Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles

º Tesis Doctoral Ingeniería en Automática, Robótica y Telecomunicación Dpto. Ingeniería de Sistemas y Automática Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla 2019 Autor: Francisco Alarcón Romero Directores: Dr.-Ing. Aníbal Ollero Baturone Director: Aníbal Ollero Baturone Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Dr.–Ing. Antidio Viguria Jiménez i Propuesta de tesis doctoral para la obtención del título de Doctor por la Universidad de Sevilla Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Autor: Francisco Antonio Alarcón Romero Director 1: Aníbal Ollero Baturone Director 2: Antidio Viguria Jiménez Doctorado en Ingeniería Automática, Electrónica y de Telecomunicación Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2019 ii iii A Marta, Martita y Carlota, las niñas de mis ojos. iv v Acknowledgements I would first like to thank Antidio Viguria and Anibal Ollero for supervising my thesis. It has been a luck and a privilege to receive your guidance and advice during the last ten years. Special thanks to Antidio, his support has been invaluable and he has given me the opportunity of combining this thesis with the projects in which I have participated. Moreover, it is necessary to say that this dissertation would not have been possible without the incredible work carried out by the CATEC staff and other extraordinary engineers that currently are spread out by the world. During these years they have become not only colleagues but also friends. I would like to mention especially to Manuel García, Paco Cuesta, Miguel Cordero, Daniel Santamaría, Antonio Jiménez and, of course, to my favorite pilots: José Ramón López and Allan Bell. Finally, I would like to thank all my family and friends, as always, for their neverending support. Very special thanks to my parents and my brother, without any doubt; they have been the key to become who I am. Also to my “other family”, which is the one that is composed of my closest and faithful friends, thanks for being my Gladiators, the brothers that provide me the Force And Honor to enjoy and overcome any circumstance. And most of all, thanks to my loved Marta, certainly you are the cornerstone and the partner of my life. Thanks for your continued support, patience and understanding in the final stages of my work. Francisco Alarcón Romero Sevilla, 2019 vi vii Abstract Drones are quickly developing worldwide and in Europe in particular. They represent the future of a high percentage of operations that are currently carried out by manned aviation or satellites. Compared to fixed-wing UAVs, rotary wing UAVs have as advantages the hovering, agile maneuvering and vertical take-off and landing capabilities, so that they are currently the most used aerial robotic platforms. In operations from ships and boats, the final approach and the landing maneuver are the phases of the operation that involves a higher risk and where it is required a higher level of precision in the position and velocity estimation, along with a high level of robustness in the operation. In the framework of the EC-SAFEMOBIL and the REAL projects, this thesis is devoted to the development of a guidance and navigation system that allows completing an autonomous mission from the takeoff to the landing phase of a rotary-wing UAV (RUAV). More specifically, this thesis is focused on the development of new strategies and algorithms that provide sufficiently accurate motion estimation during the autonomous landing on mobile platforms without using the GNSS constellations. In one hand, for the phases of the flights where it is not required a centimetric accuracy solution, here it is proposed a new navigation approach that extends the current estimation techniques by using the EGNOS integrity information in the sensor fusion filter. This approach allows improving the accuracy of the estimation solution and the safety of the overall system, and also helps the remote pilot to have a more complete awareness of the operation status while flying the UAV In the other hand, for those flight phases where the accuracy is a critical factor in the safety of the operation, this thesis presents a precise navigation system that allows rotary-wing UAVs to approach and land safely on moving platforms, xiv Figure 3-21: Helicopter standing on the landing platform (Idle phase) ...................... 38 Figure 4-1: Position errors of GPS, INS and combined INS/GPS (Bijker's, 2006). ..... 43 Figure 4-2: A GPS/INS Loosely coupled integration scheme. ....................................... 44 Figure 4-3: INS/GPS Tightly Coupled integration scheme ............................................ 45 Figure 4-4: Loosely coupled architecture of the EIW global navigator. ...................... 47 Figure 4-5: Scheme of the estimation process. ................................................................... 50 Figure 4-6: Mechanization Equations (Solimeno, 2007) .................................................. 55 Figure 4-7: New Tuning procedure using the EGNOS protection levels. .................. 67 Figure 5-1: Architecture of the T-GRANT module .......................................................... 69 Figure 5-2: Architecture of the R-GRANT ......................................................................... 70 Figure 5-3: VICON camera and indoor testbed ................................................................ 75 Figure 5-4 Roll comparison of the different AHRS algorithms. .................................... 76 Figure 5-5 Pitch comparison of the different AHRS algorithms ................................... 76 Figure 5-6: Yaw comparison of the different AHRS algorithms ................................... 77 Figure 5-7: Landing scenario frames and elements that play a relevant role in the landing procedure based on the tether device. ................................................................. 79 Figure 5-8: Landing scenario frames and elements that play an important role in the landing procedure based on the radio-beacon device. ................................................... 82 Figure 6-1: Test areas. (a)ATLAS Runway and (b) Kirkkonummi flight zone .......... 92 Figure 6-2: Flight plans created for data collection: (a) ATLAS FP1, (b) ATLAS FP2, (c) FINLAND FP1, (d) FINLAND FP2 ............................................................................... 93 Figure 6-3: Comparison of the trajectories in North-East axes in the first campaign of flights. (a) ATLAS FP1 complete trajectory (b) Zoom of the ATLAS FP1 trajectory (c) ATLAS FP2 Complete trajectory, (d) ) Zoom of the ATLAS FP2 trajectory. ....... 95 Figure 6-4 :Comparison of the North position over the time in the first campaign of flights. (a) ATLAS FP1 North position trajectory (b) Zoom of the ATLAS FP1 North position trajectory (c) ATLAS FP2 Complete North position trajectory, (d) ) Zoom xv of the ATLAS FP2 .................................................................................................................... 96 Figure 6-5:Comparison of the Altitude over the time in the first campaign of flights. (a) ATLAS FP1 Altitude position trajectory (b) Zoom of the ATLAS FP1 Altitude trajectory (c) ATLAS FP2 Complete Altitude trajectory, (d) ) Zoom of the ATLAS FP2 Altitude trajectory ........................................................................................................... 97 Figure 6-6: Errors obtained from the different navigation solutions during the first campaign of flights. (a) ATLAS FP1 horizontal errors (b) ATLAS FP1 vertical errors (c) ATLAS FP2 horizontal errors (d) ATLAS FP2 vertical errors ................................. 98 Figure 6-7: Comparison of the trajectories in North-East axes in the second campaign of flights. (a) FINLAND FP1 complete trajectory (b) Zoom of the FINLAND FP1 trajectory ..................................................................................................... 100 Figure 6-8: Comparison of the trajectories in North-East axes in the second campaign of flights. (a) FINLAND FP2 Complete trajectory, (b) Zoom of the FINLAND FP2 trajectory. ................................................................................................... 101 Figure 6-9: Comparison of the North position over time in the first campaign of flights. (a) FINLAND FP1 North position trajectory (b) Zoom of the FINLAND FP1 North position trajectory (c) FINLAND FP2 Complete North position trajectory, (d) Zoom of the FINLAND FP2................................................................................................ 102 Figure 6-10: Comparison of the Altitude over the time in the first campaign of flights. (a) FINLAND FP1 Altitude position trajectory (b) Zoom of the FINLAND FP1 Altitude trajectory (c) FINLAND FP2 Complete Altitude trajectory, (d) Zoom of the FINLAND FP2 Altitude ........................................................................................... 103 Figure 6-11: Errors obtained from the different navigation solutions during the first campaign of flights. (a) FINLAND FP1 lateral errors (b) FINLAND FP1 vertical errors (c) FINLAND FP2 lateral errors (d) FINLAND FP2 vertical errors ............... 104 Figure 6-12: Complete experimental setup ...................................................................... 107 Figure 6-13: Integration of main RBS equipment in the helicopter research platform ................................................................................................................................................... 109 Figure 6-14: Distance to the landing platform and RBS status during the manual flight experiment. .................................................................................................................. 111 Figure 6-15: RBS status changes with the distance. ....................................................... 112 xvi Figure 6-16: Effect of the sensor status in the accuracy of the positioning solution of the navigator in the (a) North axis and (b) altitude. ...................................................... 112 Figure 6-17: Manual approaches with distances to the LP shorter than 30m. ......... 113 Figure 6-18: horizontal position and velocity during an autonomous landing with the platform static in both axes. .......................................................................................... 115 Figure 6-19: Altitude during an autonomous landing with the platform static in both axes. ................................................................................................................................. 116 Figure 6-20: RPA maintaining the relative altitude to the landing platform which is in movement in the vertical axis ........................................................................................ 116 Figure 6-21: Rotary wing UAV trajectory (blue) landing on the moving platform (red) ........................................................................................................................................... 117 Figure 6-22: UAV Relative vertical position, platform altitude and North position during the straight movement test using the Radio-beacon based navigator and different phases of the operation........................................................................................ 118 Figure 6-23: Comparison among the R-GRANT solution (red) and the GNSS-RTK measurements (blue) during a test where the landing platform is moving following a straight trajectory: (a) position in the horizontal plane, (b) velocity in the horizontal plane, (c) relative altitude, and (d) relative vertical velocity.................... 119 Figure 6-24: Helicopter descent phase in the straight movement test: (a) shows the altimeter measurements of the relative altitude, (b) compares the AGL of the RUAV and the moving platform, (c) shows the horizontal distance between the helicopter and the landing point, and (d) represents the vertical velocity during the descent. .................................................................................................................................................... 121 Figure 6-25: RPA with radio-beacon based navigator performing a landing. ......... 122 Figure 6-26: Curvilinear trajectories. Blue line: helicopter. Red Line: moving platform. .................................................................................................................................. 122 Figure 6-27: Landing manoeuver data regarding curvilinear paths using the R_GRANT module: (a) Relative altitude measured by the altimeter, (b) comparison between the AGL of the RUAV and the moving platform, (c) relative distance in the horizontal plane between the helicopter and the landing point, and (d) linear velocity of the moving platform during the test. ............................................................ 123 xvii Figure 6-28: XY representation of trajectory in time ...................................................... 124 Figure 6-29: Comparison among the R-GRANT solution (red) and the GNSS-RTK system (blue) during a test where the landing platform is moving following a curvilinear trajectory: (a) measurements of the position in the horizontal plane, (b) relative velocity in the horizontal plane, (c) relative altitude and (d) relative vertical velocity. .................................................................................................................................... 125 Figure 6-30: Relative mode is switched on if the tension is bigger than a threshold value during a predefined time interval. ......................................................................... 127 Figure 6-31: Actors of the complete experimental setup during a landing test. ..... 129 Figure 6-32: Rotary wing UAV LOGO 800 avionics ..................................................... 131 Figure 6-33: Flight tests with the static platform in Utrera airfield. ........................... 132 Figure 6-34: Relation between altitude (a), vertical velocity (b) and the horizontal relative position (c) with the torque (d) applied to the tether in a landing procedure over a static platform by using the developed T-GRANT module. .......................... 133 Figure 6-35: Comparison of the Horizontal Position solution obtained with the T- GRANT estimator (red line) and the RTK-GNSS sensor (blue line) during the complete test ........................................................................................................................... 134 Figure 6-36: Comparison between the Vertical Position obtained with the T- GRANT estimator (red line) and the altimeter (blue line) in the last phase of the landing test. ............................................................................................................................. 134 Figure 6-37: Comparison between the Horizontal velocity solution obtained with the T-GRANT estimator (red line) and the RTK-GNSS sensor (blue line) during the complete test. .......................................................................................................................... 135 Figure 6-38: Comparison between the Vertical velocity solution using the T- GRANT estimator (red line) and the velocity solution o (blue line) during the complete test. .......................................................................................................................... 135 Figure 6-39: Relative vertical position during the straight movement test and its different phases: Static platform, tension applied to the tether, and start of the landing platform motion. .................................................................................................... 137 Figure 6-40: Rotary wing UAV keeps its relative altitude to the moving platform xviii when it oscillates vertically. The altitude of the helicopter in NWU coordinates is shown in red, in blue the platform coordinates in NWU coordinates, and in black the relative altitude between both systems measured by the altimeter. ................... 137 Figure 6-41: Comparison among the T-GRANT estimation solution (red) and the GNSS-RTK measurements (blue) during a test where the landing platform is moving following a straight trajectory: (a) position in the horizontal plane, (b) relative velocity in the horizontal plane, (c) relative altitude, and (d) relative vertical velocity. .................................................................................................................................... 138 Figure 6-42: Rotary wing UAV trajectory landing on the moving platform using the tether in the straight trajectory test. ................................................................................... 139 Figure 6-43: Helicopter descent phase in the straight movement test: (a) shows the altimeter measurements of the relative altitude, (b) compares the AGL of the RUAV and the moving platform, (c) shows the horizontal distance between the helicopter and the landing point, and (d) represents the vertical velocity during the descent. .................................................................................................................................................... 140 Figure 6-44: Helicopter goes downs vertical to the platform ...................................... 141 Figure 6-45: Curvilinear trajectory of the rotary-wing UAV for landing on the moving platform using the tether. ..................................................................................... 142 Figure 6-46: Landing maneuver data regarding curvilinear paths: (a) Relative altitude measured by the altimeter, (b) comparison between the AGL of the RUAV and the moving platform, (c) relative distance in the horizontal plane between the helicopter and the landing point, and (d) linear velocity of the moving platform during the test. ........................................................................................................................ 143 Figure 6-47: Comparison among the tether based estimation solution (red) and the GNSS-RTK system (blue) during a test where the landing platform is moving following a curvilinear trajectory: (a) measurements of the position in the horizontal plane, (b) relative velocity in the horizontal plane, (c) relative altitude and (d) relative vertical velocity. ........................................................................................ 144 Figure 6-48: Landing maneuver data regarding high velocity test: (a) Altimeter readings during the landing procedure where it is shown the variations in the relative altitude caused by the displacement of the helicopter from a position that is over the ground to another that is over the platform, (b) AGL of the RUAV and the xix moving platform, (c) relative position in the horizontal axes, and (d) evolution of the landing platform velocity following a constant acceleration profile. ................. 146 Figure 6-49: Comparison among the T-GRANT solution (red) and the GNSS-RTK (blue) measurements during a test where the landing platform is moving with a constant acceleration and reaches up to 35 km/h: (a) position in the horizontal plane, (b) relative velocity in the horizontal plane, (c) relative altitude and (d) relative vertical velocity. ...................................................................................................... 148 Figure A-1: Landing platform simulating vertical ship movements under sea 3, sea 4 and sea 5 at 0.2 m/s ............................................................................................................. 167 Figure A-2: Landing platform simulating vertical ship movements under sea 3, sea 4 and sea 5 at 0.5 m/s ............................................................................................................. 168 Figure B-1: Inertial Frame .................................................................................................... 169 Figure B-2: ECEF coordinate system ................................................................................. 170 Figure B-3: LLA coordinate system ................................................................................... 170 Figure B-4: Relations between ECEF and local tangent frames. ................................. 171 Figure B-5: Body frame ........................................................................................................ 172 Figure B-6: Euler Angles ...................................................................................................... 174 Figure C-1: Relationship between INS and IMU ........................................................... 177 Figure C-2: Representation of measures of the yaxis against the measurements on the navigation x-axis in the absence of magnetic disturbances (Caruso, 2000) ....... 184 Figure C-3: Representation of measures of the y-axis against the measurements on the navigation x-axis in the absence of magnetic disturbances [4] ............................ 185 Figure C-4: GPS position Calculation ............................................................................... 186 xxi Tables Table 3-1: Comparison of the errors that affect GPS and EGNOS ............................... 14 Table 3-2: Comparison of the positioning solution performance with GPS and EGNOS ...................................................................................................................................... 15 Table 5-1: Comparison of the roll accuracy ....................................................................... 77 Table 5-2: Comparison of the pitch accuracy .................................................................... 78 Table 5-3: Comparison of the yaw accuracy...................................................................... 78 Table 6-1: ATLAS FP1 Errors obtained from the comparison of the PPK solution and the different navigator configurations, RPA’s speed, protection levels and satellites used............................................................................................................................ 99 Table 6-2: ATLAS FP2 Errors obtained from the comparison of the PPK solution and the different navigator configurations, RPA’s speed, protection levels and satellites used............................................................................................................................ 99 Table 6-3: FINLAND FP1 Errors obtained from the comparison of the PPK solution and the different navigator configurations, RPA’s speed, protection levels and satellites used.......................................................................................................................... 105 Table 6-4: FINLAND FP2 Errors obtained from the comparison of the PPK solution and the different navigator configurations, RPA’s speed, protection levels and satellites used.......................................................................................................................... 105 Table 6-5: Accuracy of the navigational solution regarding the distance to the platform ................................................................................................................................... 113 Table 6-6: Navigator accuracy in the autonomous tests experiments with the platform static in the vertical plane ................................................................................... 117 Table 6-7: RMS error and Standard Deviation of the position (m) and velocity estimation solution (m/s) during a landing over a platform that is following a xxii straight trajectory. Calculations have been performed using the RTK-GNSS system as ground truth....................................................................................................................... 120 Table 6-8: RMS error and Standard Deviation of the position (m) and velocity estimation (m/s) solution of the radio-beacon based sensor during a landing over a platform that is following a curvilinear trajectory. Calculations have been performed using the RTK-GNS .......................................................................................... 126 Table 6-9: RMS error and Standard Deviation of the position estimation solution (m). Calculations have been performed using the RTK-GNSS system as ground truth .......................................................................................................................................... 134 Table 6-10: RMS error and Standard Deviation of the velocity estimation solution (m/s). Calculations have been performed using the RTK-GNSS system as ground truth .......................................................................................................................................... 136 Table 6-11: RMS error and Standard Deviation of the position (m) and velocity estimation solution (m/s) during a landing over a platform that is following a straight trajectory. Calculations have been performed using the RTK-GNSS system as ground truth....................................................................................................................... 139 Table 6-12: RMS error and Standard Deviation of the position (m) and velocity estimation (m/s) solution during a landing over a platform that is following a curvilinear trajectory. Calculations have been performed using the RTK-GNSS system as ground truth. ....................................................................................................... 145 Table 6-13: RMS error and Standard Deviation of the position (m) and velocity estimation (m/s) solution during a landing over a platform that is moving at high velocity with a constant acceleration. Calculations have been performed using the RTK-GNSS system as ground truth .................................................................................. 149 Table A-1: Beaufort scale which relates local wind with the sea state(U.K National Meteorological Library and Archive, 2012) ..................................................................... 164 Table C-1: errors in the INS outputs .................................................................................. 181 xxiii Acronyms AL Alert Limit AGL Altitude above ground level ATLAS Air Trafic Laboratory for Advanced unmanned Systems AHRS Attitude and Heading Reference System CG Center of Gravity UCARS Common Automatic Recovery System UTC Coordinated Universal Time CP Contact Point DOP Dilution of Precision ECSAFEMOBIL Estimation and Control for SAFE wireless high MOBILity cooperative industrial systems ECEF Earth-centered earth-fixed frame EGNOS European Geostationary Overlay Service EIRE EGNOS IntegRity wEighted EKF Extended Kalman Filter GNSS Global Navigation Satellite System GPS Global Positioning System GIVE Grid Ionospheric Vertical Error GCS Ground Control Station GSU Ground Segment Units GNC Guidance, Navigation and Control HDOP Horizontal Dilution of Precision HPL Horizontal Protection Level ICAO International Civil Aviation Organization IMU Inertial Measurement Unit INS Inertial Navigation System ILS Instrumental Landing System 4 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles developed navigation systems. Here, it is possible to note the strong experimental focus of this dissertation; in fact, throughout this thesis, more than 70 flights were performed in order to measure the performance of the different estimation algorithms implemented. In that way, this chapter summarizes the different test campaigns and presents the main results obtained.  Chapter 7 presents the main conclusions and future lines of work.  Appendix A contains the assumptions and the constraints of the landing platform motion in order to study its similarities with the movement of a ship under different environmental conditions.  Appendix B presents the main coordinated frames used along this thesis and how to perform the transformations between them.  Appendix C This section presents the sensors used by the global navigation system (excepting EGNOS ) and their main characteristics and error properties, which will be used for building the mathematical models of the fusion algorithms. 1.3. Thesis Framework On one hand, work related with the landing phase of the helicopter has been performed in the framework of the European Commission FP-7 project ECSAFEMOBIL (Estimation and Control for SAFE wireless high MOBILity cooperative industrial systems). Under this framework, this thesis proposes the use of two different navigation and guidance strategies for performing a safe landing in a moving platform:  The use of a tether as relative sensor,  The use of a system based on radio-beacons signals (RBS) as relative sensor. On the other hand, the experimental campaigns that validate the work related to the UAV global navigation phases have been carried out under the project REAL (RPAS EGNOS Assisted Landings). REAL has received funding from the European GNSS Agency within the framework program "EGNOS ADoption in Aviation". Introduction 5 Under this framework, this thesis has validated a new navigation algorithm based on the benefits that the EGNOS constellation provides to the aviation users. 1 2. STATE OF THE ART AND CONTRIBUTIONS 2.1. Autonomous landing of rotary-wing UAVs on moving platforms In the next decade, it is expected that civil applications of Unmanned Aerial Vehicles will increase exponentially up to a market of 11.000 millions of euros in 2035 only in Europe. Moreover and due to the intrinsic low risk of maritime operations with UAVs, it is foreseen an important increase in the use of UAVs from ships, for different applications: environmental monitoring, fishing support, surveillance, etc. In operations from ships and boats, the final approach and the landing maneuver are the phases of the operation that involves a higher risk and where it is required a higher level of precision in the position and velocity estimation, along with a high level of robustness in the operation. Although landing of rotary-wing UAVs has raised the attention of multiple researchers during the last 15 years, it has not been yet completely solved in a robust and reliable manner. In fact, one of the three challenges at the Mohamed Bin Zayed International Robotics Challenge (MBZIRC) Competition in 2017 was the landing of a UAV on a moving platform (Acevedo et al., 2018). One of the first research works that tackle the autonomous landing problem on mobile platforms was (Saripalli, Montgomery and Sukhatme, 2003) in 2003, where a real-time, vision-based landing algorithm was developed. Later, references(Saripalli et al., 2006),(Merz et al., 2006) presented vision-based algorithms that were able to estimate the helicopter position from images of a specially designed landing pad with the necessary level of precision and accuracy for the landing maneuver, most of the data was achieved from manual flights and simulations. More recently, references(Falanga et al., 2017),(Polvara et al., 2018) also have applied vision-based landing techniques increasing the autonomy level by including real-time trajectory generation. Also, it is possible to find recent works that study the problem of landing in an oscillating platform by using visual sensors. For instance, the authors in (Polvara et al., 2018) use a fiducial marker in 2 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles order to obtain the pose of the platform and implement an Extended Kalman Filter (EKF) to estimate the ship position. Simulations provide results very accurate by using only the odometry and the inertial measurements for the estimation. However, measurements from these sensors may not always be available, and they can suffer physical interferences and limitations in their fields of view. Additionally, these approaches generally only work under good light or visibility conditions so its performance has a strong dependency with the weather conditions, seriously limiting their applicability under a wide range of realistic scenarios for the landing operation. Moreover, some of these vision-based techniques assume the use of the Global Navigation Satellite System (GNSS) on their navigation systems, since the vision system is only used as an input that increases the precision of the relative estimation of position and velocity with respect to the landing platform. Therefore, the robustness of these solutions is compromised due to the known problems of current GNSS systems in environments without enough visibility. Other methodologies used in the autonomous approach and landing phases of UAVs are based on the implementation of ground system infrastructures that help the vehicle to obtain its position. Commonly, in general aviation, the approach procedures are exclusively based on the ground navigation aids, such as Instrumental Landing System (ILS), VHF Omnidirectional Range (VOR) and Non- Directional Beacon (NDB)(Chiesa et al., 2014). However, in this kind of procedures, it is required expensive and big infrastructures, GNSS technology is usually involved, the landing location is generally a static runway and the aircraft has previous knowledge of the fixed position of the radio transmitter radio beacon. These reasons do not allow implementing traditional architectures in a mobile platform for aiding in the guidance and navigation tasks. Some other types of ground infrastructures have been explored for UAV autonomous landing in GNSS- denied environments, such as laser range finders, millimeter-wavelength radar, etc (Weiwei et al., 2017). Also, it is possible to find several commercial systems that pretend to solve the autonomous landing task through the implementation of ground infrastructures. For example, the company RUAG developed a solution called OPATS (object position and tracking sensor) (RUAG, n.d.). Their system is based on a laser-based automatic landing system for UAS that represents an alternative to radar-based landing systems. Its key feature system is the continuous position measurement of State of the art and contributions 3 the approaching unmanned aircraft using an infrared laser beam which is echoed back from a passive heated retro-reflector on the aircraft. This system can measure the position of an approaching aircraft at a distance around 4000 m. Another commercial system is the Common Automatic Recovery System (UCARS) (Sierra Nevada Corporation, n.d.) developed by Sierra Nevada Corporation. This system is based on a millimeter-wavelength ground radar and provides precision approach (within 2.5 cm) in adverse weather condition and without using the GNSS. While those solutions are effective, these technologies are not valid for this project due to the limited payload of small UAVs and the needed of a communication channel between the ground infrastructure and the aerial vehicle. In (Kim and Choi, 2016), the authors deployed passive Ultra Wide Band (UWB) anchors in the landing location, which listen for the UWB signals emitted from a UAV. The position of the target is computed on ground and sends it back to the UAV through an aviation communication channel. This work achieves a positioning accuracy of 40 cm. However, here also it is needed a communication channel. Besides this, in this work all the presented tests have been performed in static scenarios. In this dissertation, one of the novelties presented is the implementation of a new system based on a ground infrastructure for the approach and autonomous landing phases of a rotary unmanned aerial system. This system is based on several radio-beacon deployed on the ground following a specific pattern and with an operation similar to the GNSS constellation. Each radio-beacon transmits its own radio signal, then the UAV receives them and perform a triangulation that allows positioning itself. The position accuracy obtained by using this system has tested to be under one meter. Furthermore, this system can be deployed in any landing platform, both static and moving, and does not rely on GNSS signals or a communication channel. Another advantage of this system is that the vehicle equipment is low weight, allowing its integration into UAVs with a maximum take-off weight (MTOW) under 25 kg. Related to the final landing phase in a moving platform with cm accuracy and without the use of GNSS sensors, this thesis proposes the use of a tether. The use of a cable or tether that physically connects the UAV and the moving platform is not new, although as it will be explained in the following, most of the existing works were theoretical and only with simulation results. Some works were focused on the study of the control and stabilization problems of tethered rotorcrafts such as (Schmidt and Swik, 1974). Also in (Rye, 1985) it can be found a study of the longitudinal stability of a hovering tethered rotorcraft. The first use of a tether for 4 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles helping in the landing phase of a UAV can be found in (Oh et al., 2006) where a controller is developed in order to use the tether tension to couple the translation of the helicopter to the rotation. In (Sandino et al., 2015), an Unscented Kalman Filter is applied to the attitude and relative position estimation of a small-size tethered unmanned helicopter. For that purpose, the state prediction is performed using a kinematic process model driven by measurements of the inertial sensors (accelerometer and gyroscope) onboard the helicopter and the subsequent correction is done using information from additional sensors like magnetometer, radar altimeter and magnetic encoders measuring the tether orientation relative to the helicopter. This approach avoids the need of a global positioning system (GPS) as the position is estimated relative to the anchor point. Simulation results show a good performance in terms of estimation errors as well as CPU time. However, an improvement point mentioned by the authors in their conclusions is the dependence of the filter performance on the information related to the platform state. Although simulation results have shown that this performance is good enough for execution within the controller feedback when platform motion is totally unknown, the performance improves considerably when this information is taken into account. In (Mfiri et al., 2016) the authors describe the design of a flight control system architecture for a tethered quad-rotor aircraft where the tether is also used for transmitting power to the UAV. Results from simulated waypoint navigation and hovering of the tethered vehicle suggest that the designed system is fit for use in an automated landing mission. In (Nicotra, Nald and Garone, 2017), the authors take advantage of the tensile force acting along the taut cable and solve the nonlinear control of the tethered UAV by using a cascade control scheme based on thrust vectoring and using a novel ''Reference Governor scheme''. The work presented in (Glick and Arogeti, 2018) is also focused on the control design problem of a tethered drone and uses the tether as a position sensor. Simulations results show that a fully autonomous flight could be achieved indoors by using its approach. However, in all these works the tether is used just for control and stability purposes and all the results and conclusions are obtained from simulations. There are very few experimental results regarding the use of a tether with a UAV for landing purposes. The first experimental results can be found in (Sandino et al., 2014), where a tethered helicopter lands autonomously over a static landing platform in an outdoor scenario. This work explores an alternative approach to State of the art and contributions 5 GPS sensors to avoid typical drawbacks, such as inaccuracies of standalone sensors or weight/cost for Real Time Kinematic (RTK) setups. Appropriate sensing of tether attitude relative to the helicopter together with an altitude measurement, allows estimation of the helicopter's linear position relative to the landing point. However, landing in mobile platforms is not considered and the relative estimation is simply based on geometrical considerations. Previous work was extended in (Sandino et al., 2016) with more experimental tests but in this case the main focus was on the control strategy and the advantages that a tether can provide to the stability of a UAV. In (Kiribayashi, Yakushigawa and Nagatani, 2017), a power-feeding tethered micro UAV is used and a position estimation method based on observing the slack tether is proposed. Some indoor experiments are carried out in order to prove the feasibility of this method. The authors in (Xiao et al., 2018) propose to localize a UAV in indoor environments by using only a quasi-taut tether. The tether's sensory feedback is fed into a catenary-based mechanics model to localize the UAV in an indoor global frame defined by the tether reel center. Their localization method was tested on a real robot (Fotokite Pro). Although it is true that it is possible to find real experimental data in (Kiribayashi, Yakushigawa and Nagatani, 2017) and (Xiao et al., 2018), landing tests in these works were performed over static platforms and in indoor scenarios where the weather conditions do not affect the navigation capabilities. The rope system developed in this work has been designed for landing a rotarywing UAV (RUAV) on a mobile platform with a high level of accuracy and robustness, and without using GNSS. The design has been inspired by the Recovery Assist, Secure and Transverse (RAST) system used by manned helicopters to improve the stability using a tether during the landing operation (Mcgeer and Von Flotow, 2013). Main contributions of this work are: the use of the radio-beacon and/or a tether to estimate the relative position and velocity between the UAV and the mobile platform without using GNSS, the design of a robust guidance approach to perform landings in a safe and robust manner, and the validation of the designed algorithms in a large number of flying tests, including landings with speeds of the mobile platform up to 40 km/h. The relative information obtained from the navigator developed along this thesis is entirely independent of the GNSS and represents an alternative, low cost and reliable positioning system for tethered helicopter UAVs or multicopters. Therefore, the main contributions of this thesis regarding the final approach to a moving landing platform are listed below, along with relevant related publications: 6 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles  Research and development of a new fusion filter that models the relative motions between a UAV and a moving platform through an improvement of a generic Singer model. Here, the relative accelerations have been modeled as a non-zero mean first-order stationary Markov process that makes use of the accelerations measured in the vehicle. This novel model is more effective than other approaches because it includes in the model most of the dynamics of the relative motion. This contribution has been published in (Alarcón et al., 2019).  Research, development and testing of a new Attitude and Heading Reference System (AHRS) filter. This filter uses the Euler angular errors measured in the body frame and reduces the computational complexity of those filters that use the Euler angles directly. The measurement model of this filter has been built by using a new logic that indicates when it is possible to use the accelerometers and magnetometers for calculating the measurement vector. It also weights in real-time the filter matrices depending on the module of the acceleration vector. This novel algorithm has been called the TWA (Threshold and Weighted by Accelerations) AHRS.  Research, development, and implementation of a new robust estimation method that makes use of a novel tether system that provides relative position measurements at 100 Hz. The developed navigation system does not depend on GNSS measurements and is able to calculate a relative vector with cm accuracy. The tether system has been designed, manufactured and integrated into a rotary-wing UAV in the framework of this thesis. This new Tether-based GNSS-free RelAtive NavigaTor has been called the T-GRANT module. This contribution has been published in (Alarcón et al., 2015), (Alarcón, Santamaría and Viguria, 2015) and (Alarcón et al., 2019).  Research, development, and implementation of a new navigation and guidance system that switches between different sensors, fusion filters and guidance strategies depending on the UAV flight phase and on the equipment integrated. This contribution has been partially published in (Alarcón et al., 2015), (Alarcón, Santamaría and Viguria, 2015) and (Alarcón et al., 2019). State of the art and contributions 7  Implementation and the first field experiments of a new estimation method that allows calculating a relative navigation solution at 100 Hz with sub-meter accuracy by using the measurements provided by a ground infrastructure based on a radio-beacon system integrated on a moving platform. The system model implemented in the navigator has been published in (Alarcón et al., 2019). This new Radiobeacon –based GNSS-free RelAtive NavigaTor has been called (R-GRANT) module. A video showing the final tests can be found in (CATEC, 2019).  To the best of our knowledge, tests included in this work were the first worldwide field experiments with a tethered unmanned helicopter landing on a mobile platform by using the tether as its only positioning source. Contributions based on the navigation module has been published in (Alarcón et al., 2019). A video showing the final tests can be found in (CATEC, 2019) 2.2. EGNOS-based navigator for unmanned aerial systems Global Navigation Satellite Systems have been the primary positioning source in most applications over the last three decades. However, applications are progressively requiring higher accuracy requirements and, at the same time, lower price levels. For example, in some remote sensing applications, it is usually necessary to achieve a level of accuracy below the meter to characterize and know what is the state of a crop accurately. In the User Guide for EGNOS application developers(ESA, 2009), it is presented that the expected performance of the Global Positioning System (GPS) signals uses to be between 7 and 13 meters. In order to improve and complement the GPS performance, in the last decades, numerous augmentation systems have been launched. EGNOS (European Geostationary Overlay Service) is a Satellite Based Augmentation System (SBAS) designed to complement the GPS positioning system improving the integrity and the positioning and timing service accuracy. The use of the EGNOS system jointly with GPS can provide a horizontal accuracy better than 3 meters and a vertical accuracy better than 4 meters at 95 % of the time. In the field of the UAVs, several systems benefit from the EGNOS services. Most of them take advantage of the accuracy improvement that an EGNOS-capable GNSS 14 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Figure 3-2: EGNOS Infrastructure One of the main advantages of EGNOS is the improved accuracy in relation to a position calculated solely using GPS. This is possible by the broadcasting of differential corrections to GPS orbits, GPS clocks, and the ionosphere. Table 3-1 shows some of the corrections made by the EGNOS infrastructure in comparison with the GPS solution. Error type GPS EGNOS Orbit and clock synchronization 1 m 0,5 m Tropospheric error 0,25 m 0,25 m Ionospheric error 2 m 0,3 m Receiver noise 0,5 m 0,5 m Multipath 0,2 m 0,2 m UERE (quadratic sum of errors - 1 σ) 2,31 m 0,83 m Table 3-1: Comparison of the errors that affect GPS and EGNOS Summarizing, Table 3-2 compares the expected performance of a navigator without and with EGNOS enabled. Here the horizontal accuracy corresponds to a 95% confidence bound of the 2-dimensional position error in the horizontal local plane for the Worst User Location and the vertical accuracy corresponds to a 95% confidence bound of the 1-dimensional unsigned position error in the local vertical Autonomous mission: involved systems and flight phases 15 axis for the Worst User Location (European Space Agency, 2019) Accuracy GPS EGNOS Horizontal 7.1 m 3 m Vertical 13.2 m 4 m Table 3-2: Comparison of the positioning solution performance with GPS and EGNOS Despite its accuracy, the reliability of data supplied by the GPS system is not guaranteed, for example, a malfunction of an atomic clock on-board a satellite may lead to very significant positioning errors. Caution is therefore called for, especially on critical applications like aviation. Moreover, the GPS system does not make possible to guarantee the position or time calculated by the user. In particular:  The probability of loss of integrity of a GPS satellite is far greater than that which is required for the purposes of navigating an aircraft.  In the event of system breakdown or malfunction (clock drift, broadcasting of erroneous data, etc.), pseudorange measurement can be biased from a few meters to a few kilometers. Due to its system architecture, these errors may impact the user for several hours. GPS system errors or breakdown can also have serious repercussions for user safety if not detected in time and have the effect of restricting the number of possible applications. In particular, they make the system unsuitable for critical applications. It is with a view to overcoming the limitations of GPS with respect to integrity, that augmentation systems were developed. This is where EGNOS input will be a key in the modern navigation systems. Thanks to permanent monitoring of the GPS constellation, EGNOS detects distortions affecting the signals transmitted by GPS and prevent users from tracking unhealthy or misleading signals. It assigns a confidence level to the data transmitted to the user. These data are used by the GPS/EGNOS receiver to work out the protection levels. Basically, by using an SBAS system, the user obtains three types of information:  satellite geometry information  ranging information  measurement quality-related information The satellite geometry information comprises the ephemeris data of the ranging satellites from which the position of the satellites as a function of time can be 16 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles derived, and contains the satellite ephemeris data and the differential corrections to the satellite positions. The ranging information consists of three different contributions: the ranges, the clock and ephemeris corrections, and the ionospheric corrections. Finally, measurement quality information is provided in the form of variances that are related to the two types of corrections: the user differential range error (UDRE) for the ephemeris and clock corrections and the L1 residual user ionospheric range error (UIRE) for the ionospheric corrections. The measurement flows from the ranging sources and the SBAS messages are asynchronous. Therefore, the SBAS information needs to be synchronised with the range measurements. For the ionospheric correction, rather than a timesynchronization, an ionospheric path correction is applied in which the received values are all transformed to relate to the user’s position. For the scope of this thesis, it will be assumed that all these synchronizations have been performed and all parameter values relate to the same point in space and the same moment in time. The user equipment translates the differentially corrected ranges into a position solution by a weighted least squares algorithm. To determine the optimal position solution, measurements with a small noise variance will be more heavily weighted than more noisy measurements. The variances of the differentially corrected ranges are computed from the UDRE and the UIRE, combined with the local noise variance: 𝜎𝑖2=𝑈𝐷𝑅𝐸𝑖+𝑈𝐼𝑅𝐸𝑖+𝜎𝑙𝑜𝑐𝑎𝑙,𝑖 2 (3-1) where:  𝜎𝑖2: variance of the position error distribution.  UDREi: variance of residual clock and ephemeris errors in corrected range to the ith ranging satellite.  UIREi: variance of residual ionospheric errors in corrected range to the ith ranging satellite.  𝜎𝑙𝑜𝑐𝑎𝑙,𝑖 2: variance of the local receiver noise and multipath. This information is fed to the SBAS integrity equation, which describes the position error distribution obtained by using differentially corrected measurements where the validity of these measurements have been checked by the ground network in the absence of failures that are local to the user. It gives a simple means to assess the externally provided accuracy and the integrity performance. The equation is: Autonomous mission: involved systems and flight phases 17 𝑒𝑝𝑜𝑠~𝑁(0,𝜎𝑝𝑜𝑠 2) (3-2) which means that the positioning error 𝑒𝑝𝑜𝑠 has a Gaussian distribution with mean 0 and variance 𝜎𝑝𝑜𝑠 2. Integrity is specified in terms of the protection level, which is related to the probability that the alert limit may be exceeded. Depending on the satellite geometry, the GPS system errors or malfunctions may have serious repercussions for user safety, especially if they are not detected in time. To validate a GNSS based navigation systems, it has to be guaranteed that the position that the system provides has sufficient integrity. For the navigation system, it is required to deliver an alarm when the error in the derived user position solution exceeds an alarm limit (XAL). This warning must be issued within a given period and with a given probability or integrity risk. In contrast to GPS for which no guarantee is given, EGNOS broadcasts an integrity signal provide the possibility of calculating a confidence interval. This interval can give an alert when a GPS satellite malfunctions and is not advisable to use it for an application where safety is a major factor. Four parameters characterize integrity: • Alarm limit; • Protection level; • Integrity risk; • Time To Alarm (TTA). Ideally, the user would like that the difference between the computed position and the true position (called the true position error or PE) to be smaller than the Alert Limit (AL). However, an alternative approach is required since it is not possible to know the true position, and therefore, the PE cannot be determined. So that, for each solution that the receiver gives in position, a predicted position error is estimated. This estimation is called protection level (PL) and it is performed for:  Horizontal Protection Level (HPL): The Horizontal Protection Level is the radius of a circle in the horizontal plane tangent to the WGS-84 ellipsoid WGS-84(ESA, n.d.) Whose center if the true position of the vehicle. The importance of this parameter resides in that the horizontal position of the UAV is assured to be contained in this circle. 18 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles  Vertical Protection Level (VPL): The Vertical Protection Level is half the length of a segment perpendicular to the horizontal plane of WGS-84 ellipsoid. Its center is also the true position of the UAV and it describes the region certain to contain the real vertical position. This calculation is based on the real-time processing of the data broadcast by EGNOS, which contains correction information for all the pseudorange measurements. These data arrive at the user position by many types of messages coordinated through Issues of Data (IOD): types of messages 1, 2 to 5, 6, 7, 9, 12, 24 and 25 provide the fast and long term corrections, and UDRE, those due to ephemeris and clock errors. Messages 18 and 26 contain ionospheric corrections and the Grid Ionospheric Vertical Error (GIVE). Finally, message 10 contains degradation parameters (José Santa, 2006). Once these values are available, the integrity algorithm must proceed to evaluate some mathematical expressions (they can be found described in (The Radio Technical Comission for Aeronautics., 2016) or (Bruckner, Graas and Skidmore, 2011)). Finally, these calculations are translated to the HPL and the VPL. If the predicted position error exceeds the stated protection level, an alarm must be transmitted to the user. This alarm must be received by the user within the Time To Alarm limit. Users of a GNSS system wishing to obtain a certain degree of integrity must state their needs in line with these four parameters for a given application. Then, the EGNOS Integrity concept can be summarized in the following way: The solution of navigation and the protection levels are calculated by the receiver. As the user is not able to measure the real position error, the user relies on this estimation to determine the system integrity (predicted position error). Next, the computed protection levels are compared to the alert limits that have been previously defined for the type of operation. Three situations are possible and are shown in Figure 3-3 Autonomous mission: involved systems and flight phases 19 Figure 3-3: Possible situations with the integrity signal.  If the computed protection levels are smaller than the alert limits defined for the intended operation, the system is declared available as the safety of the operation is ensured.  If the protection levels are larger than the corresponding alert limits, the system becomes unavailable (the performance level provided by the system at that time is not sufficient to ensure the safety of the intended operation).  If the error is not properly bounded by EGNOS (HPE>HPL), safety issues could arise if the error is larger than the alert limits defined for the intended operation. However, the probability of this situation is minimal by design. 3.2.2. Radio Beacon System The Radio Beacon System (RBS) works on similar principles as Global Navigation Satellite Systems (GNSS): multilateration based on independent RF-based ranging signals. The user segment calculates its 3D position in a relative coordinate frame by measuring the distances to multiple ground stations, of which the positions are known in the ground segment's body-frame. The RBS ground stations can be installed on any fixed or moving ground base and its RF band is fully independent of GNSS. The measurement technique that this system applies has been specifically designed to determine the range between the ground stations' antennas and the 20 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles user segment antennas with highest accuracy in a local area. With six ground segment units (GSU) integrated into the landing platform, it is possible to determine the position of a moving user segment relative to the ground segment. Figure 3-4shows the integration of the GSUs over the landing platform developed in this thesis. Figure 3-4: Ground segments units installed over a landing platform. The main airborne components regarding the RBS equipment are:  RMU (Range Measurement Unit): Unit connected to two small-size airborne antennas. It computes the range measurements based on RF- signals between the two airborne antennas and the six antennas on the moving platform.  PCU (Positioning Calculation Unit): processing unit that takes data from the altimeter and the RMU and fuses data in order to compute accurate relative positioning to the moving platform.  Altimeter: sensor based on RF-signals which measures relative height to the ground/moving platform.  Airborne Antennas: these antennas receive the signals emitted by the Ground Station Units on the landing platform. Autonomous mission: involved systems and flight phases 21 It is important to note that both the RMU and the altimeter are operating in GNSS- independent frequency bands. Figure 3-5 shows the airborne segment equipment required. Figure 3-5: Airborne segment equipment for standard operation (AIRBUS) The system underlies the same problematic as other multilateral positioning systems with respect to the constraints posed by the geometry formed between the roving (here airborne) element and the elements that send the positioning signals. I.e., the accuracy of the relative position information provided by the RBS is dependent on the relative ground segment ↔ airborne segment geometry. This effect is known as Dilution of Precision (DOP) in satellite navigation applications. In general, it holds that the horizontal position accuracy gets better when approaching the dedicated landing spot that is surrounded by the GSUs (Ground Segment Unit). The same holds true for the vertical position accuracy. However, the vertical positioning component is much more affected by the geometry conditions, even in medium vicinity to the Ground Segment. That’s why the use of an altimeter is essential for providing independent height measurements as input data to the positioning software of the RBS and the navigator. 3.2.2.1. Landing Maneuver Constraints As it has been described before, the expected RBS relative positioning accuracy is 22 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles strongly dependent on the relative geometrical state of the two vehicles, which can be expressed through DOP values. The smaller the DOP value, the better is the expected relative positioning accuracy. The operation radius strongly depends on the local system geometry determined by the GSUs. As an example, a rectangular ground station geometry with 8 m x 10 m side lengths would lead to an operating radius of 100 m. Consequently, a Vertical Take-Off and Landing (VTOL) UAV would use the RBS solely in the near field of the target landing platform, i.e. for the final approach and landing phase. In a horizontal radius from 100 m to 50 m to the landing spot the navigation solution still relies on GPS, but in parallel the RBS relative position information is available. This allows for health monitoring and consistency checking of both system solutions. A flight height of at least 20 m is desirable. At a horizontal distance to the landing spot of approximately 50 m it has to be decided whether the final approach can be started or not. This decision is based on the previous monitoring phase. During the final approach and landing the relative position information provided by the RBS is used for navigation and the GPS based information can be ignored. Some flight paths are better suited than others due to the resulting helicopter - ground infrastructure local geometry. The optimum flight height has been derived from the criterion of minimizing the PDOP (Positional DOP) value. The smaller the PDOP value, the better the expected relative position accuracy. The threedimension position accuracy gets continuously better when approaching the dedicated landing point. In Figure 3-6, it is shown that the optimum glide slope angle from a RBS performance perspective, when no altimeter data is available, is approximately 40°. The increase of the optimum flight height and the PDOP close to the dedicated landing spot at (0,0,0) results from the exclusion of altimeter data. If threedimensional relative position information is required when the airborne segment is close to the x-y-plane of the RBS ground segment (assumption: all GSUs are in the same plane), altimeter data has to be provided to the RBS PM module. Autonomous mission: involved systems and flight phases 23 Figure 3-6: Optimum Flight Height (when altimeter data cannot be used) Note, that the previously presented glide slope considerations are only relevant if the altimeter data cannot be used during the whole flight path. As shown in Figure 3-7 (top) the PDOP value is dominated by the vertical component (VDOP) if no altimeter data can be processed. Then glide-slope angles of 3° do hardly make sense except from the direct vicinity to the landing point. As soon as altimeter data can be processed by RBS, the PDOP value is dominated by the horizontal component (HDOP), see Figure 3-7 (bottom). Then the operation area of the RBS can be extended significantly independent from the actual glide slope angle. If only the horizontal relative position information is relevant, it is also possible to extend the RBS operation area without the need of introducing an altimeter. Even if altimeter data can be processed by the RBS during the whole flight path, it holds that the relative positioning accuracy gets the better the closer the airborne vehicle is to the dedicated landing point. 010 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 Optimum Glide Slope (without altimeter data) PDOP Horizontal Distance [m] to Landing Spot 010 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 opt. Flight Height [m] without altimeter data 30 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles coordinates. Once the UAV is close to the landing platform and the autopilot receives the approach command from the ground control station (GCS), the vehicle enters in a new operational phase. For the approaching to the landing point, it is advisable to use a system more with more accuracy than the GNSS and, if it is possible, that be able to provide information about the distance to the landing position. In our approach, if the radio-beacon sensor is integrated into both the helicopter and the landing platform; the navigator will be able to obtain directly with sub-meter accuracy the relative positioning information between the vehicle and the landing platform. Relative coordinates will allow guiding the UAV to the vertical of the landing point without the need for external guidance commands. However, if this sensor is not integrated on the helicopter or if it is not working correctly, the autopilot will have to perform the approach by using the absolute coordinates (GNSS sensor) and also it will be necessary to receive guidance commands from the GCS or external information about the location of the landing point. Once the RUAV is over the landing platform, three different cases are possible.  If the tether device has been integrated on the helicopter, the estimator will make use of the measurements obtained from this device to calculate accurately the relative position and velocity of the vehicle with respect the landing point. In this thesis, the use of this sensor is the best strategy possible for the landing phase because it has proved to be the most accurate among all the sensors integrated into the UAV. Furthermore, the tether strategy also improves the stability of the system and the robustness of the controller during the descent of the helicopter (this is demonstrated in (Sandino Velásquez, 2016)).  In the cases where the rope is not equipped, but the RBS system is integrated into the UAV, this will be the sensor chosen for performing the landing procedure. In this case, it is important to note that the accuracy of the RBS is around one meter, so the landing platform should be prepared for a landing procedure with this margin of error (for example a landing platform of several meters).  For the last, the worst case is that in which the navigator only can rely on the GNSS sensor measurements. In this situation, the operator should decide if it is safe to land or it is better to abort the mission and perform Autonomous mission: involved systems and flight phases 31 this operation in a different location where the GNSS solution is enough for performing the maneuver safely. 3.3.1. Operation phases for landing in a moving platform The UAV landing guidance block is the logical module that contains the state machine that guides the helicopter during the last phase of the operation by using the information provided by the different positioning systems integrated into the vehicle. Figure 3-13 shows the state machine that manages the different phases of flight. Figure 3-13: State machine for the autonomous landing phase 32 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Below, the phases presented in the Figure 3-13 are explained in detail. Take Off and Way-Point navigation For the take-off and those operations where the UAV navigates following global coordinates, it has been developed a logic based on the integrity information provided by EGNOS. In general, autopilots enter in an emergency state when the GPS sensor fails In these cases, the aerial vehicle enters in a degraded operation mode where the most usual procedure is to hover and wait for the satellite signals recovery. In those cases where the GPS is not recovered, the vehicle starts a landing procedure, or the remote pilot takes control of the aircraft. This degraded behavior has a high intrinsic risk due to during the hover maneuver, if not positional information is managed by the autopilot, the control of the aircraft is usually performed by commanding a roll and pitch angles of zero degrees and trying to maintain the altitude calculated with a barometer. This kind of control usually causes the UAV moves in the longitudinal axis, because any external force (usually the wind) can push the vehicle without the autopilot can realize this behavior. Besides, if the GPS is not recovered and the UAV starts the landing procedure, the descent can be carried out in any place, which is a risk for the platform and the surrounding. Using the EGNOS integrity information, it is possible to anticipate this situation of completely loss of the satellites and to know in every moment which is the confidence level of the solution that the sensor is calculating. This information allows differentiating between four possible situations that can be mapped in navigation modes of the UAV: 1- Signals are providing reliable values, and therefore, the solution of the GNSS sensor is expected to have good accuracy. This reliability has a close relationship with the value of the protection limits. 2- The sensor is not receiving information from the EGNOS infrastructure, so the corrections cannot be performed, and the protection levels are not calculated. In this case, the GPS is used just for positional purposes, as it is done in a standard navigator. 3- The GPS constellation state has poor quality, and the protection levels are higher than limits imposed in the autopilot logic. In this case, GPS Autonomous mission: involved systems and flight phases 33 measurements are not accurate and it is possible that the solution gets worse with time, even losing the signal coverage completely. 4- The receiver does not receive enough satellites and is not able to calculate a solution. Figure 3-14 presents the scheme of the states machine implemented for the global navigation phases. Here, it is shown how the EGNOS integrity information can be used and the transitions between the different states. Depending on these states, the autopilot is programmed to perform different actions. In this case, the protection and alarm levels are user parameters managed by the logic of the autopilot. In addition to the protection levels, the guidance logic also manages the information about the number of satellites in view and its quality, however this information is redundant and uses to be implicit in the integrity information. Figure 3-14: States Machine Using EGNOS The behavior of the autopilot can be summarized as follows:  In the states 1 and 2, navigation is allowed. However, the number of satellites is monitored and if it is lower than a programmed threshold, the autopilot goes to the state 3 or 4.  In the states 3 and 5, the quality of the solution is not accurate enough. In this case, the UAV is commanded to perform a “return to home” procedure, preventing to enter in a lost of signal state.  In the state 4, the GPS signals are lost. The only procedure possible is the indicated previously. The UAV is commanded to hover and wait for 34 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles recovering the GPS signal. After several seconds, if not enough satellites are received for calculating the position, the UAV starts a landing procedure or the remote pilot takes control of the platform. The use of the EGNOS capabilities in this thesis also allows the improvement of its geo-fencing capabilities. Geo-fencing concept aims to use geographical information to establish boundaries or fences, to prevent hazardous UAV flights in sensitive areas. This is used to limit flights near airports, or above certain altitudes. The navigation positioning solution based on EGNOS, provides the means to determine better whether the UAV is crossing a geo-fence by assessing not only the position computed but the protection levels. Protection levels describe the region assured to contain the UAV, and it is based upon the error estimates provided by EGNOS. Hence, even if the UAV calculated position is outside a sensitive area, the protection levels may lay inside, meaning that UAV may be really crossing the geofences (see Figure 3-15). Here the behavior programmed is the following, if the HPL crosses a geo-fence, the UAV stops waiting for a new route. After a time, if this new route is not commanded, the aircraft perform a return to home procedure. Figure 3-15: RPAS horizontal protection levels interference with geo-fencing. Autonomous mission: involved systems and flight phases 35 Approach using INS/GNSS In this phase, the position and velocity solution used in the controller are the provided by the UAV global INS/GNSS-based estimator. The RBS relative data is used to calculate the ship position by subtracting the relative to the absolute position. In this case, the relative measurements are used only for guidance purposes; the navigator continues estimating the global state vector. Ship position≈absolute position−relative position (3-3) The desired position commanded to the controller is the landing platform position with an altitude offset of 30m over the ship deck. By using this approach, the UAV helicopter starts to follow the ship and gets a velocity approximately equal to the ship velocity. Figure 3-16 shows the approach maneuver using UAV estimator absolute states: Figure 3-16: Approach maneuver using UAV estimator absolute states Approach transition to RBS When the UAV guidance block detects that the relative velocity module is smaller than a threshold value (for example 1 m/s), the module generates a signal that changes the position and velocity states from absolute to relative coordinate systems, and also is used by the UAV controller to initialize the integrators of its control loops. At the same time, the position reference is changed for keeping the same position error than before the change in the navigation algorithm. Approach using RBS 36 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Once the relative architecture is running, the position references in the horizontal plane are changed to zero. This means that the horizontal coordinates of the touchdown point are sent to the UAV. The vertical reference is set to 10 meters over the landing point and it is added a height increment proportional to the module of the horizontal distance of the helicopter multiplied by the optimal glide slope angle ∝opt (this angle has been calculated based on the different tests performed along this thesis).The vertical reference is calculated using the following equation: 𝑧∗=10+∝opt√𝑥𝑟𝑒𝑙2+𝑦rel2 (3-4) Figure 3-17 shows the approach maneuver using RBS relative states: Figure 3-17: Approach maneuver using RBS relative states Once the helicopter is over the platform at 10 meters approximately, it is possible to start the landing maneuver by using both the tether or the RBS system. a) Landing maneuver using the tether: This state covers the preparation of the rope system and the descent with the rope tethered to the moving platform.: 1st phase (rope preparation) While the helicopter hovers above the landing point (end of the approach phase), the guiding-tether is deployed by the helicopter and locked into the device installed in the landing platform for controlling the tether tension and velocity. Figure 3-18 depicts some of the different actions to be carried on in order to prepare the tether. Autonomous mission: involved systems and flight phases 37 (a) (b) Figure 3-18: Rope preparation for landing maneuver : (a) Tether deployment during 1st phase (rope preparation) and (b) Detail of device onboard landing platform for tether control 2nd phase (landing with rope): “UAV guidance controller (tether mode)”: In this phase, the tether itself is used as a guiding element. More precisely, the pulling movement of the tether commands a decreasing altitude reference whereas longitudinal and lateral references are given by the corresponding coordinates of the tether’s fixed point at ground. Figure 3-19: Tether is pulled during 2nd phase (landing with rope) 38 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles b) Landing using RBS If the sensor chosen for landing is the RBS, the landing phase is as follows. When the helicopter is at a distance of approximately 10m over the landing point, the desired altitude is changed to 3m below the ship deck height. Once this altitude is reached, the helicopter starts the final descent up to land. Figure 3-20 shows the final descent maneuver using RBS relative states. Figure 3-20: Final landing descent maneuver using RBS relative states Idle: When it is detected that the landing skids of the UAV have finally touched the landing platform, an idle signal is sent to the autopilot for stopping the engine. This state finish when the rotor is stopped. Figure 3-21: Helicopter standing on the landing platform (Idle phase) Autonomous mission: involved systems and flight phases 39 Emergency states: Secure state hover from RBS: The sequence previously described is used when no failure is detected by the UAV RBS supervisor. If this module detects a failure in the RBS signal, a secure state hover is activated. This state implies a safe an imminent transition to the absolute reference controller, which is based on the INS/GPS positioning solution provided by the global estimator. Additionally, a safe absolute position reference over the current UAV position is sent in order to stop the translational movement of the UAV and let the moving platform get away. Secure state hover from the tether: In this emergency state, the rotary wing UAV flies in a controlled way towards a hovering location far from the moving platform. This state is triggered in case of degradation on tether measurements reliability/consistency during the landing approach. In this situation, the UAV supervisor sends a signal to the guidance controller that releases the tether from the UAV. Secure state above landing point: This state is triggered when the rotary-wing UAV is performing the last maneuver for landing. In this case, the helicopter is commanded to ascend to a safe altitude and to follow the platform in the horizontal plane if possible. In other cases, the rope is released of the helicopter and it remains in a hovering state. 3.4. Conclusions This chapter starts with a presentation of the main systems and coordinate frames used during this thesis. It is focused on the key technologies used for the new navigators: EGNOS, the tether system, and the RBS. From the EGNOS presentation it is possible to conclude that, apart from the accuracy improvements that this sensor provides to the GPS constellation, the protection levels calculated from this sensor can be used for improving the performance o the navigator and guidance modules. From the RBS system, it is explained that it can work with two different altitude 46 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles measurements of the GPS and the predicted ones by using the Ephemeries information and the INS calculations. The loosely coupled scheme has as advantages that the processing time is faster than the tightly coupled one. This is because the dimension of its state vector is smaller than the used in the tightly scheme. Also, the implementation of this architecture is simple and it is possible to build it with the most commons GNSS receivers interfaces (no need to access to information that it is usually handled internally by the GNSS receiver). However, the disadvantages of this scheme are that the GPS receiver needs at least 4 satellites for computing the solution and that the capabilities of filtering are reduced because the process noise is added to two different fusion filters. On the other hand, the tightly coupled integration can provide a solution of navigation even if there are less than 4 satellites visible. The existence of a single filter provides a statistically rigorous information framework between filter states and improves the filtering capabilities because the process noise is only added to this unique filter. Another advantage of the tightly coupled algorithms is the use of the individual data provided by the satellites in the measurement update since satellites with poor measurements can be rejected. However, the TC implementation has some problems because it uses a larger size of the state vector so the computational cost of the fusion algorithm is increased with respect to the LC one. Furthermore, another disadvantage is that requires complete access to the GNSS raw data information, and this is not usually available by regular receivers, so the list of devices that can be used for this approach is drastically reduced. In this thesis, the global navigator algorithm is implemented as a loosely-coupled scheme. The filter developed manages the following information: accelerations, angular rates, magnetic field measurements and the position, velocity and integrity solution of the EIRE receiver. In Figure 4-4, it is shown the scheme of the implemented filter architecture. The sensor fusion algorithm is based on an Extended Kalman Filter whose system model has been implemented by using the INS error dynamic equations (see section 4.4). Egnos-Integrity-Weighted Global Navigator 47 Figure 4-4: Loosely coupled architecture of the EIW global navigator. In Figure 4-4, 𝜓𝑀𝐴𝐺 is the heading calculated by the magnetometer, 𝛿𝜓 is the difference between the headings calculated with the magnetometer and the INS, 𝒃𝑎 and 𝒃𝑔 are the bias correction terms for the accelerometers and the gyroscopes respectively, and PL are the protection levels calculated by using the integrity information provided by EGNOS. In the developed algorithm, the measurement model of the fusion filter uses as inputs the differences between the positions and velocities calculated through the INS and the GNSS receiver respectively. It also uses the heading difference calculated comparing the magnetometer calculations and the INS solution. Here, one of the novelties is the use of the integrity information provided by the EGNOS satellites for weighting the filter parameters, allowing the adaptation of the algorithm to the current state of the satellite constellations (this is described in section 4.5.3). This algorithm provides estimations of all observable INS errors, which are used to correct the IMU raw measurements and also to compensate for the navigation solution calculated previously through the mechanization equations. Through this approach, it is possible to obtain a navigational solution with both higher update rate and smaller positioning error than the standalone GPS-receiver and with better accuracy than those navigation algorithms that do not make use of the EGNOS properties. 48 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles 4.2. Estimation Process: Fusion Algorithm In this thesis, the algorithm in charge of fusing the different sensors is based on an Extended Kalman filter. The Kalman filter is a recursive algorithm that uses a series of predictions and measurement update steps to obtain an optimal estimate of the state vector in the sense of minimizing the mean square errors. This algorithm assumes that the process x(t) to be estimated can be modeled in discrete time and the measurement of the process occurs at discrete points in time. It further assumes that the dynamics noise and the measurement noise have white noise characteristics (i.e. zero-mean and zero-correlation). The equations in the Kalman filter algorithm fall under two groups. The first group of equations predicts the state (and the associated covariance) of the system, based on the current state and the assumed system model, in order to obtain an a priori estimate for the next time step, as indicated by 𝒙(𝑘+1|𝑘)=𝝓𝑘𝒙(𝑘|𝑘) (4-1) 𝑷(𝑘+1|𝑘)=𝝓𝑘𝑷(𝑘|𝑘)𝝓𝑘𝑇+𝑸𝑘 (4-2) 𝑷(𝑘+1|𝑘) and 𝑷(𝑘|𝑘) are the error covariance matrices associated with the estimated state vector at the prediction and time update steps, respectively. The second group of equations updates the predicted states and covariance estimates with the currently available measurements in accordance with the measurement model: 𝒙(𝑘|𝑘)=𝒙(𝑘|𝑘−1)+𝑲𝑘[𝒛𝑘−𝑯𝑘𝒙(𝑘|𝑘−1)] (4-3) 𝑷(𝑘|𝑘)=[𝑰−𝑲𝑘𝑯𝑘]𝑷(𝑘|𝑘−1) (4-4) The term [𝒛𝑘−𝑯𝑘𝒙(𝑘|𝑘−1)] is called the innovation sequence; it is the difference between the actual observation and the predicted observation, thus it represents the amount of new information introduced into the system by the actual measurement. The Kalman gain matrix 𝑲𝑘 is a weighting factor indicating how much of the new information contained in the innovation sequence should be accepted by the system. As such, the gain matrix is optimized to produce a minimum error variance, and its expression is given by: Egnos-Integrity-Weighted Global Navigator 49 𝑲𝑘=𝑷(𝑘|𝑘−1)𝑯𝑘𝑇[𝑯𝑘𝑷(𝑘|𝑘−1)𝑯𝑘𝑇+𝑹𝑘]−1 (4-5) The Kalman Filter is used in linear systems, however, in this case, the navigational equations are not linear. So it is necessary to use another approximation for the estimation of the navigation solution. The Extended Kalman Filter (EKF) extends the scope of Kalman filter to nonlinear optimal filtering problems by forming a Gaussian approximation to the joint distribution of state x and measurements by using a transformation based on Taylor series. This work implements a first-order EKF where the navigation equations are linearized around the output of the INS. The filtering model used in the EKF is: 𝒙𝑘=𝒇(𝑥𝑘−1,𝑘−1)+𝒘𝑘−1 (4-6) 𝒛𝑘=𝒉(𝑥𝑘,𝑘)+𝒓𝑘 (4-7) where 𝒙𝑘 is the state, 𝒛𝑘 is the measurement, 𝒘𝑘−1 ~𝑵(0,𝑸𝑘−1) is the process noise, 𝒓𝑘−1 ~𝑵(0,𝑅𝑘−1) is the measurement noise, 𝒇 is the nonlinear dynamic model function and 𝒉 is the measurement model function. The first order EKF approximate the distribution of state 𝒙𝑘 given the observations 𝒛1:𝑘 with a Gaussian: 𝒑(𝒙𝑘|𝑦1:𝑘)≈𝑵(𝒙𝑘|𝒎𝑘,𝑷𝑘) (4-8) The EKF is separated into two steps. The steps for the first order EKF are as follows: Prediction: 𝒎𝑘−=𝑓(𝑚𝑘−1,𝑘−1) (4-9) 𝑷𝑘−=𝑭𝑥(𝒎𝑘−1,𝑘−1)𝑷𝑘−1𝑭𝑥𝑇(𝒎𝑘−1,𝑘−1)+𝑸𝑘−1 (4-10) Update: 𝒗𝑘=𝒛𝑘−𝒉(𝑚𝑘−,𝑘) (4-11) 50 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles 𝑺𝑘=𝑯𝑥(𝒎𝑘−,𝑘)𝑷𝑘−𝑯𝑥𝑇(𝒎𝑘−,𝑘) (4-12) 𝑲𝑘=𝑷𝑘−𝑯𝑥𝑇(𝒎𝑘−,𝑘)𝑺𝑘−1 (4-13) 𝒎𝑘=𝒎𝑘−+𝑲𝑘𝒗𝑘 (4-14) 𝑷𝑘=𝑷𝑘−−𝑲𝑘𝑺𝑘𝑆𝑘𝑇 (4-15) where the matrices 𝑭𝑥(𝒎𝑘−1,𝑘−1)and 𝑯𝑥(𝒎𝑘−,𝑘) are the Jacobians of f and h, with elements [𝑭𝑥(𝑚𝑘,𝑘−1)]𝑗,𝑗′=𝛿𝑓𝑗(𝑥,𝑘−1) 𝛿𝑥𝑗′ ]𝑥=𝑚 (4-16) [𝑯𝑥(𝑚𝑘,𝑘−1)]𝑗,𝑗′=𝛿ℎ𝑗(𝑥,𝑘) 𝛿𝑥𝑗′ ]𝑥=𝑚 (4-17) The estimation process follows the scheme presented in the Figure 4-5. Figure 4-5: Scheme of the estimation process. Egnos-Integrity-Weighted Global Navigator 51 In the beginning, an initialization step is performed to initialize and calibrate the sensors, the initial values are given to the algorithms and the alignment is done automatically. Once this step has finished, the estimation process begins. If one of the sensors of the measurement model (GPS/ EGNOS and/or the magnetometer) has new data, the solution calculated using the INS equations is compared with the measurements and the error is estimated, then the covariance is updated, the errors are corrected and the integrators of the INS are reset. Once the estimation measurement update step is finished, or if there are not new measurements from the sensors, the bias of the accelerometers and gyroscopes are calculated, the covariance is updated and the bias of the IMU sensors is corrected. Finally, the equations of the INS are solved and the new navigational solution is calculated. These steps are performed at the IMU rate, providing a faster solution than the GPS sensors typically provide. 4.3. Mechanization equations of the inertial navigation system The mechanization equations are a set of differential equations that convert the output of the Inertial Measurement Unit, which includes rotation rates and specific force measurements, into position, velocity, and attitude information. Kinematic equations describe mathematically the movement of the vehicle; its derivation can be divided into three parts: position, velocity, and attitude. The position in the navigational frame is expressed in curvilinear coordinates. 𝒓𝑛=[𝜑 𝜆 ℎ]𝑇 (4-18) where 𝑟𝑛 is the position vector in the navigation frame, 𝜑 is the latitude, 𝜆 the longitude and h is the altitude of the RPA in the Worl Geodetic System 1984(WGS84). While the velocities (𝑣𝑛) are expressed with respect to the north, east and down (NED) 𝒗𝑛=[𝑣𝑁𝑣𝐸𝑣𝐷]𝑇 (4-19) And they are defined in the n-frame by: 52 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles 𝒗𝑛=(𝑣𝑁 𝑣𝐸 𝑣𝐷)=((𝑅𝑚+ℎ) 0 0 0 (𝑅𝑁+ℎ)𝑐𝑜𝑠𝜑 0 0 0 −1)(𝜑𝜆󰇗ℎ󰇗󰇗) (4-20) Where 𝑅𝑁 and 𝑅𝑁 are radii of curvature in the meridian and prime vertical at a given latitude (see section 3.1 ). So, the time derivative of the curvilinear coordinates can be defined by: 𝒓󰇗𝑛=𝑫−1𝒗𝑛 (4-21) where: 𝑫−𝟏=𝒅𝒊𝒂𝒈( 1 𝑅𝑚+ℎ,1 (𝑅𝑝+ℎ)cos(φ),−1 ) (4-22) In order to obtain the velocity dynamics equations, it is possible to start from the following equation (similar derivations can be found in (Esmat, 2007) and (Noureldin, Karamat and Georgy, 2013)): 𝒗𝑛=𝑹𝑒𝑛𝒓󰇗𝑒 (4-23) Now the time derivative of the coordinates is expressed in the earth frame: 𝒓󰇗𝑒=𝑹𝑖𝑒(𝒓󰇗𝑖−𝛀𝑖𝑒 𝑖𝒓𝑖) (4-24) Where Ω represents the skew-symmetric matrix form of the vector ω and 𝑅𝑖𝑒is the rotation matrix from the inertial to the earth frame. If eq.(4-24) is substituted into (4-23), it is obtained: 𝒗𝑛=𝑹𝑖𝑛(𝒓󰇗𝑖−𝛀𝑖𝑒 𝑖𝒓𝑖) (4-25) Where 𝑹𝑖𝑛 is the rotation matrix from the inertial to the navigation frame. So, considering the Earth’s rotation rate as a constant, the velocity dynamics can be obtained as follows: Egnos-Integrity-Weighted Global Navigator 53 𝒗󰇗𝑛=𝑹𝑖𝑛𝛀𝑛𝑖 𝑖(𝒓󰇗𝑖−𝛀𝑖𝑒 𝑖𝑟𝑖)+𝑹𝑖𝑛(𝒓󰇘𝑖−𝛀𝑖𝑒 𝑖𝒓󰇗𝑖) = 𝑹𝑖𝑛𝒓󰇘𝑖+𝑹𝑖𝑛(𝛀𝑛𝑖 𝑖−𝛀𝑖𝑒 𝑖)𝒓𝑖−𝑹𝑖𝑛𝛀𝑛𝑖 𝑖𝛀𝑖𝑒 𝑖𝒓𝑖 (4-26) From eq.(4-26), if the position rate is written in the inertial frame: 𝒗󰇗𝑛=𝑹𝑖𝑛𝛀𝑛𝑖 𝑖(𝒓󰇗𝑖−𝛀𝑖𝑒 𝑖𝒓𝑖)+𝑹𝑖𝑛(𝒓󰇘𝑖−𝛀𝑖𝑒 𝑖𝒓󰇗𝑖) =𝑹𝑖𝑛𝒓󰇘𝑖+𝑹𝑖𝑛(𝛀𝑛𝑖 𝑖−𝛀𝑖𝑒 𝑖)𝒓𝑖−𝑹𝑖𝑛𝛀𝑛𝑖 𝑖𝛀𝑖𝑒 𝑖𝒓𝑖 (4-27) and taking into account that 𝑰=𝑹𝑛 𝑖𝑹𝑖𝑛 , it is possible to use this relation in (4-26) to obtain: 𝒗󰇗𝑛=𝑹𝑖𝑛𝑟󰇘𝑖+𝑹𝑖𝑛(𝛀𝑛𝑖 𝑖−𝛀𝑖𝑒 𝑖)𝑹𝑛 𝑖𝑹𝑖𝑛𝑹𝑒𝑖(𝒓󰇗𝑒+𝛀𝑖𝑒 𝑒𝒓𝑒)−𝑹𝑖𝑛𝛀𝑛𝑖 𝑖𝛀𝑖𝑒 𝑖𝒓𝑖 = 𝑹𝑖𝑛𝒓󰇘𝑖+(𝛀𝑛𝑖 𝑛−𝛀𝑖𝑒 𝑛)𝑹𝑒𝑛𝒓󰇗𝑒+(𝛀𝑛𝑖 𝑛−𝛀𝑖𝑒 𝑛)𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝒓𝑒−𝑹𝑖𝑛𝛀𝑛𝑖 𝑖𝛀𝑖𝑒 𝑖𝒓𝑖 =𝑹𝑖𝑛𝒓󰇘𝑖+(𝛀𝑛𝑖 𝑛−𝛀𝑖𝑒 𝑛)𝑹𝑒𝑛𝒓󰇗𝑒+𝛀𝑛𝑖 𝑛𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝒓𝑒−𝛀𝑖𝑒 𝑛𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝒓𝑒−𝑹𝑖𝑛𝛀𝑛𝑖 𝑖𝛀𝑖𝑒 𝑖𝒓𝑖 (4-28) If now, the equation (4-25) is used with the following expression: 𝛀𝑛𝑖 𝑛𝑹𝑒𝑛𝛀𝑖𝑒 𝑖𝑟𝑒=𝑹𝑛 𝑖𝑹𝑖𝑛𝛀𝑛𝑖 𝑛𝑹𝑖𝑛𝑹𝑛 𝑖𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝑹𝑖𝑒𝑹𝑒𝑖𝒓𝑒)= 𝑹𝑖𝑛𝛀𝑛𝑖 𝑖𝛀𝑖𝑒 𝑖𝒓𝑖 (4-29) It is possible to reduce the velocity dynamics to: 𝒗𝑛󰇗=𝑹𝑖𝑛𝒓󰇘𝑖+(𝛀𝑛𝑖 𝑛−𝛀𝑖𝑒 𝑛)𝒗𝑛−𝛀𝑖𝑒 𝑛𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝒓𝑒 =𝑹𝑖𝑛𝒓󰇘𝑖−(2𝛀𝑖𝑒 𝑛+𝛀𝑒𝑛 𝑛) 𝒗𝑛−𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝛀𝑖𝑒 𝑒𝒓𝑒 (4-30) If we come back to the equation of the specific force introduced in section 0: 𝒇=𝒓󰇘𝑖−𝒈 (4-31) and we use it in the equation (4-30), this yields 𝒗𝑛󰇗=𝑹𝑖𝑛(𝒇𝑖+𝒈𝑖)−(2𝛀𝑖𝑒 𝑛+𝛀𝑒𝑛 𝑛) 𝒗𝑛−𝑹𝑒𝑛𝛀𝑖𝑒 𝑒𝛀𝑖𝑒 𝑒𝒓𝑒 =𝑹𝑖𝑛𝒇𝑖−(2𝛀𝑖𝑒 𝑛+𝛀𝑒𝑛 𝑛)𝒗𝑛+𝑹𝑒𝑛 (𝒈𝑒−𝛀𝑖𝑒 𝑒𝛀𝑖𝑒 𝑒𝒓𝑒) =𝑹𝑏𝑛𝒇𝑏−(2𝛀𝑖𝑒 𝑛+𝛀𝑒𝑛 𝑛)𝒗𝑛+𝒈𝑛 (4-32) 54 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Finally, eq.(4-32) can be expressed as: 𝒗󰇗𝑛=𝑹𝑏𝑛𝒇𝑏−(2𝝎𝑖𝑒 𝑛+𝝎𝑒𝑛 𝑛)×𝒗𝑛+𝒈𝑛 (4-33) For the attitude dynamics, it is used the following definition: 𝑹󰇗𝑏𝑛=𝑹𝑏𝑛𝛀𝑛𝑏 𝑏=𝑹𝑏𝑛(𝛀𝑖𝑏 𝑏−𝛀𝑖𝑛 𝑏) (4-34) Finally, through the equations (4-22), (4-32) and (4-33), it is possible to obtain the navigation equations that are used in the fusion algorithm of the global navigator system developed in this thesis: [𝒓󰇗𝒏 𝒗󰇗𝒏 𝑹󰇗𝒃𝒏]=[ 𝑫−1𝒗𝑛 𝑹𝑏𝑛𝒇𝑏−(2Ω𝑖𝑒 𝑛+Ω𝑒𝑛 𝑛)𝒗𝑛+𝒈𝑛 𝑹𝑏𝑛Ω𝑖𝑏 𝑏−(Ω𝑖𝑒 𝑛+Ω𝑒𝑛 𝑛)𝑹𝑏𝑛] (4-35) Where 𝒇𝑏 and Ωibb are the outputs of the IMU and g is the gravity vector. In order to update the attitude, we have that the increment of the angular velocity with respect the navigation plane is given by the equation: 𝝎𝑛𝑏 𝑏=𝝎𝑖𝑏 𝑏−𝑹𝑛 𝑏(𝝎𝑖𝑒 𝑛+𝝎𝑒𝑛 𝑛) (4-36) Generally, the computation of the attitude update is performed by using quaternions. In this way, it is possible to avoid the singularities and to improve the computational load. The update of the quaternions is given by: 𝒒󰇗=0.5 [ 0 −𝜔𝑛𝑏,𝑥 𝑏−𝜔𝑛𝑏,𝑦 𝑏−𝜔𝑛𝑏,𝑧 𝑏 𝜔𝑛𝑏,𝑥 𝑏0 𝜔𝑛𝑏,𝑧 𝑏−𝜔𝑛𝑏,𝑦 𝑏 𝜔𝑛𝑏,𝑦 𝑏−𝜔𝑛𝑏,𝑧 𝑏0 𝜔𝑛𝑏,𝑥 𝑏 𝜔𝑛𝑏,𝑧 𝑏𝜔𝑛𝑏,𝑦 𝑏−𝜔𝑛𝑏,𝑥 𝑏0 ] 𝑞 (4-37) 𝒒𝑘+1=𝒒𝑘+𝒒󰇗𝑑𝑡 (4-38) Where 𝑑𝑡 is the time between two measures of the gyros. Once the quaternions are obtained, the DCM is built by using: Egnos-Integrity-Weighted Global Navigator 55 𝑹𝑏𝑛=((𝑞12+𝑞22+𝑞32+𝑞42)2(𝑞1𝑞2−𝑞3𝑞4)2(𝑞1𝑞3+𝑞2𝑞4) 2(𝑞1𝑞2+𝑞3𝑞4) (𝑞22−𝑞12−𝑞32+𝑞42)2(𝑞2𝑞3−𝑞1𝑞4) 2(𝑞1𝑞3−𝑞2𝑞4)2(𝑞2𝑞3+𝑞1𝑞4) (𝑞32−𝑞12−𝑞22+𝑞42)) (4-39) As it was explained through the equation (4-33), the velocity in the navigation plane is obtained by applying the Coriolis and gravity corrections. The velocity in the following time frame is calculated as: 𝒗𝑘+1=𝒗𝑘+𝒗󰇗𝑑𝑡 (4-40) Finally, in order to update the position, a trapezoidal integration is applied: 𝒓𝒌+𝟏 𝒏=𝒓𝑘𝑛+12𝑫−1(𝒗𝑘𝑛+𝒗𝑘+1 𝑛)𝑑𝑡 (4-41) Using these equations, the mechanization equations in the UAV navigaton system can be calculated by following four basic steps: 1. Correction of raw data through known or estimated errors. 2. Attitude update. 3. Transformation of specific force to the navigation frame. 4. Calculation of velocity and position. These steps are summarized in the scheme presented in Figure 4-6. Figure 4-6: Mechanization Equations (Solimeno, 2007) 62 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles equations need to be discretized for its implementation in the computer algorithms. In that way the continuous-time system matrix F is transformed to its corresponding discrete-time form: 𝒙𝑘+1=𝚽𝑘𝒙𝑘+𝒘𝑘 (4-78) Where k denotes the instant of time 𝑡𝑘 and 𝚽𝑘 is the state transition matrix. This matrix can be calculated from the dynamic matrix as (Grewal and Andrews, 2001): 𝚽𝑘=𝑒𝑭(𝑡𝑘)𝑑𝑡=𝑰+𝑭(𝑡𝑘)𝑑𝑡+(𝑭(𝑡𝑘)𝑑𝑡)2 2+⋯ (4-79) Where 𝑑𝑡 is the rate of the INS and I is the identity matrix. In this thesis, this matrix is calculated using up to the second-order of the equation (3-3). Higher terms can be neglected without changes in the performance of the navigator. In the same way, the discrete-time noise sensor associated covariance matrix 𝑸𝑘 can be calculated following the following expression (Shin, 2005): 𝑸𝑘≈12[𝚽𝑘𝑮(𝑡𝑘)𝑸(𝑡𝑘)𝑮𝒕(𝑡𝑘)+𝑮(𝑡𝑘)𝑸(𝑡𝑘)𝑮𝒕(𝑡𝑘)𝚽𝑘𝑡]𝑑𝑡 (4-80) 4.5.2. Measurement Model In this work, the measurement vector 𝒛 of the fusion filter is compound by the differences between the position and velocity of the GNSS+EGNOS measurements and the navigational solution. Also, this vector includes the difference between the heading measurements calculated through the magnetometer and the INS solution. In this way, the measurement vector is given by: 𝒛= [ (𝑅𝑀+ℎ)𝜑𝐼𝑁𝑆−𝜑𝐺𝑃𝑆+𝐸𝐺𝑁𝑂𝑆 [(𝑅𝑀+ℎ)cos(𝜑)]𝜆𝐼𝑁𝑆−𝜆𝐺𝑃𝑆+𝐸𝐺𝑁𝑂𝑆 ℎ𝐼𝑁𝑆−ℎ𝐺𝑃𝑆+𝐸𝐺𝑁𝑂𝑆 𝑣𝐼𝑁𝑆−𝑣𝐺𝑃𝑆+𝐸𝐺𝑁𝑂𝑆 𝜓𝐼𝑁𝑆−𝜓𝑀𝑎𝑔𝑛𝑒𝑡𝑜𝑚𝑒𝑡𝑒𝑟 ] (4-81) Egnos-Integrity-Weighted Global Navigator 63 𝑯= [ 𝑅𝑀+ℎ 0 0 0 𝑅𝑁+ℎ 0 0 0 1 03𝑥3 03𝑥3 03𝑥3 03𝑥3 03𝑥3 𝐼3𝑥3 03𝑥3 03𝑥3 03𝑥3 03𝑥3 03𝑥3 tan (𝜃)cos (𝜓) tan (𝜃)sin (𝜓) 1 03𝑥3 03𝑥3 ] (4-82) The term 𝑅𝑀+ℎ is introduced in the equations in order to solve numerical instabilities that could appear when the Kalman gain is calculated. These instabilities occur because the measurements of the latitude and longitude are very small values. Finally, the initial measurement noise covariance matrix is given by: 𝑹𝑖𝑛𝑖= ( 𝜎𝜑20 0 0 0 0 0 0 𝜎𝜆20 0 0 0 0 0 0 𝜎ℎ20 0 0 0 0 0 0 𝜎𝑉𝑁 20 0 0 0 0 0 0 𝜎𝑉𝐸 20 0 0 0 0 0 0 𝜎𝑉𝐷 20 0 0 0 0 0 0 𝜎𝜓2 ) (4-83) The values for the individual weights of 𝑹𝑖𝑛𝑖 use to be initially fixed as the expected accuracy of the sensors in use. In this thesis, this matrix will be modified using the EGNOS protection levels; the modification of 𝑹𝑖𝑛𝑖 is presented in the following section 4.5.3 4.5.3. Improving the filter performance with EGNOS In this section, it is presented a new strategy that allows improving the estimation filter accuracy through the modification in real-time of the Kalman matrices using the integrity parameters calculated through the EGNOS’ integrity signals. The accuracy and behavior of a Kalman filter rely on the values placed in the different covariance matrices. These values have to be found through a process that leads to an optimal result, and this is called tuning. The behavior of the filter as a result of the adjustment of the 𝑸𝑖𝑛𝑖 and 𝑹𝑖𝑛𝑖 matrices is the following:  The system noise or state covariance matrix Q provides the statistical description of the error model. A large value in Q indicates increased 64 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles parameter uncertainty and implies noisy estimations. During the prediction, if the uncertainty in the IMU data grows, the GNSS+EGNOS position estimation will correct the INS at a higher level. In other words, a large value in Q will cause the INS to closely follow the GPS position estimations. This, in turn, can lead to an inaccurate navigation solution, if the GPS estimations are noisy.  How well the measurement noise is modeled is determined by the measurement noise covariance matrix R. Imperfect modeling of the noise of the measurement observables leads to a bad estimation quality. Choosing a large value for R reflects inaccurate and noisy measurements and might not correct the INS sufficiently. Otherwise, a small value implies an accurate measurement and it will cause the system to rely more on the measured data than on the model. The uncertainty in the covariance parameters of Q and R has a significant impact on the performance of the Extended Kalman Filter (Salychev, 2004). These matrices directly influence the weight that the filter applies between the existing process information and the latest measurements. Errors in any of them may result in the filter being suboptimal or even cause it to diverge. In practice, the Q and R values are generally fixed and applied during the whole operation of the vehicle. Due to the process noise and measurement errors are dependent on the application environment and process dynamics, settings of the stochastic parameters have to be conservative in order to stabilize the filter for the worst-case scenario, which leads to performance degradation. Here, the innovation of the system developed in this thesis is based on the utilization of the vertical and horizontal protection levels calculated from the EGNOS integrity messages for weighting the Q and R parameters. These levels can provide information to the fusion algorithm and be used for tunning their matrix gains. In this way, these protection levels perform a real-time adaptation of the matrices and, in this way, to change the behavior of the filter depending on the quality and accuracy information that EGNOS provides concerning the GPS satellites. For using this new procedure in the estimation algorithm, the first step consists of performing the tuning of the 𝑹𝑖𝑛𝑖 and 𝑸𝑖𝑛𝑖 matrices in the usual way. These matrices have the expressions introduced in eq. (4-77) and eq.(4-88). Egnos-Integrity-Weighted Global Navigator 65 Once these preliminary matrices have been chosen, it is possible to start using the EGNOS integrity information by weighting the values of 𝑹𝑖𝑛𝑖 and 𝑸𝑖𝑛𝑖. In this way, we obtain two new matrices (𝑹𝐸𝑔𝑛𝑜𝑠 and 𝑸𝐸𝑔𝑛𝑜𝑠) which depend on the protection and the alarm levels. 𝑹=𝑹𝑖𝑛𝑖 ∗𝑹𝐸𝑔𝑛𝑜𝑠 (4-84) 𝑸=𝑸𝑖𝑛𝑖 ∗𝑸𝐸𝑔𝑛𝑜𝑠 (4-85) Where the new matrices have the following form: 𝑹𝐸𝑔𝑛𝑜𝑠= ( 𝐻𝑃𝐿 𝐻𝑈𝐿∗𝑟𝑥𝑦 0 0 0 0 0 0 0𝐻𝑃𝐿 𝐻𝑈𝐿∗𝑟𝑥𝑦 0 0 0 0 0 0 0 𝑉𝑃𝐿 𝑉𝑈𝐿∗𝑟𝑧 0 0 0 0 0 0 0 𝐻𝑃𝐿 𝐻𝑈𝐿∗𝑟𝑥𝑦𝑣 0 0 0 0 0 0 0 𝐻𝑃𝐿 𝐻𝑈𝐿∗𝑟𝑥𝑦𝑣 0 0 0 0 0 0 0 𝑉𝑃𝐿 𝑉𝑈𝐿∗𝑟𝑧𝑣 0 0 0 0 0 0 0 1 ) (4-86) 𝑸𝐸𝑔𝑛𝑜𝑠= ( 𝐻𝑈𝐿 𝐻𝑃𝐿∗𝑞ℎ 0 0 0 0 0 0𝐻𝑈𝐿 𝐻𝑃𝐿∗𝑞ℎ 0 0 0 0 0 0 𝑉𝑈𝐿 𝑉𝑃𝐿∗𝑞𝑎 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ) (4-87) Where:  HUL is the Horizontal User Level, it is a constant that the user imposes to the filter.  HPL is the Horizontal Protection Level  VUL is the Vertical User Level,it is a constant that the user imposes to the filter 66 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles  VPL is the Vertical Protection Level.  rxy, rz, rxyv, rzv, qh and qa allows to give more or less importance to the integrity parameters. These parameters are imposed by the designer and must fulfill the following conditions: ∀𝜏𝑖>0 𝑟𝑥𝑦,𝑟𝑧,𝑟𝑥𝑦𝑣,𝑟𝑧𝑣= { 1 𝜏1𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿≤1 𝜏2 𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿>1 (4-88) ∀𝜏𝑖>0 𝑞ℎ,𝑞𝑎= { 1 𝜏3𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿>1 𝜏4 𝑖𝑓 𝐻𝑃𝐿 𝐻𝑈𝐿≤1 (4-89) Depending on these matrices, the behavior of the filter is the following:  If the signals of the GPS and EGNOS satellites are available and are offering a good accuracy (protection levels are lower than the xUL field), then the weights of the elements of the matrix 𝑹𝐸𝑔𝑛𝑜𝑠 are smaller and the elements of the matrix 𝑸𝐸𝑔𝑛𝑜𝑠 become bigger. In this case, the filter relies more in the measurement model than in the system model, so the outputs are corrected following the GPS+EGNOS measurements.  If the protection levels are higher than the alarm xUL field, then the weights of the variances of the matrix 𝑹𝐸𝑔𝑛𝑜𝑠 are increased because the confidence on the GPS+EGNOS signal decreases. In this situation, the values of 𝑸𝐸𝑔𝑛𝑜𝑠 become smaller, the inertial sensors gain importance in the estimation and the measurement model corrects the outputs of the filter in a softer way.  If the receiver is not receiving the EGNOS signals, then the matrix 𝑹𝐸𝑔𝑛𝑜𝑠 and the matrix 𝑸𝐸𝑔𝑛𝑜𝑠 remain constants with the weights calculated in the initial tuning procedure (𝑹𝑖𝑛𝑖 and 𝑸𝑖𝑛𝑖). Egnos-Integrity-Weighted Global Navigator 67 Figure 4-7 shows a summary of the real-time tuning process. Figure 4-7: New Tuning procedure using the EGNOS protection levels. 4.6. Conclusions In this chapter, it has been presented the EIRE navigator system. This navigator is used for the take-off and waypoint navigation phases of the autonomous mission. Here, two fusion integrations strategies are presented: The Tighly Coupled and the Loosely Coupled schemes. From the characteristics of both of them, it is concluded that the Loosely Coupled scheme is the most appropriate architecture for the navigator developed in this thesis. This is due to the LC processing time is faster than the obtained with the TC architecture, and also, due to the implementation of the LC architecture is more straightforward than the TC one, making possible to 68 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles add more sensors to the fusion filter in a faster way. Through this chapter, it is also derived the navigation and mechanization equations of the Inertial Navigation System. This derivation is done because the EKF that is running in the EIRE navigation algorithm has been built by perturbing the kinematics equations. In this filter it was decided to add the bias in the state vector by modeling this error as a Gaussian Markov process. Although the turn-on bias could be added also to this filter, it is concluded that this error can be removed from the navigational solution with an initial calibration stage and, in this way, the filter is reduced by 6 dimensions. Finally, this chapter presents a new strategy that improves the performance of the fusion filter in real-time by using the protection level information provided by the EGNOS sensor. 69 5. GNSS-FREE RELATIVE NAVIGATION SYSTEM The accuracy provided by usual algorithms, most of them based on fusing a GNSS sensor with an INS, it is not typically enough to perform a safe approach and landing, especially in moving platforms. Therefore a new technique to estimate the position in real-time with high accuracy is needed to successfully accomplish with these maneuvers in an autonomous and safe way. In this work, two new relative estimators have been developed and implemented in an autonomous helicopter for their use during the approach and landing phases on both static and mobile platforms. The main differences between these estimators are based on the sensor that they use as the source of the positioning relative measurements, and the transformations needed to convert these measurements to the frame in which the fusion algorithm is working. In Figure 5-1, it is shown the architecture of the Tether –based GNSS-free RelAtive NavigaTor (T-GRANT) module. As it can be seen, the inputs to this module are the data provided by the tether system (angles η, λ and tension of the tether T), the altitude of the altimeter halt, the accelerations and angular velocities of the INS (ab, ω) and the magnetic field measurements of the magnetometer (mb). Figure 5-1: Architecture of the T-GRANT module 70 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles In Figure 5-2, it is shown the architecture of the Radiobeacon –based GNSS-free RelAtive NavigaTor (R-GRANT). The inputs to this module are the relative position to the landing platform provided by the radio-beacon system (𝒑𝑟𝑟𝑏), the altitude measured by the altimeter sensor, the accelerations and angular velocities of the INS integrated into the helicopter(ab, ωb) and the magnetic field measurements of the magnetometer (mb). Figure 5-2: Architecture of the R-GRANT In the schemes presented in Figure 5-1 and Figure 5-2, leaving apart the sensors, it is possible to see that the navigators are built mainly by three different blocks:  Attitude and Heading Reference System (AHRS) block: This is the module in charge of calculating the attitude of the UAV (roll φ, pitch θ and yaw ψ). The attitude is defined as the inclination of its body-axes reference frame to the navigation reference frame. Also in this block, the accelerations are rotated to the navigation axes (an) in order to be used in the fusion algorithm.  Conversion blocks This block performs all the geometric and rotation operations needed to transform the raw measurements of the RBS or tether device to a relative position vector (Prel) expressed in the navigational frame.  Sensor Fusion: This block fuses all the information obtained from the AHRS and the conversion block, and estimates the relative state vector that will be used by the controller of the RUAV. GNSS-free relative Navigation System 71 While the AHRS system is the same for both architectures, the conversion block and the measurement model of the fusion filter of these estimators are different. In this section, these blocks are derivated for both navigators. 5.1. Thresholded and Weighted by Accelerations AHRS The Attitude and Heading Reference System is the module in charge of calculating the attitude of the UAV. In this thesis, a new algorithm has been developed departing from the proposed by Setoodeh in (Setoodeh, Khayatian and Frajah, 2004) and improving it by introducing a new criteria for building the measurement vector. This new algorithm has been called the TWA (Threshold and Weighted by Accelerations) AHRS algorithm. In this filter, the angular rate measurements obtained from the gyroscopes (ωib b) are used for updating the previous attitude estimation. In this case, the attitude is parameterized with unitary quaternion and calculated by using quaternion kinematics equations. qk = qk-1 + q󰇗k (5-1) q󰇗 = 1 2[𝑞0−𝑞1−𝑞2−𝑞3 𝑞1𝑞0−𝑞3𝑞2 𝑞2𝑞3𝑞0−𝑞1 𝑞3−𝑞2𝑞1𝑞0][0 ωnb b] (5-2) After updating the previous attitude solution with the gyroscope measurements, the resulting estimation is corrected using an Extended Kalman Filter. The goal of this EKF is to estimate the attitude errors in the current attitude estimation to remove them. For this purpose, the attitude error is used as the state vector. Once the attitude error is estimated, the attitude solution is corrected to remove the error. After this, the attitude error can be assumed to be zero so the state vector is set to zero. The measurements of the attitude errors of the current attitude estimation are obtained using the measurements provided by the auxiliary sensors (i.e. the accelerometers and the magnetometer). The magnetometer measurements are used to calculate the yaw angle of the RPAS and the difference between this value and the current estimation is used as the measurement of the yaw error. In a similar way, the outputs of the accelerometers are used to calculate the measurements of the roll and pitch errors. Nevertheless, the accelerometers only can be used for this 78 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles AHRS Pitch accuracy of AHRS Algorithms Mean error (RMS) [deg] Standard deviation [deg] TWA-AHRS 0.55 0.67 Setoodeh 0.71 0.82 Wang 0.57 0.67 Xsens MTi-G 0.78 0.61 Table 5-2: Comparison of the pitch accuracy AHRS Yaw accuracy of AHRS Algorithms Mean error (RMS) [deg] Standard deviation [deg] TWA-AHRS 1.23 0.99 Setoodeh 1.76 1.20 Wang 1.78 1.15 Xsens MTi-G 3.09 1.48 Table 5-3: Comparison of the yaw accuracy It can be seen from Table 5-1 to Table 5-3 that the TWA-AHRS and the Wang algorithm provide better accuracies when estimating the roll and pitch angles than the obtained with the Setoodeh’s algorithm and the one calculated by the Xsens MTi-G system. In addition, the TWA-AHRS algorithm provides the best accuracy in comparison with the other three algorithms in the heading estimation. Hence, through the results obtained in these experiments, it can be concluded that the algorithm developed in this thesis provides the best overall accuracy when it is compared with some of the most common AHRS used in navigation. 5.2. Conversión block: Tether Measurements In order to obtain the measurement vector by using the tether, some calculations and transformation have to be performed over the raw measurements of the sensor. In Figure 5-7, it is shown the different elements that are used by the Tether Calculation Block (see Figure 5-1) for the computation of the vector z. In this figure: GNSS-free relative Navigation System 79 the center of gravity of the RUAV is presented as CG; the contact point (CP) is the location where the tether system is installed in the fuselage of the UAV; hal is the altitude above ground level (AGL) measured by the altimeter, hcp is the AGL in the CP, lt is the distance to the landing point O, lcg is the lever arm between the CG and the CP, and lalt is the lever-arm between the CP and the altimeter. For the sake of clarity, in Figure 3-1 it was shown a model of this device with the tether and body coordinate systems represented over it. Figure 5-7: Landing scenario frames and elements that play a relevant role in the landing procedure based on the tether device. The first step for obtaining the relative positioning measurements consists of calculating the altitude to the landing point from the contact point. Since the altimeter is not installed in the same location than the CP and looking for the highest possible accuracy, it is necessary to correct the lever arm according to the following equations: 80 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles 𝐑b n=(Rn b)t=(cθcψ −cϕsψ+sϕsθcψ sϕsψ+cϕsθcψ cθsψ cϕcψ+sϕsθsψ −sϕcψ+cϕsθsψ −sθ sϕcθ cϕcθ ) (5-12) hCP=hal−𝐑b n(3,:)lalt=hal−sθlx+sϕcθly+cϕcθlz (5-13) where Rb n is the rotation matrix from the body to the navigation frame calculated in the AHRS block and “c” and “s” denotes cosine and sine respectively. The cardan joint is rigidly attached to the helicopter and perfectly aligned with the Xb and Yb body axes of the vehicle. This device rotates η and ρ angles with respect to the helicopter fuselage around its Xb and Yb axes respectively, so the rotation matrix from the tether to the body frame is 𝐑tb= ( cβ 0 −sβ −sαsβ cα −sαcβ cαsβ sα cαcβ) (5-14) Once the altitude hCP has been calculated, it is necessary to compute the relative position in navigation axes from the CP to the landing point as: 𝐩CP n=𝐑b n𝐑tb𝐩CP t=𝐑tn𝐩CP t (5-15) where 𝐩CP n and 𝐩CP t are the positions vectors of the contact point in the navigation and the tether frames respectively. In the tether frame, the horizontal XY coordinates of the landing point are equal to 0, therefore the position vector in this location can be expressed as [0, 0, zt] and eq.(5-15) can be re-written as: (xCP n ycp n hCP)=𝐑tn(00 zt) (5-16) By using the eq.(5-16), it is possible to obtain the relative coordinates of the contact point in the navigation frame as: zt=hCP 𝐑tn(3,3)=hCP sθsβ−sϕcθsαcβ+cϕcθcαcβ (5-17) GNSS-free relative Navigation System 81 xCP n=𝐑tn(1,3)zt=(sαcβ(cϕsψ−sϕsθcψ)+cαcβ(sϕsψ+cϕsθcψ)−sβcθcψ)zt (5-18) yCP n=𝐑tn(2,3)zt=(cαcβ(cϕsθsψ−sϕcψ)−cθsψsβ−(cϕcψ+sϕsθsψ)sαcβ)zt (5-19) The last step is to translate this relative position to the center of mass of the vehicle. This operation is done by applying another lever arm correction: 𝐩n=𝒑CP n−𝐑b n𝐥CG (5-20) 5.3. Conversión block: Radio-beacon Measurements In order to obtain the measurement vector by using the radio-beacon sensor, some calculations and transformation have to be performed over the raw measurements. The radio-beacon system provides relative positioning on its local north, which is determined by the location of the Ground Station Coordinates. This local north must be corrected for the estimation algorithm of the helicopter, which works in absolute North-West coordinates. Hence, the orientation of the platform should be provided during the whole operation to be able to correct and convert the relative positioning to the required navigational frame. For this purpose, different strategies are possible:  An AHRS integrated on the landing deck sending through a radio channel the attitude of the landing platform to the UAV. In this way, the helicopter is able to compute the relative orientation of the ship and corrects the relative positioning measurement provided by the RBS. However, in this work, this approach has been discarded because the navigator of the RPA cannot rely on a communication channel.  The relative orientation of the landing platform with respect the helicopter could be calculated by using vision algorithms. Comparing this orientation with the calculated by the onboard navigator, it should be possible to correct the relative measurements of the radio-beacon system. Although this is a suitable approach, and it could provide a very good performance, in this thesis vision techniques have not been taken into consideration.  Integrating two antennas in the helicopter. In this way, the Range 82 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Measurement Unit (see section 3.2.2) is able off computing the range measurements to the landing platform from both antennas and calculates the relative orientation between the ship and the helicopter. Figure 5-8 presents the different relations used by the Calculation Block that was shown in Figure 5-2 for the computation of the vector z. In this figure, CG is the center of gravity of the helicopter, ψrbs is the angle between the radio-beacon system and the navigation frame, larbs is the lever-arm between the CG and the antenna of the radio-beacon receiver, and laalt is the lever-arm between the CG of the vehicle and the altimeter sensor. Figure 5-8: Landing scenario frames and elements that play an important role in the landing procedure based on the radio-beacon device. For obtaining the relative positioning vector, it is necessary to calculate the relative position vector of the antenna radio-beacon receiver (𝑝𝑟𝑏𝑠 𝑟𝑏𝑠) in the navigation frame (𝑝𝑟𝑏𝑠 𝑛). In order to do this, it is necessary to rotate the measurements of the integrated device by the angle 𝜓𝑟𝑏 . This can be done solving the following equation GNSS-free relative Navigation System 83 𝒑𝑟𝑏𝑠 𝑛=(𝑐𝜓𝑟𝑏 𝑠𝑐𝜓𝑟𝑏 0 −𝑐𝜓𝑟𝑏 𝑐𝜓𝑟𝑏 0 0 0 0)𝒑𝑟𝑏𝑠 𝑟𝑏𝑠 (5-21) Once the antenna’s position has been expressed in the navigational frame, it is necessary to apply lever-arm corrections to the radio-beacon calculated position and to the altimeter sensor for obtaining the relative distance of the landing point to the helicopter ‘s CG. In the particular case of this work, this step is essential due to the radio-beacon antenna receiver was integrated with a separation from the CG greater than one meter. In this way, the relative vector used by the fusion algorithm can be calculated as: xCP=𝒙𝑟𝑏𝑠 𝑛−cθcψlrbs,x+(−cϕsψ+sϕsθcψ)lrbs,y+(sϕsψ+cϕsθcψ)lrbs,z (5-22) yCP=𝒚𝑟𝑏𝑠 𝑛−cθsψlrbs,x+(cϕcψ+sϕsθsψ)lrbs,y+(−sϕcψ+cϕsθsψ)lrbs,z (5-23) hCP=hal−sθlalt,x+sϕcθlalt,y+cϕcθlalt,z (5-24) 5.4. Fusion Filter block: System model In this section, it is presented a new system model for the estimation of relative motions. The developed model has used a Singer model as a basis and has extended and improved it for the application treated in this thesis. The Singer acceleration model (Singer, 1970) is a popular model (see (Cloutier, Evers and Feeley, 1989), (Blackman and Popoli, 1999) and (Bar-Shalom, Li and Kirubarajan, 2001)) for target maneuvers that characterizes the unknown target acceleration as a time-correlated stochastic process. It was the first model in characterizing the unknown target acceleration as a time-correlated (i.e., colored) stochastic process. It is an a priori model since it does not use online information about the target maneuver, although it can be made adaptive through an adaptation of its parameters. In the Singer model, the acceleration is modeled as a zero-mean firstorder stationary Markov process with an autocorrelation function (Rong Li and Jilkov, 2003): 𝑅𝑎(𝜏)=𝐸[𝑎(𝑡+𝜏)𝑎(𝑡)]=𝜎2𝑒−𝛼|𝜏| (5-25) 84 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles where σ2 is the variance process noise and α is the reciprocal of a maneuver time constant τ that depends on how long the maneuver lasts. For instance, in a slow turn of an aircraft τ~60s and in an evasive maneuver τ~10−20s (see (Singer, 1970)). In a Markov process, the value at a given time depends on values at other times only through its nearest neighbors. In this work, in order to provide values for these parameters, some assumptions for the ship model were taken (see(Rapatz, 1991) and (Price and Bishop, 1974)): Regarding the landing platform, it is supposed that it follows a straight trajectory with (nearly) constant velocity. Regarding the helicopter, it is assumed that the autopilot is able of following the ship in a soft way during the maneuver (this last assumption was proved through the results of the tests campaigns that are described in chapter 6). One of the shortcomings of the Singer model is that the acceleration has a zero mean at any moment (Rong Li and Jilkov, 2003). However, due to in our application is possible to use the information of the inertial sensors onboard the RUAV, this model has been modified in a new way that overcomes this limitation and improves the results obtained in the estimation module. In the landing scenario, as the ship is assumed to have a slow dynamic, most of the changes in the relative velocity between both vehicles are due mainly to the accelerations of the helicopter. These accelerations are not zero and can be measured by the accelerometers onboard. Hence, the Singer model is modified to have a non-zero mean of the acceleration. This approach is more effective than the Singer model because it includes in the model most of the dynamics of the relative motion, which is that associated with the helicopter accelerations. In this way the acceleration model satisfies: a(t)=a(t)+a(t) (5-26) where a(t)is the mean acceleration of the helicopter in the navigation frame, which is assumed to be constant during the sampling period. On the other hand a(t)is the zero-mean Markov process of the Singer model, with the autocorrelation function showed in eq.(5-25) and it satisfies a󰇗(t)=−αa(t)+w(t) (5-27) In eq.(5-27), w(t) is modeled as a zero-mean white noise. If a(t) is expressed in eq. (5-26) and plugged in eq.(5-27), it is possible to obtain GNSS-free relative Navigation System 85 a󰇗(t)=−αa(t)+αa(t)+w(t) (5-28) If we note from eq. (5-26) that a󰇗(t)=∂ ∂t(a(t)−a(t)) and it is assumed that the acceleration of the helicopter a(t) is constant over a sampling interval Ts, we obtain: a󰇗(t)=−αa(t)+αa(t)+w(t) (5-29) Through eq.(5-29) it is possible to write the complete stochastic differential equation as: 𝒙󰇗(t)=(0 1 0 0 0 1 0 0 −α)𝒙(t)+(00α)a(t)+(001)𝒘(t) (5-30) In eq.(5-30), x(t) is the relative state vector [pr(t),vr(t),ar(t)] where pr(t), vr(t) and ar(t) are the relative position, velocity and acceleration respectively. By applying a standard discretization step in eq.(5-30)(5-43), it is possible to obtain the discrete state equation: 𝐅α= [ 1 T 1 α2(αTs−1+e−αTs) 0 1 1α(1−e−αTs) 0 0 e−αTs ] (5-31) 𝐔α= [ −Ts+αT2 2+1−e−αTs α α T−1−e−αTs α 1−e−αTs ] (5-32) 𝐐(k)=E(𝐰(k)𝐰T(k))=2ασα2[q11 q12 q13 q12 q22 q23 q13 q23 q33] (5-33) where the terms of the process noise covariance matrix (a similar methodology can be found in (Peng, Yang and Liu, 2015) and (Kristan et al., 2010) where a velocity 86 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles model is derived) are given by: q11=1 2α5(1−e−2αTs+2αTs+2α3Ts3 3−2α2Ts2−4αTse−αTs) q12=1 2α4(e−2αTs+1+2e−αTs+2αTse−αTs−2αTs−α2Ts2) q13=1 2α3(1−e−2αTs−2αTse−αTs) q22=1 2α3(4e−αTs−3−e−2αTs+2αTs) q23=1 2α2(e−2αTs+1−2e−αTs) q33=1 2α(1−e−2αTs) (5-34) In eq.(5-33), σαis a conditional density modelled as a Rayleigh distribution variance of the acceleration for ak+1and its equation is given by eq. (5-35) σα 2={4−π π(amax−a(t))2, a(t)>0 4−π π(−amin−a(t))2, a(t)<0 (5-35) where a(t) is the current predicted acceleration and amax and aminare design parameters that correspond to the maximum and minimum accelerations respectively. In this equation, if the absolute values of the design parameters are small, the accuracy of the estimation will tend to be high, however, in cases where the changes of the relative motion are very aggressive, the filter will have a slow response. On the other hand, if the maximum and minimum values are larger, the model allows a quick response to the dynamics changes, but the tracking accuracy becomes lower. In this work, the helicopter can follow the mobile platform in a soft manner, so it has been preferred to model these acceleration parameters using a low profile and, in this way, to obtain more accurate estimations. By generalizing the 1-dimension eq.(5-30), the equations of the model for three dimensions are given by GNSS-free relative Navigation System 87 𝐱k+1=(𝐅α𝟎3x3 𝟎3x3 𝟎3x3 𝐅α𝟎3x3 𝟎3x3 𝟎3x3 𝐅α)+(𝐔α𝟎1x3 𝟎1x3 𝟎1x3 𝐔α𝟎1x3 𝟎1x3 𝟎1x3 𝐔α)𝒂k+𝒘k (5-36) 5.5. Fusion Filter block: Measurement model Once the discrete-time dynamic equations have been modeled, the measurement equation of the discrete-time system is presented as 𝒛k=𝑯𝑘𝒙𝑘+𝒗𝑘 (5-37) where 𝐳k is the measurement vector that contains the relative positions between the rotary-wing UAV and the landing point calculated using the relative system, 𝐇k is the measurement matrix, and 𝐯k is the noise in the measurements. In the relative estimator, a loosely couple scheme has been followed for both relative sensors, so the measurement matrix for the tether and radio-beacon based estimator is the same and is given by 𝐇k=[1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0] (5-38) Once the relative position vector has been computed from the sensors’ outputs (this step is explained in section 5.1.1 and section 5.3), it can be used as the measurement vector 𝒁𝑘 of the eq.(5-37). Due to this vector has been calculated through rotations and translations in order to work in the navigation frame, the components of the measurement noise covariance become correlated. In order to calculate the terms of the covariance matrix, it is necessary to calculate the error propagation in a multiinput multi-output system. The measurement noise covariance matrix has the form: 𝐑k=[σxx 2σxy 2σxz 2 σxy 2σyy 2σyz 2 σxz 2σyz 2σzz 2] (5-39) where the terms of the diagonal of the covariance matrix can be calculated as: 94 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles 6.1.3. Flight Data Analysis This section presents an analysis of the flight data logged during the different campaigns of flights. Aiming to assess the benefits provided by EGNOS, two different navigation solutions have been computed in post-processing for comparison purposes:  The first one has been calculated by using the EIRE navigator developed in this thesis and detailed in chapter 4. It uses the data logged with the ublox sensor that was configured for receiving the SBAS constellation, and also the protection levels calculated with the AsteRx4. In this chapter, this solution will be represented in black.  The second solution is calculated with the same navigator scheme than the first one (based on a loosely coupled architecture), but in this case the estimation algorithm uses as its measurement vector the solution computed by the ublox receiver that was configured with the EGNOS constellation disabled. In this case, the Q and R matrices of the EKF are static with the values obtained by the preliminary tunning process (see section 4.5). This solution will be represented in red color through this chapter. In order to assess which are the real differences between both solutions, the precise trajectory followed by the UAV has been computed in post-processing using the raw data measurements (pseudo-range, Doppler, carrier phase, phase lock and signal quality) logged by the AsteRx4 for generating a RINEX multi-GNSS observation file. This solution has been obtained through a post-processed kinematic (PPK) assessment, performed in differential processing mode using GPS, GLONASS and Galileo constellations when available. Two base stations and precise GNSS files were used for each trajectory processing. Solutions in forward & reverse directions were calculated and combined. This solution will be represented along this chapter using the color blue. 6.1.3.1. First campaign: ATLAS To study the performance of the EIRE navigator developed during the first test campaign, one flight per route is analyzed in this section. The first step for comparing the accuracy obtained with the different approaches is Experimental Results 95 to compare their calculated trajectories. Figure 6-3 presents the horizontal trajectories calculated in the navigational frame (North-East), where the origin is the take-off location. (a) (b) (c) (d) Figure 6-3: Comparison of the trajectories in North-East axes in the first campaign of flights. (a) ATLAS FP1 complete trajectory (b) Zoom of the ATLAS FP1 trajectory (c) ATLAS FP2 Complete trajectory, (d) ) Zoom of the ATLAS FP2 trajectory. As it is possible to see in (a) and (c), the lateral solution is very similar for both navigators, so that a zoom of a slice of the trajectory is presented in (b) and (d). In these pictures, it is shown how the EIRE algorithm (in black) follows the true trajectory more accurately than the solution based only in the GPS satellites (red line). To study this behavior over time, Figure 6-4 compares the North coordinates obtained from the different navigators. 96 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles (a) (b) (c) (d) Figure 6-4 :Comparison of the North position over the time in the first campaign of flights. (a) ATLAS FP1 North position trajectory (b) Zoom of the ATLAS FP1 North position trajectory (c) ATLAS FP2 Complete North position trajectory, (d) ) Zoom of the ATLAS FP2 In Figure 6-4,the zoom applied to (a) and (c) shows how the EIRE navigation solution is, in general, more accurate than the GPS one. Here, the convergence of the EIRE algorithm is faster, allowing to be closer to the real trajectory more quickly than the solution obtained with the GPS sensor. Through Figure 6-3 and Figure 6-4, it is demonstrated that the horizontal performance is improved using the EGNOS services in the estimation filter; however, this improvement is under one meter, so it is possible to say that both solutions will have a very similar performance in missions where it is not necessary to dispose of centimeter accuracy. Most relevant results can be found in the vertical axis. Figure 6-5 shows the altitudes over the Experimental Results 97 ground followed by the UAV during this flight campaign. (a) (b) (c) (d) Figure 6-5:Comparison of the Altitude over the time in the first campaign of flights. (a) ATLAS FP1 Altitude position trajectory (b) Zoom of the ATLAS FP1 Altitude trajectory (c) ATLAS FP2 Complete Altitude trajectory, (d) ) Zoom of the ATLAS FP2 Altitude trajectory In the first route, all the waypoints were planned to have the same altitude while in the ATLAS FP2, the route was configured to have different altitudes, allowing to study the performance of the estimators when the dynamic in the Z axis changes. As it is shown in Figure 6-5, the solution provided by the GPS estimator has higher errors than the obtained using the EIRE architecture. In this case, this behavior can be also seen in the complete trajectories (a) and (c). In (b) and (d), it is shown how the new navigator is able of following the true 98 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles trajectory more accurately and with a time convergence faster than the architecture that only relies on the GPS positioning source. In that way, it is validated that it is possible to improve the altitude accuracy in some meters by using the new navigator. Figure 6-6 shows the errors over the time obtained from the different navigators when they are compared with the PPK solution. (a) (b) (c) (d) Figure 6-6: Errors obtained from the different navigation solutions during the first campaign of flights. (a) ATLAS FP1 horizontal errors (b) ATLAS FP1 vertical errors (c) ATLAS FP2 horizontal errors (d) ATLAS FP2 vertical errors In Figure 6-6 it is possible to see that the new approach improves the solution in both horizontal and vertical axes. As it was presented previously, in the horizontal axis, the error committed by both estimators is very similar. It is in the vertical axis where the EIRE navigator improves the behavior of the estimation solution in some meters, allowing the UAV to have a better Experimental Results 99 knowledge of its real position. To quantify and compare the errors in both configurations, Table 6-1 and Table 6-2 shows some results of the accuracy obtained during these flights and some additional information as the velocity, protection levels and satellites used during these tests. Difference between EIRE navigator and PPK solution Difference between EGNOS disabled navigator and PPK solution RPA’s Horizontal Speed (m/s) Satellites Used Lateral Vertical Lateral Vertical Total Maximum 1,677 0,79 2,286 4,66 6,675 16 Minimum 0,554 0,002 0,355 1,9 0,024 14 Average 1,203 0,171 1,218 3,339 5,79 15,056 Percentile 95% 1,465 0,391 1,653 3,972 6,221 16 Table 6-1: ATLAS FP1 Errors obtained from the comparison of the PPK solution and the different navigator configurations, RPA’s speed, protection levels and satellites used. Difference between EIRE navigator and PPK solution Difference between EGNOS disabled navigator and PPK solution RPA’s Horizontal Speed (m/s) Satellites Used Lateral Vertical Lateral Vertical Total Maximum 1,826 2,159 1,824 5,471 6,948 12 Minimum 0,665 0,001 0,425 0,001 3,347 10 Average 1,037 0,753 1,001 2,722 6,004 11,638 Percentile 95% 1,178 1,226 1,505 4,241 6,384 12 Table 6-2: ATLAS FP2 Errors obtained from the comparison of the PPK solution and the different navigator configurations, RPA’s speed, protection levels and satellites used. The diagrams and tables below aim to present the differences between the precise trajectory and the positioning solution computed by using the EIRE navigator and the GPS solution. As can be observed, lateral deviations from both solutions are similar on the average values; however, in EIRE solution, the dispersion is slightly lower, obtaining a small decrement in the 95th percentile. On the other side, 100 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles noticeable differences are obtained in the vertical axis, where the EIRE solution improves the error between 2m and 3m with respect to the GPS-based solution. 6.1.3.2. Second campaign: FINLAND The second campaign of flights allowed collecting more real data under a different scenario, date and weather conditions. These changes have allowed analyzing the data obtained under different constellations geometries and with EGNOS receiving corrections from different base stations. In that way, it has been possible to check if the results obtained during the first campaign can be replicated under different test conditions. As it was done in the study of the first campaign, inFigure 6-7 and Figure 6-8 , the trajectories calculated by the different navigators are compared with the true solution obtained through the PPK algorithm. (a) (b) Figure 6-7: Comparison of the trajectories in North-East axes in the second campaign of flights. (a) FINLAND FP1 complete trajectory (b) Zoom of the FINLAND FP1 trajectory Experimental Results 101 (a) (b) Figure 6-8: Comparison of the trajectories in North-East axes in the second campaign of flights. (a) FINLAND FP2 Complete trajectory, (b) Zoom of the FINLAND FP2 trajectory. In the flights presented in Figure 6-7 and Figure 6-8, the results obtained from the different fusion filters are again very similar in the horizontal plane, so it is necessary to make a zoom on both figures (a) to be able to appreciate the differences in the behavior of the estimations. Once the zoom is applied, (b) figures show how the EIRE navigator solution follows the true trajectory more accurately. However, it is important to note that the solution of the navigator that only relies on the GPS constellation also seems to have a good performance with errors under three meters. To study this behavior in a more detailed way, Figure 6-9 shows the North position over time in two of the flights performed during the second campaign. 102 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles (a) (b) (c) (d) Figure 6-9: Comparison of the North position over time in the first campaign of flights. (a) FINLAND FP1 North position trajectory (b) Zoom of the FINLAND FP1 North position trajectory (c) FINLAND FP2 Complete North position trajectory, (d) Zoom of the FINLAND FP2 If a zoom is performed in (a) and (c), it is possible to check that effectively the EIRE solution has a lower error than the other configuration. Also, in (b) and (d) it is shown how in the straight sections of the trajectory, the new navigator use to be faster in its approach to the true position than the other solution. However, in these figures, it is again confirmed that both behaviors are quite similar. In order to see a more relevant improvement in the comparison of the new navigator with the GPS estimator, it will be necessary to study the vertical solution obtained during these tests. Figure 6-10 presents the results obtained in the vertical plane for both flight plans. While in (a) the waypoints of the flight plan had different altitudes, in the Experimental Results 103 second flight (c) the altitude was maintained at 60 m approximately during the whole operation. (a) (b) (c) (d) Figure 6-10: Comparison of the Altitude over the time in the first campaign of flights. (a) FINLAND FP1 Altitude position trajectory (b) Zoom of the FINLAND FP1 Altitude trajectory (c) FINLAND FP2 Complete Altitude trajectory, (d) Zoom of the FINLAND FP2 Altitude As it happened in the first campaign, the altitude calculated by the estimator that does not make use of EGNOS in the fusion filter has an error of several meters. This error uses to have a constant part (like a bias) and another one that changes continuously along the time due to the corrections performed by the Extended Kalman Filter in the measurement phase of the filter. The EIRE navigator departs with a lower constant error due to the corrections that EGNOS provides to the GNSS filter. Also, the magnitude of the variating error is lower because the estimation filter is receiving more accurate corrections so it is able to converge to a 110 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles 6.2.2.1. Sequence of steps The complete experiment comprises both the approach and the landing of the rotary-wing UAV to the moving platform. The following lines explain the sequence of steps followed during the operations:  Initial condition: the rotary-wing UAV flies autonomously with the global navigator inside the RBS coverage.  Step 1: check that the UAV is inside the RBS area, so the relative positioning solution is valid and consistent. Guide the rotary-wing UAV in relative coordinates so that it goes over the landing platform, always inside the RBS area.  Step 2: when the rotary-wing UAV is located over the platform, the altimeter starts to control the height AGL (in this case above platform level). When activating the altimeter, the relative height to the platform is maintained.  Step 3: command a horizontal displacement in relative coordinates to the origin of the platform (0,0). In this phase, the relative height commanded over the platform is maintained, so if the landing platform is in movement, the helicopter must follow the platform maintaining the relative horizontal position and height.  Step 4: once the rotary-wing UAV is above the origin, the descent to the landing platform is commanded, with a certain velocity, until the helicopter touches down. 6.2.2.2. Approaches in manual flights In this stage, flights were carried out manually. They consisted of multiples approaches to the landing platform at different angles and heights in order to study the performance of the RBS and the estimator at different distances from the landing platform where the GSUs were installed. In these operations, the landing platform remained completely static. In order to be able of obtaining the accuracy of the solution calculated with the developed navigation system, the position calculated with the relative estimator will be compared with the data collected from the GPS RTK sensor installed in the setup. One of the main objectives of these flights was to test the operational distance Experimental Results 111 under the RBS works correctly and is able of providing an accurate enough solution for the approaching and landing procedures. Figure 6-14 shows the distance from the helicopter to the landing platform (LP) and the quality status of the RBS system during one of these tests. Figure 6-14: Distance to the landing platform and RBS status during the manual flight experiment. The RBS quality status is a signal that indicates the quality in the solution of the radio-beacon sensor. When this signal is equal to 0, it indicates that the solution quality is the best than the sensor can provide. If its value is 50, the radio-beacon system does not assure to provide an accurate solution. In other cases, the solution is degraded and it is not recommended its use. As it is possible to see in Figure 6-14, the status of the sensor uses to change its value when the distance to the platform is larger than 50 meters approximately. In Figure 6-15, it has been zoomed the flight graph in two approach maneuvers. In this picture, it has been marked with a red cross the points in which the sensor switches to another state. 112 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Figure 6-15: RBS status changes with the distance. In order to study the effect of the RBS status in the accuracy solution of the navigator estimation, Figure 6-16 presents the position North (a) and altitude (b) calculated by the navigator in some of the slots of time in which the RBS switches its quality signal. In this case, the navigator has used the RBS sensor in both horizontal and vertical axes (altimeter was not used). (a) (b) Figure 6-16: Effect of the sensor status in the accuracy of the positioning solution of the navigator in the (a) North axis and (b) altitude. As it is possible to check in Figure 6-16, the error grows up when the helicopter gets away from the landing platform (where the GSUs are installed). This error is more Experimental Results 113 appreciable in the altitude, where the behavior of the solution does not follow the real trajectory. Figure 6-17 shows another manual flight with several approaches to the landing platform where the RPA flew at a distance lower than 30m from the radio beacon infrastructure on ground and the RBS quality signal was the best possible during the whole maneuver. In this case, the R-GRANT estimation solution is more accurate and there are not important deviations from the RTK solution, being the error in the horizontal axes under 1 m. (a) (b) Figure 6-17: Manual approaches with distances to the LP shorter than 30m. In order to quantify the error of the estimator at different distances from the landing platform, Table 6-5 summarizes the results of this first campaign of flights. Distance to the landing point < 15 m <30 m < 60 m > 60 m RMS North 0.1945 0.6948 0.9888 2.2287 East 0.2562 0.5842 1.1647 2.2161 Altitude 0.8724 1.4605 3.0370 7.0861 STD North 0.3071 0.7249 1.2254 3.3620 East 0.4407 1.0008 1.5722 3.4795 Altitude 0.4793 1.8442 3.9172 9.5538 Table 6-5: Accuracy of the navigational solution regarding the distance to the platform 114 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles From these results several considerations were taken into account for the following tests:  Horizontal accuracy is enough for the approach phase of the RPA to the landing platform once it is at a distance lower than 60 m. From the results obtained in the different flights, it is possible to conclude that this solution could be used for performing the approach phase without problems; even it could be possible to carry out the autonomous landing maneuver if the landing platform is not under movement. However, for performing this last step, it is advisable to improve the accuracy of the final solution. In order to do this, the data logged during these tests was used for tunning the filter's parameters and improving the overall performance of the autopilot.  The altitude accuracy provided by the RBS system is not enough for performing the landing maneuver or the tracking procedure safely. Due to the variations in this variable, it was decided to use the altimeter installed in the RPA as the main sensor used by the navigator for calculating the relative altitude to the landing point. 6.2.2.3. Autonomous Landing with the platform static in the horizontal plane From the results obtained in the previous step, the estimator was tunned and it was possible to create a guidance strategy based on the distances of the helicopter to the landing platform. Tests presented in this section consist of performing autonomous landing procedures by using the radio-beacon sensor as the position source of the navigation algorithm and feeding the controller with the outputs of the relative estimator. In this scenario, the landing platform remains static during the whole operation in the horizontal plane. Regarding the vertical plane, first landings were performed with the platform also static. However, once it was checked that the helicopter was able to land correctly without human intervention, the platform was commanded to move in the vertical axis. Figure 6-18 shows the comparison between the position and velocity solutions of the R-GRANT module and the RTK sensor in the horizontal plane during a landing with the platform completely static. At the beginning of this test, the helicopter is at 14 meters from the landing point. At time 870s, the approach is commanded and, once the RPA is over the platform at 935s, the descent starts. Experimental Results 115 (a) (b) Figure 6-18: horizontal position and velocity during an autonomous landing with the platform static in both axes. These pictures show how the horizontal position and velocity calculated with the estimator are very similar to the solution obtained with the RTK sensor. The accuracy uses to be under one meter. However, there are some slots of time (for example from 900 to 950) where the RBS sensor fails and the accuracy of the estimator gets worst. Due to this behavior depends only on the RBS sensor, it is not advisable to perform the landing maneuver in scenarios with complex conditions like could be a landing procedure over a ship with strong sea dynamic. In these tests, the altitude measurement used by the estimator is the provided one by the altimeter. In Figure 6-19, it is shown as the vertical position and velocity solutions of the navigator have good accuracy and follow the measurements provided by the RTK sensor. In this graph, the difference between the estimator and the RTK sensor flight at the beginning of the flight is due to, at this time, the RPA was not flying over the platform, so the altimeter was measuring the distance to the ground and not to the landing platform. Once the RPA is on the top of this platform (at 870 s approximately), the altimeter is able to measure the distance directly to the landing point (in this case the platform was elevated approximately 2 meters AGL). 116 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles (a) (b) Figure 6-19: Altitude during an autonomous landing with the platform static in both axes. Once several landings were performed successfully, it was started a new phase where the landing platform was commanded to move in its vertical axis. During these tests, it was checked that the accuracy of the R-GRANT module had not variations with respect to the scenario in which the landing platform remained completely static. It means that the vertical movements do not substantially affect the calculations that the RBS sensor performs in the horizontal plane. Figure 6-20 shows an interval of time of one flight where the moving platform is oscillating in the vertical axis and the UAV has been commanded to maintain the relative vertical altitude over the landing point. Figure 6-20: RPA maintaining the relative altitude to the landing platform which is in movement in the vertical axis Experimental Results 117 Table 6-6 presents the RMS errors and the standard deviation of the navigator solution in both position and velocity. As it is possible to see, the error in the horizontal plane is less than 0.7 meters. Although this accuracy is better than the obtained with a typical GNSS sensor, it would be advisable to improve it in order to be able of performing the final maneuver in any platform and scenario safely. The performance in the vertical axis is very good, obtaining an accuracy of 10 cm approximately. Position Velocity North East Altitude North East Up RMS 0.4182 0.3945 0.1098 0.4287 0.5338 0.0512 STD 0.7273 0.4524 0.2522 0.7535 0.8152 0.0681 Table 6-6: Navigator accuracy in the autonomous tests experiments with the platform static in the vertical plane 6.2.2.4. Landing with horizontal displacement In this phase of the tests, both guidance and navigation filters were tested over operations where the unmanned helicopter was commanded to land on the landing platform when it was moving horizontally and vertically. Figure 6-21 shows the trajectory in Google Earth of both the helicopter and the moving platform during the operation. Figure 6-21: Rotary wing UAV trajectory (blue) landing on the moving platform (red) 118 Accurate navigation applied to landing maneuvers on mobile platforms for unmanned aerial vehicles Figure 6-22 shows the relative vertical position, the platform local altitude and the platform North position during a complete test. These experiments were composed of two different phases: static and dynamic. At the beginning of the first phase, the landing platform is static in the horizontal plane. Once all the systems are ready and the UAV has taken off (t=370s), the GCS commands the vertical movement to the driver of the platform and it begins to oscillate in the vertical axis (t=435 s). Once the helicopter is in the air and the landing platform oscillating, the second phase starts. In this phase, the landing platform begins its movement also in the horizontal plane (t=538 s) until the helicopter lands (t=610). Figure 6-22: UAV Relative vertical position, platform altitude and North position during the straight movement test using the Radio-beacon based navigator and different phases of the operation In order to study the estimation accuracy achieved during these tests, Figure 6-23 shows a comparison between the relative position calculated with the GNSS-RTK system (used again as ground-truth) and the relative position solution obtained with the radio-beacon based navigator. Experimental Results 119 (a) (b) (c) (d) Figure 6-23: Comparison among the R-GRANT solution (red) and the GNSS-RTK measurements (blue) during a test where the landing platform is moving following a straight trajectory: (a) position in the horizontal plane, (b) velocity in the horizontal plane, (c) relative altitude, and (d) relative vertical velocity. Figure 6-23 shows how in the dynamic phase of the operation, when the landing platform starts the horizontal movement, the error in the position estimation grows. This error appears if the helicopter does not have information about the landing platform orientation. In those cases, when the RBS measurements (in the body frame of the landing platform) are converted to the navigation frame, the relative heading error is translated to errors in the relative position and velocity estimated in the horizontal plane. The magnitude of these errors depends on the relative orientation error and the distance to the platform. In this experimental phase, the platform was moved following a straight line parallel to the ATLAS