CN112484721A - Underwater mobile platform navigation method and underwater mobile platform navigation device - Google Patents
Underwater mobile platform navigation method and underwater mobile platform navigation device Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
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Abstract
The application provides a navigation method for an underwater mobile platform. The underwater mobile platform navigation method comprises the following steps: acquiring first navigation information generated by a strapdown inertial navigation system; acquiring second navigation information generated by the Doppler velocity sonar system; acquiring corrected navigation information generated by a Beidou satellite navigation system or a magnetic compass system; generating first fusion navigation information according to the first navigation information and the second navigation information; generating second fusion navigation information according to the first fusion navigation information and the corrected navigation information; generating navigation control information according to the second fusion navigation information; and controlling the underwater mobile platform to move according to the navigation control information. The underwater mobile platform navigation method corrects errors accumulated by the SINS along with time by adopting a high-precision navigation technology and simultaneously ensures the autonomy and the concealment of the AUV.
Description
Technical Field
The application belongs to the technical field of underwater wireless platforms, and particularly relates to an underwater mobile platform navigation method and an underwater mobile platform navigation device.
Background
The accuracy of the underwater navigation technology of the Autonomous Underwater Vehicle (AUV) is a powerful guarantee for carrying out tasks such as searching, detecting and anti-diving under water. Most of the existing AUV navigation methods mainly use a Strapdown Inertial Navigation System (SINS).
The current position of the strapdown inertial navigation system is calculated on the basis of the position of the previous moment, errors are accumulated along with the increase of iteration times, and the positioning accuracy of the strapdown inertial navigation system is greatly reduced by the factors of the errors and the inherent errors in the processes of equipment installation, measurement and the like.
Accordingly, a technical solution is desired to overcome or at least alleviate at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The present application is directed to an underwater mobile platform navigation method to solve at least one of the above problems.
In a first aspect of the present application, an underwater mobile platform navigation method includes:
acquiring first navigation information generated by a strapdown inertial navigation system;
acquiring second navigation information generated by the Doppler velocity sonar system;
acquiring corrected navigation information generated by a Beidou satellite navigation system or a magnetic compass system;
generating first fusion navigation information according to the first navigation information and the second navigation information;
generating second fused navigation information according to the first fused navigation information and the corrected navigation information;
generating navigation control information according to the second fusion navigation information;
and controlling the underwater mobile platform to move according to the navigation control information.
Optionally, the acquiring the first position information generated by the strapdown inertial navigation system includes:
acquiring acceleration information of an underwater mobile platform;
acquiring triaxial acceleration information of an underwater mobile platform;
and generating the first position information according to the acceleration information and the triaxial acceleration information.
Optionally, the acquiring the second navigation information generated by the doppler velocity sonar system includes:
acquiring speed information acquired by a Doppler log;
and generating second navigation information according to the speed information.
Optionally, the acquiring of the modified navigation information generated by the beidou satellite navigation system or the magnetic compass system includes:
judging whether a satellite navigation signal exists or not, and if so, generating the corrected navigation information through the Beidou satellite navigation system;
and if not, generating the corrected navigation information through the magnetic compass system.
Optionally, the generating the modified navigation information by the beidou satellite navigation system includes:
sending position request information to a Beidou satellite;
acquiring position information sent by a Beidou satellite;
and generating the corrected navigation information according to the position information.
Optionally, the generating the modified navigation information by the magnetic compass system comprises:
acquiring an initial matching position;
judging whether the initial matching position is larger than a preset error value, if so,
processing by adopting a T algorithm to generate position deviation information;
generating matching position information according to the position deviation information;
and generating corrected navigation information according to the deviation information and the position matching information.
Optionally, the generating the modified navigation information by the magnetic compass system further comprises:
judging whether the initial matching position is larger than a preset error value, if not,
the modified navigation information is generated using the S algorithm.
The present application further provides an electronic device comprising a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the underwater mobile platform navigation method as described above when executing the computer program.
The present application also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, is capable of implementing an underwater mobile platform navigation method as described above.
The application has at least the following beneficial technical effects:
the underwater mobile platform navigation method mainly comprises the steps of carrying out error correction on an auxiliary navigation technology by taking a Strapdown Inertial Navigation System (SINS) as a main part and using a Doppler velocity sonar (DVL), a Beidou satellite navigation system (BDS) and a magnetic compass navigation (MCP) through a combined navigation technology, and aims to correct errors accumulated by the SINS along with time by adopting a high-precision navigation technology and ensure the autonomy and the concealment of an AUV (autonomous underwater vehicle).
Drawings
Fig. 1 is a schematic flow chart of a method for navigating an underwater mobile platform according to an embodiment of the present application.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are a subset of the embodiments in the present application and not all embodiments in the present application. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
It should be noted that the terms "first" and "second" in the description of the present invention are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The underwater mobile platform navigation method shown in fig. 1 comprises the following steps:
step 1: acquiring first navigation information generated by a strapdown inertial navigation system;
step 2: acquiring second navigation information generated by the Doppler velocity sonar system;
and step 3: acquiring corrected navigation information generated by a Beidou satellite navigation system or a magnetic compass system;
and 4, step 4: generating first fusion navigation information according to the first navigation information and the second navigation information;
and 5: generating second fusion navigation information according to the first fusion navigation information and the corrected navigation information;
step 6: generating navigation control information according to the second fusion navigation information;
and 7: and controlling the underwater mobile platform to move according to the navigation control information.
Compared with the prior art, the underwater mobile platform navigation method has the following advantages:
1. in order to improve the overall performance of the navigation system, the system needs to combine various navigation systems for use, has complementary advantages, overcomes the defect that one navigation device works independently, and adopts a Kalman filtering algorithm to combine the navigation systems to form a combined navigation system.
2. After the navigation depth and speed of the AUV are stable, the BDS signal receiving antenna floats to the water surface to receive BDS signals, active calibration is carried out on the SINS, and the BDS signal receiving antenna is recovered after the calibration is finished. The mode ensures the concealment of the AUV in the navigation process and reduces the energy consumption in the ascending process of the AUV.
3. In the process of correcting SINS navigation deviation by using geomagnetic navigation, a combined mode of T + S + Kalman is adopted, respective advantages of a T algorithm and an S algorithm are fully utilized, and the advantages of the T algorithm and the S algorithm are made good use of, so that the characteristic that a T system can still work well when the initial matching error is large is utilized, the reliability of the S algorithm is increased, the limitation that the S algorithm causes mismatching when the initial error is large is relaxed, the characteristic that the S algorithm has high precision when the initial error is not large is utilized, the optimal matching position is obtained, the optimal estimated position is obtained through a Kalman filter, and the optimal estimated position is output to an inertial navigation system to compensate the accumulation of the error.
In this embodiment, the obtaining the first position information generated by the strapdown inertial navigation system includes:
acquiring triaxial acceleration information of an underwater mobile platform, wherein the triaxial acceleration information comprises acceleration information of an x axis, a y axis and a z axis of a motion coordinate system of the underwater mobile platform;
and generating first position information according to the triaxial acceleration information.
In this embodiment, the acquiring of the second navigation information generated by the doppler velocity sonar system includes:
acquiring speed information acquired by a Doppler log;
and generating second navigation information according to the speed information.
In this embodiment, acquiring the modified navigation information generated by the beidou satellite navigation system or the magnetic compass system includes:
judging whether a satellite navigation signal exists or not, and if so, generating the corrected navigation information through a Beidou satellite navigation system;
and if not, generating the corrected navigation information through a magnetic compass system.
In this embodiment, generating the modified navigation information through the beidou satellite navigation system includes:
sending position request information to a Beidou satellite;
acquiring position information sent by a Beidou satellite;
and generating the corrected navigation information according to the position information.
In this embodiment, the generating of the modified navigation information by the magnetic compass system includes:
acquiring an initial matching position;
judging whether the initial matching position is larger than a preset error value, if so,
processing by adopting a T algorithm to generate position deviation information;
generating matching position information according to the position deviation information;
and generating corrected navigation information according to the deviation information and the position matching information.
In this embodiment, the generating of the modified navigation information by the magnetic compass system further includes:
judging whether the initial matching position is larger than a preset error value, if not,
the modified navigation information is generated using the S algorithm.
The application also provides an underwater mobile platform navigation device, which comprises a first navigation information acquisition module, a second navigation information acquisition module, a corrected navigation information acquisition module, a first fusion navigation information generation module, a second fusion navigation information generation module, a navigation control information generation module and a power system, wherein,
the first navigation information acquisition module is used for acquiring first navigation information generated by the strapdown inertial navigation system;
the second navigation information acquisition module is used for acquiring second navigation information generated by the Doppler velocity sonar system;
the corrected navigation information acquisition module is used for acquiring corrected navigation information generated by a Beidou satellite navigation system or a magnetic compass system;
the first fusion navigation information generation module is used for generating first fusion navigation information according to the first navigation information and the second navigation information;
the second fusion navigation information generation module is used for generating second fusion navigation information according to the first fusion navigation information and the correction navigation information;
the navigation control information generating module is used for generating navigation control information according to the second fusion navigation information;
and the power system is used for controlling the underwater mobile platform to move according to the navigation control information.
It should be noted that the foregoing explanations of the method embodiments also apply to the apparatus of this embodiment, and are not repeated herein.
In this embodiment, the strapdown inertial navigation system is an autonomous dead reckoning navigation system in which inertial measurement units (a gyroscope and an accelerometer) are directly mounted on a main body, and the attitude, the azimuth, the velocity, and the position of a vehicle are determined using the reference direction of the inertial measurement unit and initial position information. The laser inertial measurement unit establishes a coordinate conversion matrix from a gyro sensitive carrier coordinate system to a navigation coordinate system through a quaternion integral algorithm by using the angular velocity in the direction of the gyro sensitive carrier coordinate system and the specific force in the direction of the accelerometer sensitive carrier coordinate system, and converts specific force increment to the navigation coordinate system, thereby establishing a mathematical platform. And integrating the specific force increment to obtain speed and position parameters, and calculating the course and attitude parameters of the carrier to complete the calculation of pure inertial navigation. And receiving data of the Doppler log by serial communication, finishing a Kalman filtering algorithm to obtain corrected speed, position, course and attitude parameters, and then sending the parameters to a central control unit through a serial communication port.
An underwater Doppler log generally adopts a four-wave speed system with a fixed wave speed direction. Namely, the direction of the transmitted sound wave speed is fixed relative to the angle position of the instrument coordinate system of the Doppler velocimeter, when the Doppler velocimeter is installed on an AUV, the instrument coordinate system of the Doppler velocimeter is parallel to all axes of an AUV carrier coordinate system, and the direction of the Doppler velocimeter is kept consistent, and the speed reflected in the instrument coordinate system of the Doppler velocimeter is also the speed of the AUV carrier coordinate system. The Doppler log is mainly used for correcting the speed error of the laser inertial measurement unit. The speed measurement error of the acoustic wave log is converted into a flight distance error through one-time integration, some random quantities in the speed measurement error can be offset through long-time integration, and some drift quantities are finally reflected as the flight distance error. According to the error characteristic of the current Doppler log, when the speed measurement error is not more than 0.5%, the integrated navigation precision can be ensured.
When a magnetic compass system is adopted for navigation, the algorithm matching implementation scheme is as follows: t-computing (as an external environment) is introduced. The T algorithm has the characteristics that the positioning accuracy is not influenced by a detection blind area, but under an ideal condition, the positioning accuracy is not high compared with that of the S algorithm. Therefore, T algorithm is used for pre-matching, and initial matching error is reduced, so that the problem that S algorithm is easy to diverge when the initial matching error is large is solved.
Specifically, when the AUV starts to perform auxiliary navigation, if the initial matching position error delta X _ SINS > psix _ SINS of the inertial navigation system, a large-range search is performed by using a T algorithm, and a track which is closer to a real track is found to reduce the position deviation of the inertial navigation system; on the basis, further matching is carried out by utilizing an S algorithm, so that the optimal matching position can be obtained; and taking the difference between the two positions as the observed quantity of a Kalman filter to obtain the optimal estimation, thereby correcting the navigation error of the inertial navigation system. The Ψ XSINS is a preset threshold, and needs to be set manually according to the technical requirements of actual navigation and the accuracy of a digital map. If the initial matching error is not large (within the S algorithm precision tolerance range), the large-range search of the T method is omitted, the S algorithm is directly used for matching, and then the optimal estimation is carried out through a Kalman filter. Then, whether the blind area is reached is judged according to the indicated position of the inertial navigation system, the geomagnetic map, the preset path and the precision of the depth measuring sensor. If the blind area is not reached, continuously correcting the error of the inertial navigation system by using the S algorithm to carry out auxiliary navigation; otherwise, after the AUV exits the detection blind area, the position indicated by the inertial navigation system finally is continuously used for judging whether the initial matching position error delta XSINS is larger than the preset threshold psi XSINS, and then the steps are repeated.
The application also provides an electronic device, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to realize the underwater wireless information communication method.
For example, an electronic device includes an input device, an input interface, a central processing unit, a memory, an output interface, and an output device. The input interface, the central processing unit, the memory and the output interface are mutually connected through a bus, and the input equipment and the output equipment are respectively connected with the bus through the input interface and the output interface and further connected with other components of the computing equipment. Specifically, the input device receives input information from the outside and transmits the input information to the central processing unit through the input interface; the central processing unit processes the input information based on the computer executable instructions stored in the memory to generate output information, temporarily or permanently stores the output information in the memory, and then transmits the output information to the output device through the output interface; the output device outputs the output information to an exterior of the computing device for use by a user.
The present application also provides a computer-readable storage medium storing a computer program which, when executed by a processor, is capable of implementing the above underwater wireless information communication method.
Although the present application has been described with reference to the preferred embodiments, it is not intended to limit the present application, and those skilled in the art can make variations and modifications without departing from the spirit and scope of the present application.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.
Computer-readable media include both non-transitory and non-transitory, removable and non-removable media that implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Furthermore, it will be obvious that the term "comprising" does not exclude other elements or steps. A plurality of units, modules or devices recited in the device claims may also be implemented by one unit or overall device by software or hardware. The terms first, second, etc. are used to identify names, but not any particular order.
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks identified in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The Processor in this embodiment may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, a discrete Gate or transistor logic device, a discrete hardware component, and so on. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may be used to store computer programs and/or modules, and the processor may implement various functions of the apparatus/terminal device by running or executing the computer programs and/or modules stored in the memory, as well as by invoking data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.
In this embodiment, the module/unit integrated with the apparatus/terminal device may be stored in a computer-readable storage medium if it is implemented in the form of a software functional unit and sold or used as a separate product. Based on such understanding, all or part of the flow in the method according to the embodiments of the present invention may also be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and when the computer program is executed by a processor, the computer program may implement the steps of the embodiments of the method. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying computer program code, recording medium, U.S. disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution media, and the like. It should be noted that the computer readable medium may contain content that is appropriately increased or decreased as required by legislation and patent practice in the jurisdiction.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. An underwater mobile platform navigation method, characterized by comprising:
acquiring first navigation information generated by a strapdown inertial navigation system;
acquiring second navigation information generated by the Doppler velocity sonar system;
acquiring corrected navigation information generated by a Beidou satellite navigation system or a magnetic compass system;
generating first fusion navigation information according to the first navigation information and the second navigation information;
generating second fused navigation information according to the first fused navigation information and the corrected navigation information;
generating navigation control information according to the second fusion navigation information;
and controlling the underwater mobile platform to move according to the navigation control information.
2. The underwater mobile platform navigation method of claim 1, wherein the obtaining the first location information generated by the strapdown inertial navigation system comprises:
acquiring triaxial acceleration information of an underwater mobile platform;
and generating the first position information according to the triaxial acceleration information.
3. The underwater mobile platform navigation method of claim 1, wherein the acquiring second navigation information generated by a doppler velocity sonar system comprises:
acquiring speed information acquired by a Doppler log;
and generating second navigation information according to the speed information.
4. The underwater mobile platform navigation method of claim 1, wherein the obtaining of the modified navigation information generated by a Beidou satellite navigation system or a magnetic compass system comprises:
judging whether a satellite navigation signal exists or not, and if so, generating the corrected navigation information through the Beidou satellite navigation system;
and if not, generating the corrected navigation information through the magnetic compass system.
5. The underwater mobile platform navigation method of claim 4, wherein the generating the revised navigation information by the Beidou satellite navigation system comprises:
sending position request information to a Beidou satellite;
acquiring position information sent by a Beidou satellite;
and generating the corrected navigation information according to the position information.
6. The underwater mobile platform navigation method of claim 4, wherein the generating the modified navigation information by the magnetic compass system comprises:
acquiring an initial matching position;
judging whether the initial matching position is larger than a preset error value, if so,
processing by adopting a T algorithm to generate position deviation information;
generating matching position information according to the position deviation information;
and generating corrected navigation information according to the deviation information and the position matching information.
7. The underwater mobile platform navigation method of claim 6, wherein the generating the modified navigation information by the magnetic compass system further comprises:
judging whether the initial matching position is larger than a preset error value, if not,
the modified navigation information is generated using the S algorithm.
8. An underwater mobile platform navigation device, comprising:
the first navigation information acquisition module is used for acquiring first navigation information generated by the strapdown inertial navigation system;
the second navigation information acquisition module is used for acquiring second navigation information generated by the Doppler velocity sonar system;
the system comprises a corrected navigation information acquisition module, a correction navigation information processing module and a correction navigation information processing module, wherein the corrected navigation information acquisition module is used for acquiring corrected navigation information generated by a Beidou satellite navigation system or a magnetic compass system;
the first fused navigation information generation module is used for generating first fused navigation information according to the first navigation information and the second navigation information;
the second fused navigation information generation module is used for generating second fused navigation information according to the first fused navigation information and the corrected navigation information;
the navigation control information generation module is used for generating navigation control information according to the second fusion navigation information;
and the power system is used for controlling the underwater mobile platform to move according to the navigation control information.
9. An electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor when executing the computer program implements the underwater mobile platform navigation method of any one of claims 1 to 7.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, is capable of carrying out the underwater mobile platform navigation method according to any one of claims 1 to 7.
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