérrez, G. Vachtsevanos, and B. Heck, “An approach to the adaptive mode transition control of unmanned aerial vehicles,” in Proc. 2003 American Control Conference, (Denver, Colorado), pp. 3911–3912, IEEE, June 4-6, 2003. Available: https://ieeexplore.ieee.org/document/1240446, ISBN: 0-7803-7896-2, ISSN: 0743-1619, doi: https://doi.org/10.1109/ACC.2003.1240446. pdf

[7] L. B. Gutiérrez, G. Vachtsevanos, and B. Heck, “A hierarchical/intelligent control architecture for unmanned aerial vehicles,” in Proc. of the 21st Digital Avionics Systems Conference, (Irvine, CA, USA), pp. 8.B.3–1/8.B.3–10, IEEE, October 27-31, 2002. ISBN: 0-7803-7896-0 Softbound Edition / 0-7803-7896-0 CD-ROM Edition, ISSN: 0743-1619. pdf

Categories
Aircraft Flight Control Aircraft Flight Dynamics Aircraft Flight Mechanics Embedded Systems Intelligent Control Systems

Flight Data Recorder for acquisition of flight test data in a ultra light aircraft

Flight Data Recorder for acquisition of flight test data in a ultra light aircraft

Summary

A flight data recording system was developed for an ultralight aircraft. The aircraft was instrumented to record data from certification flight tests and for mathematical modeling of the aircraft.
A set of instruments was integrated:

  1. AHRS module that includes an IMU and a GPS fused with a Kalman filter to obtain the estimated values ​​of the position, velocity and attitude of the aircraft.
  2. Air data system consisting of a five-hole pitot tube and air data processor that estimates the values ​​of air speed and the angles of attack and sideslip.
  3. An eight-channel high resolution analog to digital converter (24-bit), in conjunction with potentiometric sensors for measuring the position of the aircraft controls.
  4. An embedded processor with high computational and storage capacity, with Intel i7 dual-core processor, 16GB of RAM, 512GB SSD. This processor runs the software developed for the acquisition and processing of data from sensors in real time on the real-time operating system RT Linux.
  5. An embedded processor integrated with the digital analog converter, as an intelligent sensor of the position of the aircraft controls.

The data acquisition and processing software was developed to record the data received from the sensors in real time, with a flexible command interface that allows easy configuration, programming and implementation of the necessary communication links according to the required tests. This software was developed in C, as a service in the Linux RT operating system that starts automatically when the computer is turned on.
The equipment was integrated into a compact box that includes the processor, a battery pack, the AHRS system, an on/off switch, a terminal block for the potentiometric sensors of the aircraft controls, connectors for the batteries and the air data processor that is located near the pitot tube installation.
The equipment was installed and flight tested on a QuickSilver GT500 ultralight aircraft and is expected to be used in further research on mathematical modeling and identification of aircraft parameters.

Presentation

Gallery

Categories
Aircraft Flight Control Aircraft Flight Dynamics Aircraft Flight Mechanics Control Theory Fault Tolerant Control Intelligent Control Systems

Fault Tolerant Air Data System

Fault Tolerant Air Data System for Pitot Tube Failure

Summary

An integrated airspeed and angle of attack sensor failure detection identification, isolation and accommodation scheme is proposed. The system uses information from the inertial measurement unit, available air data sensors, and an aircraft digital twin that provides virtual measurements of the aircraft’s aerodynamic and propulsion forces to feed a nonlinear estimator capable of detecting air sensor failure and suppress its effect on the aircraft air data prediction. The novelty of the proposed approach is that sensor fault detection, identification, isolation, and accommodation are integrated into a feedback scheme where the information produced by fault detection is used to modulate the noise covariance of faulty sensors so that the nonlinear estimator is able to maintain the air data estimate with a small error despite the presence of various failures in the air data sensors.
The system was developed and tested in simulation. A Matlab/Simulink Ryan Navion aircraft simulation model was developed using flight test and wind tunnel data from Princeton University Flight Research Laboratory. Matlab/Simulink sensor models were developed using actual measured sensor data. A Dryden wind turbulence model was used to test the system against atmospheric perturbations. Flight simulations included climb, cruise, turns and descent maneuvers.
Independent and joint Pitot tube and angle of attack vane sensor failures were simulated. Simulation results showed that the fault tolerant estimation air data scheme is very accurate and robust against undetected or false alarm failures.

Short presentation

Related publications

[1] O. Hazbón, L. Gutiérrez, C. Bil, M. Napolitano, and M. L. Fravolini, Advances in Transdisciplinary Engineering, vol. 10, ch. Digital Twin Concept for Aircraft Sensor Failure, pp. 370–379. IOS Press, 2019. Available: http://ebooks.iospress.nl/volumearticle/52930, ISBN: 978-164368-020-0 (print) — 978-1-64368-021-7 (online), doi: https://doi.org/10.3233/ATDE190143. pdf

[2] O. Hazbón, L. Gutiérrez, C. Bil, M. Napolitano, and M. Fravolini, “Digital twin concept for aircraft system failure detection and correction,” in AIAA Aviation 2019 Forum, (Dallas, TX, USA), June 17-21, 2019. Available: https://arc.aiaa.org/doi/abs/10.2514/6.2019-2887, doi: https://doi.org/10.2514/6.2019-2887. pdf

[3] O. Hazbón, L. B. Gutiérrez, C. Bil, M. Napolitano, and M. L. Fravolini, “Review of methodologies for aircraft sensors fault detection and correction,” in AIAC18: 18th Australian International Aerospace Congress (2019), (Melbourne, Australia), pp. 259–264, Engineers Australia, Royal Aeronautical Society., Engineers Australia, Royal Aeronautical Society., February 24-26, 2019. Available: https://search.informit.com.au/documentSummary;dn=321908916273250;res=IELENG;type=pdf, ISBN: 9781925627213. pdf

Categories
Aircraft Flight Control Aircraft Flight Dynamics Aircraft Flight Mechanics Control Theory Embedded Systems Fault Tolerant Control Intelligent Control Systems Real-time Control Systems Remotely Operated Vehicles Robotics ROV UAV Unmanned Aerial Vehicles

Projects

Fault Tolerant Air Data System

Fault tolerant air data system for pitot failure simulation results

An integrated airspeed and angle of attack sensor failure detection identification, isolation and accommodation scheme is proposed. The system uses information from the inertial measurement unit, available air data sensors, and an aircraft digital twin that provides virtual measurements of the aircraft’s aerodynamic and propulsion forces to feed a nonlinear estimator capable of detecting air sensor failure and suppress its effect on the aircraft air data prediction.

UAV for research in Flight Mechanics and Control

UAV for research in flight mechanics and control

A UAV was developed for research in Flight Mechanics and Flight Controls. The project consists of the integration of a set of sensors with an embedded processor in a small fixed-wing aircraft and the development of a flexible software infrastructure for the implementation and testing of flight control algorithms. The sensor suite consists of an IMU, a magnetometer, a GPS, a pitot tube with a differential pressure sensor, alpha and beta vanes, control surface position sensors, and a sensor for engine RPM. An actuator interface and RF communication link are also included to allow telecommand and telemetry.

Flight Data Recorder for acquisition of flight test data in a ultra light aircraft

Flight data recorder for acquisition of flight test data

A flight data recording system was developed for an ultralight aircraft. The aircraft was instrumented to record data from certification flight tests and for mathematical modeling of the aircraft.

Structure Manager, a software infrastructure for the implementation of Real Time Control Systems

Structure manager software in a Eclipse IDE

A software infrastructure for the implementation of real time control systems have been developed in C language. The Structure Manager is composed of a library that implements all the infrastructure functionality and a tool to generate code automatically at compilation time, that connects the infrastructure with the application at hand. The infrastructure, combined with a sound programming methodology (object oriented like) enables some powerful features in the real time application accelerating the production cycle of the software.

Andean Condor UAV

Andean Condor UAV

The Andean Condor unmanned aerial system is a tactical UAV for surveillance, exploration, reconnaissance, intelligence. Possible applications in photogrammetry and precision agriculture are also considered. This development is the result of the project “Development of a fixed-wing unmanned aerial system for short-range missions – Aura Jr” (2007-2009).

Software for modeling, analysis and design of a fixed wing aircraft

Software for modeling, analysis and design of a fixed wing aircraft

Software has been developed for the modeling, analysis and design of a fixed wing aircraft. The software is composed of a set of functions written in the Matlab® m language and is fully compatible with Octave. There is also a set of simulation models developed in Simulink® that include the simulation of the aircraft non-linear model with the flight control system. There are several versions of the simulation model, some more refined than others.

VISOR 3 ROV

Visor 3 ROV

VISOR 3 is an ROV developed by the Almirante Padilla Naval Cadet School (ENAP) and Universidad Pontificia Bolivariana (UPB), through the research groups in Naval Engineering (GIIN), Automation and Design A+D and the Institute of Energy and Thermodynamics (IET), with the support of Colciencias. The ROV is an underwater robotic platform for inspecting port structures and hulls of transport vessels, in order to comply with the ISPS code.

Aura Jr UAV

Aura Jr UAV

Aura Jr was a small UAV for short-range missions. This was the first UAV developed at the Universidad Pontificia Bolivariana. This was a prototype built as a technology demonstrator for the project “Research and Design of an Automatic Remote Inspection System for Electric Power Transmission Lines” (2004-2005) sponsored by Interconectado Eléctrica SA (ISA), Colciencias and Universidad Pontificia Bolivariana. It was the starting point of the project “Development of a fixed-wing unmanned aerial system for short-range missions – Aura Jr” (2007-2009).

Preliminary design of Aura UAV for monitoring of Power Transmission Lines

Aura UAV

The preliminary design of the Aura UAV was the result of the project “Research and Design of an Automatic Remote Inspection System for Electric Power Transmission Lines” (2004-2005) had as its main objective to investigate and design the prototype of an autonomous inspection system for high and extra high voltage transmission lines.

Adaptive Mode Transition Control Architecture With an Application to Unmanned Aerial Vehicles

GTmax, Georgia Tech UAV testbed

A new approach to the adaptive mode transition control of unmanned aerial vehicles was proposed. The proposed architecture consists of three levels: the highest level is occupied by mission planning routines where information about way points the vehicle must follow is processed, The mid-level controller uses a trajectory-planning component to coordinate the task execution and provides set points for low-level stabilizing controllers. The adaptive mode transitioning control algorithm resides at the lowest level of the hierarchy consisting of a mode transitioning controller and the accompanying adaptation mechanism. A flight demonstration was done as part of a DARPA sponsored research program to validate the control algorithms using the GTmax, the Georgia Tech UAV testbed.

VISOR 2 ROV

Visor 2 ROV

VISOR 2 was an ROV developed as an underwater vehicle with dual control (1998-2000). The project was led by Julio Cesar Correa Rodríguez, Luis Benigno Gutiérrez Zea and Laszlo Jurko.

Neural Network Control of a Flexible Link

Neural network control of a flexible link

A neural network (NN) tracking controller was implemented on a single flexible link and the performance results of the neural network controller were compared to that of proportional derivative (PD) and proportional integral derivative (PID) standard controllers. The NN controller is composed of an outer PD tracking loop, a singular perturbation inner loop for stabilization of the fast flexible-mode dynamics, and an NN inner loop used to feedback linearize the slow pointing dynamics. No off-line training or learning is needed for the NN. It is shown that the tracking performance of the NN controller is far better than that of the PD or PID standard controllers. An extra friction term was added in the tests to demonstrate the ability of the NN to learn unmodeled nonlinear dynamics.

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