CN117234234A - Unmanned aerial vehicle emergency landing method and system based on elevation map - Google Patents
Unmanned aerial vehicle emergency landing method and system based on elevation map Download PDFInfo
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Abstract
The invention discloses an unmanned aerial vehicle emergency landing method and system based on an elevation map, and relates to the technical field of positioning and navigation. The method comprises the following steps: the working state of the equipment of the unmanned aerial vehicle is monitored in real time for early warning, and the equipment is judged to be in a fault state when the index is abnormal; judging homing capacity based on the elevation map, and if the homing capacity is provided, taking a waiting area which is automatically generated near the original landing point as a target point area for homing; if the area is not available, selecting a region with a relatively flat periphery around the area as a target point region based on the elevation map to return; after reaching the target point area, judging the height of the landing window in real time, and if the landing height is not met, hovering to be high and waiting; if yes, accessing automatic landing control to carry out emergency landing. The technical scheme of the invention is mature and reliable, easy to realize, strong in applicability, capable of guaranteeing the flight safety of the unmanned aerial vehicle and improving the safety of personnel, facilities and the aircraft in a landing area after the unmanned aerial vehicle is landed in an emergency.
Description
Technical Field
The invention relates to the technical field of positioning navigation, in particular to an unmanned aerial vehicle emergency landing method and system based on an elevation map.
Background
At present, as unmanned aerial vehicles are increasingly widely used and popularized, related treatments after unexpected faults, air collisions and other events which may cause the unmanned aerial vehicle to need emergency landing are considered when the unmanned aerial vehicle is used. At present, most unmanned aerial vehicles are controlled through preset routes and instructions or through a mode of sending instructions in real time through a line-of-sight link, compared with manned aircraft, after the unmanned aerial vehicle has the fault, the unmanned aerial vehicle is out of control or even crashes, and further threat is caused to personnel, facilities and the unmanned aerial vehicle in landing areas, and emergency landing under the condition is not a simple task for most unmanned aerial vehicle systems at present.
When an unmanned aerial vehicle engine fails and needs emergency landing, personnel, facilities and airplane safety in a landing area need to be properly considered, emergency landing is completed according to the situation, and the unmanned aerial vehicle emergency landing method is needed to be provided, so that the safety of the personnel, facilities and the unmanned aerial vehicle in the landing area is guaranteed.
Disclosure of Invention
Therefore, in order to solve the problems that the unmanned aerial vehicle is required to be rapidly disposed when in emergency landing due to faults, an alternative landing area is automatically calculated if a landing point cannot be expected to fly back, an emergency landing scheme is executed, and the safety of personnel, facilities and the unmanned aerial vehicle in the landing area is guaranteed.
The invention comprises the following technical scheme:
according to a first aspect of the technical scheme of the invention, an unmanned aerial vehicle emergency landing method based on an elevation map is provided, and comprises the following steps:
step 1, dangerous case monitoring: the working state of the equipment of the unmanned aerial vehicle is monitored in real time for early warning, and the equipment is judged to be in a fault state when the index is abnormal;
step 2, homing judgment: judging homing capacity based on the elevation map, and if the homing capacity is provided, taking a waiting area which is automatically generated near the original landing point as a target point area for homing; if the area is not available, selecting a region with a relatively flat periphery around the area as a target point region based on the elevation map to return;
step 3, returning to land: after reaching the target point area, judging the height of the landing window in real time, and if the landing height is not met, hovering to be high and waiting; if yes, accessing automatic landing control to carry out emergency landing.
Further, in the step 2, a lower slide track is calculated according to the unpowered sliding parameters of the unmanned aerial vehicle, and the homing capacity is determined by comparing the lower slide track with an elevation map.
Further, the unpowered downslide parameter calculating method comprises the following steps:
wherein Δs is the horizontal distance from the original drop point in unit time, and Δz is the vertical distance from the original drop point in unit time.
Further, in the step 2, in the course of the return voyage, the transverse control law is track tracking control, and the longitudinal control law is constant-speed sliding control.
Further, the track tracking control law is:
wherein delta a For aileron control, p is roll angle speed,for the track angle>Given the track angle, +.>Is the proportional control coefficient of the rolling angle speed, +.>For track deviation proportional control coefficient, +.>Is the rolling deviation proportion control coefficient, phi is the rolling angle, phi g For a roll angle set, +.>And delta Y is the lateral offset distance, which is a lateral offset distance proportional control coefficient.
Further, the constant speed downslide control law is:
wherein delta e For elevator control, q is pitch angle rate, θ is pitch angle, θ g For a given pitch angle, V is the indicated airspeed, V g For a given space velocity,is a pitch angle speed proportional control coefficient +.>Is pitch angle proportional control coefficient +>For the airspeed deviation proportional control coefficient, +.>The control coefficient is integrated for airspeed offset.
In step 2, a region with a relatively flat surrounding is selected as the target point region by combining the elevation map with the unpowered downslide parameter.
Further, the method for selecting the area with the relatively flat surrounding as the target point area by combining the elevation map with the unpowered downslide parameter comprises the following steps:
a-h are eight elevation map units,and->The unpowered downslide parameters in the horizontal and vertical directions from central cell i, x and y are the dimensions of the cell, respectively.
Further, in the step 3, after reaching the target point area, the specific method for determining the height of the landing window in real time is as follows:
wherein H is U Unmanned aerial vehicle height, H, obtained for unmanned aerial vehicle through airborne sensor g For landing window height.
Further, the calculation mode of the height of the landing window is as follows:
and S is the horizontal distance of the target area according to the landing point selected in the step 2, and the reference value of the unpowered downslide parameter is the average value of the unpowered downslide parameters of the unmanned aerial vehicle.
Further, in the step 3, the lateral control law used in the automatic landing control is track tracking control, and the longitudinal control law used is landing sliding airspeed control.
Further, the landing glide airspeed control law is:
wherein V is the indicated airspeed, V g For a given airspeed, V c To control the speed setting, H is the sinking rate, H g For a given sinking rate,is a height deviation proportional control coefficient, +.>The control coefficient is integrated for the height deviation.
According to a second aspect of the technical scheme of the present invention, there is provided an unmanned aerial vehicle emergency landing system based on an elevation map, comprising:
the dangerous case monitoring unit is used for monitoring the working state of the unmanned aerial vehicle in real time to perform early warning, and judging that the unmanned aerial vehicle is in a fault state when the index is abnormal;
a homing determination unit for determining homing ability, and if so, homing is performed by taking a waiting area autonomously generated near the original landing point as a target point area; if not, selecting a region with a relatively flat periphery nearby as a target point region for returning;
the return landing unit is used for judging the height of the landing window in real time after reaching the target point area, and if the landing height is not met, the aircraft spirals down and waits for the landing; if yes, accessing automatic landing control to carry out emergency landing.
Compared with the prior art, the invention has the following advantages:
(1) The robustness is enhanced, and the unmanned aerial vehicle can still find the fault state of the unmanned aerial vehicle in time under the condition of unmanned operation or monitoring by dangerous condition monitoring, so that the safety of personnel, facilities and the like under various conditions is guaranteed;
(2) The method has high degree of intellectualization, and by using real-time analysis of the elevation map, the landing area can be intelligently judged, the uncertainty of traditional manual judgment is avoided, the accuracy and the success rate of landing are improved, and the whole efficiency of unmanned aerial vehicle emergency landing is improved;
(3) The method has high automation degree, automatically calculates the alternative landing area through a preset algorithm, and executes an emergency landing scheme when necessary. Compared with manual operation, the automatic emergency treatment device has the advantages of being high in automation degree, capable of rapidly responding to emergency conditions, reducing the requirement of manual participation and ensuring timeliness and effectiveness of treatment.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to the structures shown in these drawings without inventive effort for a person skilled in the art.
FIG. 1 shows a flow chart of an unmanned aerial vehicle emergency landing method based on an elevation map;
FIG. 2 shows a schematic diagram of a track following control law;
FIG. 3 shows a fixed speed roll-down control law structure;
FIG. 4 shows a landing glide airspeed control law structure diagram;
FIG. 5 shows a method diagram of an elevation map calculation landing area;
FIG. 6 illustrates a schematic diagram of a track following control;
fig. 7 shows a configuration diagram of the glide control law.
The achievement of the objects, functional features and advantages of the present invention will be further described with reference to the accompanying drawings, in conjunction with the embodiments.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples are not representative of all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with some aspects of the present disclosure as detailed in the accompanying claims.
The terms first, second and the like in the description and in the claims, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the disclosure described herein may be capable of operation in sequences other than those illustrated or described herein, for example.
Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
A plurality, including two or more.
And/or, it should be understood that for the term "and/or" used in this disclosure, it is merely one association relationship describing associated objects, meaning that there may be three relationships. For example, a and/or B may represent: a exists alone, A and B exist together, and B exists alone.
The technical scheme of the invention provides an unmanned aerial vehicle emergency landing method based on an elevation map, which comprises the following steps:
step 1: the working states of all sensors and avionics of the unmanned aerial vehicle are monitored in real time, early warning is carried out, the working voltage, the rotating speed and the oil pressure of the engine are monitored in real time by taking the engine as an example, and when the indexes of the engine are inconsistent with the normal states, the dangerous case monitoring system judges that the engine is in a fault state;
step 2: after the unmanned aerial vehicle breaks down, the unmanned aerial vehicle is combined with the unpowered downslide parameters of the unmanned aerial vehicle through an elevation map, the original expected falling point position and the original expected falling point height. If the capability of returning to the original landing point is provided, a waiting area which is generated automatically near the landing point is used as a target point for returning, a transverse control law used for returning is track tracking control, a longitudinal control law used for constant-speed sliding control is used, and the step 3 is executed after the waiting area arrives at the area; if the unmanned aerial vehicle is not provided with the target point, selecting a region with a relatively flat periphery nearby as an alternative landing region by combining the unpowered downslide parameter of the unmanned aerial vehicle through an elevation map, displaying the region on the map through a ground station, manually confirming by a flight control operator and a load operator (if the unmanned aerial vehicle is provided with the target point), returning the region automatically by the unmanned aerial vehicle, controlling the transverse control law used for returning to be track tracking control, controlling the downslide of the longitudinal control law used, and executing the step 3 after the region is reached;
step 3: after reaching the area, judging the height of the landing window in real time, and if the landing height is not met, hovering to wait for the landing height; if the control method meets the requirements, the automatic landing control is accessed, the transverse control law used is track tracking control, and the longitudinal control law used is landing glide control.
The track tracking control law is as follows:
wherein delta a For aileron control, p is roll angle speed,for the track angle>Given the track angle, +.>Is the proportional control coefficient of the rolling angle speed, +.>For track deviation proportional control coefficient, +.>Is the rolling deviation proportion control coefficient, phi is the rolling angle, phi g For a roll angle set, +.>And delta Y is the lateral offset distance, which is a lateral offset distance proportional control coefficient.
The constant speed sliding control law is as follows:
wherein delta e For elevator control, q is pitch angle rate, θ is pitch angle, θ g Given as pitch angle. V is the indicated airspeed, V g For a given space velocity,is a pitch angle speed proportional control coefficient +.>Is pitch angle proportional control coefficient +>For the airspeed deviation proportional control coefficient, +.>The control coefficient is integrated for airspeed offset.
The landing glide airspeed control law is:
wherein V is the indicated airspeed, V g Given as airspeed. V (V) c To control the speed setting, H is the sinking rate, H g For a given sinking rate,is a height deviation proportional control coefficient, +.>The control coefficient is integrated for the height deviation.
The method for determining whether the expected drop point can be returned through the elevation map comprises the following steps of:
wherein Δs is the horizontal distance to the target point in unit time, Δz is the vertical distance to the target point in unit time, which is the unpowered glide parameter estimated by the pneumatic model. And calculating a lower slide track by the value, and comparing the lower slide track with an elevation map to determine whether the expected drop point can be returned.
The method for calculating the landing area through the elevation map comprises the following steps of:
wherein a-h are eight elevation map units,and->The linear elevation change rates (i.e., unpowered glide parameters) in the horizontal and vertical directions from central cell i, respectively, x and y are the dimensions of the cell.
The technical scheme of the invention also provides an unmanned aerial vehicle emergency landing system based on the elevation map, which comprises the following steps:
the dangerous case monitoring unit is used for monitoring the working state of the unmanned aerial vehicle in real time to perform early warning, and judging that the unmanned aerial vehicle is in a fault state when the index is abnormal;
a homing determination unit for determining homing ability, and if so, homing is performed by taking a waiting area autonomously generated near the original landing point as a target point area; if not, selecting a region with a relatively flat periphery nearby as a target point region for returning;
the return landing unit is used for judging the height of the landing window in real time after reaching the target point area, and if the landing height is not met, the aircraft spirals down and waits for the landing; if yes, accessing automatic landing control to carry out emergency landing.
Examples
As shown in fig. 1, a flow chart of an unmanned aerial vehicle emergency landing method based on an elevation map is shown. In the flight process, the dangerous case monitoring system continuously operates and is used for monitoring the working states of various sensors and avionics of the unmanned aerial vehicle in real time, early warning is carried out under the condition that the working states are abnormal, and taking the stopping fault of the engine as an example, the dangerous case monitoring system monitors the working voltage, the rotating speed and the oil pressure of the engine in real time, and when the indexes of the engine are inconsistent with the normal states, the dangerous case monitoring system judges that the engine is in a fault state, and further uploads the alarm information to flight control software to be manually confirmed by flight control hands, and emergency treatment is carried out after the confirmation. Firstly, the unmanned aerial vehicle flight control system combines the unpowered downslide parameters of the unmanned aerial vehicle through an elevation map and the original expected falling point position and height based on the position and the height of the unmanned aerial vehicle. If the return determination is carried out, if the return determination has the capability of returning to the original landing point, the autonomous generated waiting area near the landing point is used as a target point for returning, a transverse control law structure used for returning is shown as a track tracking control law structure diagram in fig. 2, and a longitudinal control law used for returning is shown as a constant speed sliding control law structure diagram in fig. 3. If the unmanned aerial vehicle does not have the return to the expected landing point, selecting a region with a relatively flat periphery nearby as an alternative landing region according to the position and the height of the unmanned aerial vehicle through an elevation map and combining the unpowered downslide parameter of the unmanned aerial vehicle, wherein the selection method is as shown in fig. 5, selecting a flat region through analysis of region gradients, displaying the flat region on the map through a ground station, manually confirming by a flight control operator and a load operator (if the unmanned aerial vehicle is provided with the map, automatically returning the region as a target point by the unmanned aerial vehicle, wherein a transverse control law for returning is as shown in a track tracking control law structure diagram of fig. 2, and a longitudinal control law for returning is as shown in a landing downslide control law structure diagram of fig. 4.
Fig. 6 shows a schematic diagram of the track following control. The control system comprises the following components:
the flight control computer is mainly responsible for processing the measurement signals of the sensor component, forming signals meeting control requirements through a control law, and further transmitting instructions to the execution mechanism to control the operation of the execution mechanism; the steering engine is an actuating mechanism for controlling the control surface, and the control signal output by the flight control computer is used for controlling the rotation angle of a rocker arm of the steering engine, so as to control the control surface; the airborne satellite navigation equipment is used for measuring navigation parameters such as longitude, latitude, altitude, ground speed direction, sky speed, course angle, roll angle, pitch angle and the like of the unmanned aerial vehicle; the fiber optic gyroscope is used for providing high-precision unmanned aerial vehicle attitude information and can provide angular velocity and acceleration information in real time; the magnetic heading sensor is used for measuring the magnetic declination of the unmanned aerial vehicle; the air pressure height/airspeed measuring device is used for measuring the air pressure height and indicating the airspeed of the unmanned aerial vehicle; and the radio altimeter is used for measuring the relative height of the unmanned aerial vehicle and the ground.
In the track tracking control system, a flight control computer processes magnetic declination, rolling angle rate, yaw angle rate and lateral offset information measured by the sensor, forms a signal meeting control requirements through a track tracking control law, further transmits an instruction to an aileron steering engine, and finally enables the unmanned aerial vehicle to continuously track a given track.
Fig. 7 shows a schematic of the slip-down control. The control system comprises the following components:
the flight control computer is mainly responsible for processing the measurement signals of the sensor component, forming signals meeting control requirements through a control law, and further transmitting instructions to the execution mechanism to control the operation of the execution mechanism; the steering engine is an actuating mechanism for controlling the control surface, and the control signal output by the flight control computer is used for controlling the rotation angle of a rocker arm of the steering engine, so as to control the control surface; the airborne satellite navigation equipment is used for measuring navigation parameters such as longitude, latitude, altitude, ground speed direction, sky speed, course angle, roll angle, pitch angle and the like of the unmanned aerial vehicle; the fiber optic gyroscope is used for providing high-precision unmanned aerial vehicle attitude information and can provide angular velocity and acceleration information in real time; the magnetic heading sensor is used for measuring the magnetic declination of the unmanned aerial vehicle; the air pressure height/airspeed measuring device is used for measuring the air pressure height and indicating the airspeed of the unmanned aerial vehicle; and the radio altimeter is used for measuring the relative height of the unmanned aerial vehicle and the ground.
In the sliding control system, a flight control computer processes information such as the airspeed, pitch angle rate, sinking rate and the like of the unmanned aerial vehicle measured by the sensor, forms a signal meeting control requirements through a sliding control law, further transmits an instruction to an elevator steering engine, and finally enables the unmanned aerial vehicle to continuously track given sliding.
In summary, the invention provides an unmanned aerial vehicle emergency landing method and system based on an elevation map, when unmanned aerial vehicle faults, particularly an engine is stopped and needs emergency landing, automatic treatment can be rapidly completed, the operation level of a user is prevented from being greatly relied on in a manual operation mode, meanwhile, the method uses the elevation map to carry out real-time synchronous analysis, whether the unmanned aerial vehicle has the capability of returning to an expected landing point or not is determined, if the unmanned aerial vehicle cannot fly back to the expected landing point, an alternative landing area is automatically calculated, an emergency landing scheme is executed, and the safety of personnel, facilities and unmanned aerial vehicles in the landing area is ensured.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The foregoing embodiment numbers of the present invention are merely for the purpose of description, and do not represent the advantages or disadvantages of the embodiments.
From the above description of the embodiments, it will be apparent to those skilled in the art that the above implementation may be implemented by means of software plus necessary general purpose hardware platform, or of course by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. ROM/RAM, magnetic disk, optical disk) comprising instructions for causing a terminal (which may be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to perform the method according to the embodiments of the present invention.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are to be protected by the present invention.
Claims (10)
1. An unmanned aerial vehicle emergency landing method based on an elevation map is characterized by comprising the following steps of:
step 1, dangerous case monitoring: the working state of the equipment of the unmanned aerial vehicle is monitored in real time for early warning, and the equipment is judged to be in a fault state when the index is abnormal;
step 2, homing judgment: judging homing capacity based on the elevation map, and if the homing capacity is provided, taking a waiting area which is automatically generated near the original landing point as a target point area for homing; if the area is not available, selecting a region with a relatively flat periphery around the area as a target point region based on the elevation map to return;
step 3, returning to land: after reaching the target point area, judging the height of the landing window in real time, and if the landing height is not met, hovering to be high and waiting; if yes, accessing automatic landing control to carry out emergency landing.
2. The method for emergency landing of unmanned aerial vehicle according to claim 1, wherein in step 2, the lower slide track is calculated by the unpowered downslide parameter of the unmanned aerial vehicle, the homing capacity determination is performed by comparing with an elevation map,
the unpowered downslide parameter calculation method comprises the following steps:
wherein Δs is the horizontal distance from the original drop point in unit time, and Δz is the vertical distance from the original drop point in unit time.
3. The unmanned aerial vehicle emergency landing method of claim 1, wherein in the step 2, the transverse control law is track tracking control and the longitudinal control law is constant-speed sliding control in the course of the return voyage.
4. The unmanned aerial vehicle emergency landing method of claim 3, wherein the track following control law is:
wherein delta a For aileron control, p is roll angle speed,for the track angle>Given the track angle, +.>Is the proportional control coefficient of the rolling angle speed, +.>For track deviation proportional control coefficient, +.>Is the rolling deviation proportion control coefficient, phi is the rolling angle, phi g For a roll angle set, +.>And delta Y is the lateral offset distance, which is a lateral offset distance proportional control coefficient.
5. The unmanned aerial vehicle emergency landing method of claim 3, wherein the constant speed glide control law is:
wherein delta e For elevator control, q is pitch angle rate, θ is pitch angle, θ g For a given pitch angle, V is the indicated airspeed, V g For a given space velocity,is a pitch angle speed proportional control coefficient +.>Is pitch angle proportional control coefficient +>For the airspeed deviation proportional control coefficient, +.>The control coefficient is integrated for airspeed offset.
6. The method for emergency landing of unmanned aerial vehicle according to claim 1, wherein in step 2, a region with a relatively flat surrounding is selected as the target point region by combining an altitude map with an unpowered downslide parameter,
the method comprises the following steps:
a-h are eight elevation map units,and->The unpowered downslide parameters in the horizontal and vertical directions from central cell i, x and y are the dimensions of the cell, respectively.
7. The method for emergency landing of unmanned aerial vehicle according to claim 1, wherein in step 3, after reaching the target point area, the specific way for determining the height of the landing window in real time is as follows:
wherein H is U Obtaining unmanned aerial vehicle through airborne sensorThe obtained unmanned plane is high, H g Is the landing window height;
the calculation mode of the height of the landing window is as follows:
s is the horizontal distance of the selected target area according to the landing point, and the reference value of the unpowered downslide parameter is the average value of the unpowered downslide parameters of the unmanned aerial vehicle.
8. The unmanned aerial vehicle emergency landing method of claim 1, wherein in step 3, the lateral control law used for the automatic landing control is track following control, and the longitudinal control law used is landing glide airspeed control.
9. The unmanned aerial vehicle emergency landing method of claim 8, wherein the landing glide airspeed control law is:
wherein V is the indicated airspeed, V g For a given airspeed, V c To control the speed setting, H is the sinking rate, H g For a given sinking rate,is a height deviation proportional control coefficient, +.>The control coefficient is integrated for the height deviation.
10. An unmanned aerial vehicle emergency landing system based on an elevation map, the unmanned aerial vehicle emergency landing system operating based on the unmanned aerial vehicle emergency landing method according to any one of claims 1 to 9, the unmanned aerial vehicle emergency landing system comprising:
the dangerous case monitoring unit is used for monitoring the working state of the unmanned aerial vehicle in real time to perform early warning, and judging that the unmanned aerial vehicle is in a fault state when the index is abnormal;
a homing determination unit for determining homing ability, and if so, homing is performed by taking a waiting area autonomously generated near the original landing point as a target point area; if not, selecting a region with a relatively flat periphery nearby as a target point region for returning;
the return landing unit is used for judging the height of the landing window in real time after reaching the target point area, and if the landing height is not met, the aircraft spirals down and waits for the landing; if yes, accessing automatic landing control to carry out emergency landing.
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