An on-orbit heterogeneous management system and method for motion parameters of a space manipulator

Abstract

An on-orbit heterogeneous management system and method for space manipulator motion parameters, comprising a master-slave joint controller and a joint controller FPGA in a cold backup relationship and a manipulator central controller; the manipulator central controller communicates with a spacecraft central processing unit via an external bus to save a copy of motion parameters; the motion parameters are parameters required for joint control motor calculation; the master-slave joint controller communicates with the manipulator central controller via a manipulator control bus; the master-slave joint controller and the master-slave joint controller FPGA are respectively used to store a copy of motion parameters; the master or backup joint controller loads the motion parameters from the corresponding joint controller memory into the corresponding FPGA for calculation; the joint controller FPGA performs parameter calculation and motor control.

Description

Technical Field

[0001] The present invention is applicable to the professional field of spacecraft software design technology and is used for software design of space manipulator control systems, and can effectively improve the efficiency and reliability of motion parameter management. Background Art

[0002] my country's space station manipulator control system consists of a central controller and several joint controllers. The whole arm motion control is ultimately achieved by controlling the motion of each joint motor through the joint controller. The space manipulator has a large number of complex motion modes, and the corresponding joint motion modes are also very complex. The joint controller needs to use a large number of motion parameters during the control process, which play a key role in precise motion control and whole arm safety protection. Parameter management requirements in the strong radiation environment of space are very high. It is necessary to overcome the problem of parameter errors or even loss caused by single particle effects in space, equipment failures, etc., and at the same time meet the requirements of ground operation management for usability and ease of use.

[0003] The literature related to the management of space manipulator motion parameters includes "Precise Calibration of Kinematic Parameters of Large-Span Space Manipulator" (Zhou Weigang et al., Manned Spaceflight, August 2016). This literature proposes a method for accurately calibrating the kinematic parameters of the manipulator, but this method is limited to calculations on the ground, and the parameters are pre-bound on the manipulator, which cannot meet the requirements of on-orbit management and updating. Summary of the invention

[0004] The technical problem solved by the present invention is to solve the problem of on-orbit management of complex space robot arm motion parameters. The present invention proposes a space on-orbit heterogeneous motion parameter management method based on a lightweight file system.

[0005] The technical solution of the present invention is: an on-orbit heterogeneous management system for motion parameters of a space manipulator, including a main backup joint controller and a joint controller FPGA in a cold backup relationship and a manipulator central controller;

[0006] The manipulator central controller communicates with the spacecraft central processing unit via an external bus to save a copy of motion parameters; the motion parameters are parameters required for calculating the joint control motor;

[0007] The master and backup joint controllers communicate with the central controller via the robot arm control bus; the master and backup joint controllers and the master joint controller FPGA are respectively used to store a copy of motion parameters, which are used for master and backup control respectively; the master or backup joint controller loads the motion parameters from the corresponding joint controller memory into the corresponding FPGA for calculation; the joint controller FPGA performs parameter calculation and motor control.

[0008] Preferably, the robot central controller and the primary and backup joint controllers use the ROMFS file system to store motion parameters. Several groups of motion parameters constitute a file. The parameter type is a floating point number. A group of motion parameters are external input parameters required for the joint FPGA to run the joint motion control algorithm. Each group of parameters includes the parameter name, parameter value, storage address of the parameter in the FPGA, parameter type and number of decimal places, and is stored in a table.

[0009] Preferably, three copies of each set of motion parameters are saved for two-out-of-three processing.

[0010] Preferably, the primary or backup joint controller loads the motion parameters from the corresponding joint controller memory into the corresponding FPGA for calculation, including:

[0011] S1, the joint controller inquires the value of each set of motion parameters by sending the parameter name to the central controller;

[0012] S2, the central controller finds the corresponding file from its memory according to the received parameter name, reads the parameter name, parameter value, storage address, type and decimal places of the parameter in FPGA from the file, and sends the checksum to the joint controller through the bus;

[0013] S3. After confirming that the checksum is correct, the joint controller writes the read content into its corresponding parameter name file to complete the recovery of the data content; otherwise, no writing is performed;

[0014] S4, the joint controller reads the parameter value from the written parameter name file and determines whether the parameter is a valid parameter. If it is a valid parameter, the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address; if it is invalid, the default value of the parameter is read, and the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address;

[0015] S5. The corresponding joint controller FPGA obtains the corresponding parameter value from the storage address for corresponding control signal calculation.

[0016] Preferably, the joint controller reloads the parameters according to the process in S4 at a preset time interval to avoid parameter errors caused by single particle time.

[0017] Preferably, in the operation of converting a floating point number to an integer, it is assumed that the floating point data is a and is required to be converted into a 16-bit signed fixed point. If there is 1 sign bit, m1 integer bits, and m2 decimal bits in the 16 bits, the conversion formula is as follows:

[0018]

[0019] A method for on-orbit heterogeneous management of motion parameters of a space manipulator implemented by the system, wherein each time a joint controller is started, the joint motion parameters are loaded into a corresponding FPGA, specifically comprising:

[0020] S1, the joint controller inquires the value of each set of motion parameters by sending the parameter name to the central controller;

[0021] S2, the central controller finds the corresponding file from its memory according to the received parameter name, reads the parameter name, parameter value, storage address, type and decimal places of the parameter in FPGA from the file, and sends the checksum to the joint controller through the bus;

[0022] S3. After confirming that the checksum is correct, the joint controller writes the read content into its corresponding parameter name file to complete the recovery of the data content; otherwise, no writing is performed;

[0023] S4, the joint controller reads the parameter value from the written parameter name file and determines whether the parameter is a valid parameter. If it is a valid parameter, the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address; if it is invalid, the default value of the parameter is read, and the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address;

[0024] S5. The corresponding joint controller FPGA obtains the corresponding parameter value from the storage address for corresponding control signal calculation.

[0025] Preferably, the updating of the motion parameters of the space robot arm includes an external update initiated by the ground operation and control center and an internal update caused by autonomous changes in the parameters on the FPGA.

[0026] Preferably, the external update process includes:

[0027] The joint controller receives the remote control command with motion parameters sent from the ground and forwarded by the central controller, and updates the motion parameters in the local memory after parsing;

[0028] The joint controller detects changes in local parameters, reads the set of motion parameters stored in its own memory, calculates the checksum, and sends it to the central controller;

[0029] The central controller checks whether the checksum is correct. If it is correct, the motion parameters are written into its own memory, otherwise, they are not written;

[0030] The joint controller reads the FPGA address and decimal value corresponding to the parameter value from the local memory, converts the floating point number into an integer, and then loads it into the FPGA to complete the motion parameter update.

[0031] Preferably, the internal update process includes:

[0032] The joint controller periodically reads the motion parameters stored on the FPGA. When a set of parameters changes, the joint controller performs the inverse operation of converting floating-point numbers to integers to calculate the floating-point values ​​of the parameters.

[0033] The joint controller finds the storage path of the parameter in the joint controller memory according to the FPGA address and updates the corresponding value;

[0034] When the joint controller detects that the local parameters have changed, it reads the motion parameters saved in its own memory, calculates the checksum, and sends it to the central controller;

[0035] The central controller checks whether the checksum is correct. If it is correct, the motion parameters are written into its own memory, otherwise they are not written.

[0036] The beneficial effects of the present invention compared with the prior art are:

[0037] The present invention proposes a method for managing heterogeneous motion parameters in space on-orbit based on a lightweight file system. While ensuring data security and correctness, it improves the usability of ground management and has been applied to the space station robotic arm.

[0038] The present invention utilizes a central controller memory, a joint controller memory, and a joint controller FPGA to implement a three-level and dual-redundant storage system, which effectively ensures the safety and correct use of the robot arm's motion parameters, and plays an important role in improving the reliability and safety of the robot arm.

[0039] The motion parameter storage system proposed in the present invention has a three-level and dual-redundant structure, which can ensure the correctness of the motion parameters in the event of a failure in any device, effectively ensure the consistency of the motion parameters in the system, and ensure that the motion parameters can be correctly restored after the device is restarted.

[0040] The present invention is based on a lightweight ROMFS file system design, which can effectively improve the efficiency of parameter access and modification and facilitate the use of operators compared to storage systems that do not use a file system.

[0041] The storage format designed by the present invention is suitable for a robot control system using a CPU and FPGA heterogeneous processing architecture BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a system architecture diagram of the present invention;

[0043] Figure 2 A schematic diagram of the design of the motion parameter file storage format of the present invention; DETAILED DESCRIPTION

[0044] The present invention will be further described below in conjunction with the embodiments.

[0045] The motion parameters in the present invention refer to the parameters required for calculation of the joint control motor, such as current loop, position loop, speed loop parameters, etc. These parameters need to be used continuously during the motor movement, and some parameters need to be updated in real time during use to achieve optimized control of the robot arm movement.

[0046] The spatial manipulator motion parameter management system includes a central controller memory, a master joint controller memory, a master joint controller FPGA, a backup joint controller memory, and a backup joint controller FPGA. See the attached diagram for its architecture. Figure 1 The joint controller of the present invention adopts EEPROM memory. Among them, the central controller communicates with the outside and is responsible for overall control, and a copy of motion parameters is stored in its memory. The main joint controller and the backup joint controller are in a cold backup relationship. A copy of motion parameters is stored in the main joint controller memory and FPGA respectively, which are used for main control. The joint controller loads the parameters from the memory into the FPGA for calculation. Similarly, a copy of motion parameters is stored in the backup joint controller memory respectively, which is used for backup control. FPGA is the device that ultimately performs parameter calculation and motor control. Figure 1 Among them, 1 is the central controller memory, which can communicate with the main and backup joint controller memories, and save motion parameters through the file system. 2 is the main joint controller memory, which cannot be powered on at the same time as 3 and 5, and can communicate with the central controller and the main joint controller FPGA, and save motion parameters through the file system. 3 is the backup joint controller memory, which cannot be powered on at the same time as 2 and 4, and can communicate with the central controller and the backup joint controller FPGA, and save motion parameters through the file system. 4 is the main joint controller FPGA, which cannot be powered on at the same time as 3 and 5, and can communicate with the main joint controller memory, save motion parameters through hardware registers, and actually perform motion control calculations. 5 is the backup joint controller FPGA, which cannot be powered on at the same time as 2 and 4, and can communicate with the backup joint controller memory, save motion parameters through hardware registers, and actually perform motion control calculations.

[0047] The central controller and joint controller use a lightweight ROMFS file system to store motion parameters, and several groups of parameters constitute a file. The parameter format is a floating point number. A group of motion parameters is the external input parameters required by the joint FPGA to run the joint motion control algorithm. When using the three-loop (i.e., position loop, speed loop, current loop) PID (proportional, differential, integral) control algorithm, the motion parameters at least include the position loop coefficient P, position loop coefficient D, position loop output anti-saturation value, speed loop coefficient P, speed loop system I, speed loop coefficient D, speed loop integral anti-saturation value, speed loop output anti-saturation value, speed loop input limit, current loop coefficient P, current loop coefficient I, current loop anti-saturation integral value, current loop output anti-saturation value. Each group of parameters includes parameter name, parameter value, storage address of the parameter in FPGA, parameter type and number of decimal places, and is stored in a table.

[0048] FPGA needs to use integers when calculating, so the joint controller needs to convert floating-point numbers into integer parameters. The principle of conversion should be to meet the data range and accuracy requirements, and to minimize the number of bits of integer floating-point numbers. The method of data conversion is: assuming that the floating-point data is a and needs to be converted to a 16-bit signed fixed point, the decimal places of the data must be known first. If there is 1 sign bit, m1 integer bits, and m2 decimal places in the 16 bits, then the forced conversion is

[0049]

[0050] The structure of each file in the memory of the central controller and joint controller is shown in the attached Figure 2 Each file includes several groups of parameters. Each group of parameters saves three sets of parameters for three-out-of-two processing. Each set of parameters is as follows Figure 2 The information shown includes parameter name, parameter value, storage address of the parameter in FPGA, parameter type and number of decimal places.

[0051] Each time the joint controller is started, the motion parameters are loaded into the FPGA and provided for motion calculation. The process is briefly described as follows: ① The joint controller asks the central controller for the value of the motion parameter. The central controller reads the motion parameters saved in itself and calculates the checksum, which is then sent to the joint controller. ② The joint controller checks whether the checksum is correct. If it is correct, the motion parameters are written into its own file system, overwriting the original parameters. Otherwise, no writing is performed. ③ The joint controller reads the parameter value in the memory and determines whether the parameter is a valid parameter. If it is a valid parameter, the FPGA address and decimal place value corresponding to the parameter value are read, converted according to formula (1), and loaded into the FPGA. If it is invalid, the default value of the parameter is read and loaded into the FPGA in the same way, and the FPGA performs motion calculation. ④ The joint controller periodically refreshes the parameter value in the memory to the register of the FPGA.

[0052] There are two ways to update the parameters on the robot arm: one is the external update initiated by the ground operation and management center, and the other is the internal update caused by the autonomous change of the parameters on the FPGA. The external update process is briefly described as follows: ① The joint controller receives the remote control command with motion parameters sent by the ground and forwarded by the central controller, and updates the local motion parameters after parsing; ② The joint controller detects that the local parameters have changed, reads the motion parameters saved in itself, calculates the checksum, and sends it to the central controller; ③ The central controller checks whether the checksum is correct. If it is correct, it writes the motion parameters to its own file system, otherwise it does not write; ④ The joint controller reads the FPGA address and decimal value corresponding to the parameter value, converts it according to formula (1), and loads it to the FPGA to complete the motion parameter update.

[0053] The internal update process caused by the autonomous change of parameters on the FPGA is briefly described as follows: ① The joint controller periodically reads the motion parameters stored in the FPGA register. When the parameters change, the joint controller solves the floating-point value of the parameters according to the inverse operation of formula (1); ② The joint controller finds the storage path of the parameter in the file system according to the FPGA address and updates the corresponding value; ③ The joint controller detects that the local parameters have changed, reads the motion parameters saved in itself, calculates the checksum, and sends it to the central controller; ④ The central controller checks whether the checksum is correct. If it is correct, the motion parameters are written to its own file system, otherwise they are not written.

[0054] Example

[0055] The specific implementation of the present invention is described by taking the quadrature-axis current loop parameters of a robot arm as an example.

[0056] There are 4 parameters of the cross-axis current loop of the robot arm. The storage path in the ROMFS file system is / current loop parameters / cross-axis current loop.bin. The stored file content is:

[0057] Parameter name FPGA Address data Parameter Type Decimal Places Quadrature axis current loop parameter P 0x20104090 1.7 8 10 Cross-axis current loop parameters I 0x201040A0 0.13 8 10 Anti-saturation integral value of quadrature axis current loop 0x201041D0 28 8 10 Cross-axis current loop output anti-saturation value 0x201041E0 28 8 10

[0058] System startup process

[0059] After the joint controller is powered on, the process of using the quadrature-axis current loop parameters is as follows:

[0060] Step 1: The joint controller asks the central controller for the values ​​of four parameters including the quadrature axis current loop parameter P;

[0061] Step 2: The central controller finds the file " / current loop parameter / cross-axis current loop.bin" through the received parameter name, reads the parameter name, FPGA address, data value, type and decimal places in the table above, and sends the checksum to the joint controller through the bus.

[0062] Step 3: After confirming that the checksum is correct, the joint controller writes the contents in the above table into its own file " / current loop parameters / quadrature axis current loop.bin" to complete the recovery of the data content;

[0063] Step 4: The joint controller reads " / current loop parameters / quadrature current loop.bin". The parameter type of the quadrature current loop parameter P is 8, which represents a floating point type. The value is 1.7 and the number of decimal places is 10. According to formula (1), the integer corresponding to the quadrature current loop parameter P is 1740. The joint controller loads 1740 to the FPGA address 0x20104090. Similarly, the other three parameter values ​​are loaded into the FPGA.

[0064] Step 5: FPGA obtains the value of the quadrature axis current loop parameter P from 0x20104090 as 1740, which is used in the calculation of the quadrature axis current loop control signal. The other three parameters are obtained in the same way.

[0065] Step 6: The joint controller reloads the four parameters every 500ms according to the method in step 4 to avoid parameter errors caused by single particle events.

[0066] (1) Parameter external update process

[0067] During the use of the joint controller, the ground decision changes the data of the cross-axis current loop parameter P to 0.6, and the parameter update process is as follows.

[0068] Step 1: The ground sends a remote control command, which is to change the data of the quadrature axis current loop parameter P to 0.6;

[0069] Step 2: The joint controller receives the remote control command, finds its own file " / current loop parameter / cross-axis current loop.bin" according to the parameter name, and changes the data value of the cross-axis current loop parameter P in the file to 0.6;

[0070] Step 3: The joint controller detects that the local parameters have changed, reads the parameter name, FPGA address, data value, type and decimal places of the quadrature-axis current loop parameter P, and sends the checksum to the central controller through the bus;

[0071] Step 4: The central controller confirms that the checksum is correct and writes the parameter name, FPGA address, data value, type and number of decimal places of the cross-axis current loop parameter P into its own file " / current loop parameter / cross-axis current loop.bin".

[0072] Step 5: The joint controller reads " / current loop parameters / cross-axis current loop.bin". The parameter type of the cross-axis current loop parameter P is 8, which represents a floating point type. The value is 0.6 and the number of decimal places is 10. According to formula (1), the integer corresponding to the cross-axis current loop parameter P is 614. The joint controller loads 614 to the FPGA address 0x20104090.

[0073] Step 6: FPGA obtains the value of the quadrature-axis current loop parameter P from 0x20104090 as 614, which is used in the calculation of the quadrature-axis current loop control signal.

[0074] (2) Internal parameter update process

[0075] During the use of the joint controller, the FPGA automatically updates the data of the quadrature axis current loop parameter P from 1.7 to 0.6 according to the actual changes in the joint motion state. The parameter update process is as follows:

[0076] Step 1: The data at 0x20104090 on the FPGA changes from 1740 to 614. At this time, the joint controller detects that the data at 0x20104090 has changed.

[0077] Step 2: The joint controller finds its own file " / current loop parameter / cross-axis current loop.bin" according to the address 0x20104090, and determines that the changed parameter is the cross-axis current loop parameter P. The parameter type of the cross-axis current loop parameter P is 8, which represents a floating point type, and the number of decimal places is 10. According to formula (1), the inverse operation is performed to obtain the floating point value corresponding to 614 is 0.6, and the data value of the cross-axis current loop parameter P in the file is changed to 0.6;

[0078] Step 3: The joint controller detects that the local parameters have changed, reads the parameter name, FPGA address, data value, type and decimal places of the quadrature-axis current loop parameter P, and sends the checksum to the central controller through the bus;

[0079] Step 4: The central controller confirms that the checksum is correct and writes the parameter name, FPGA address, data value, type and number of decimal places of the cross-axis current loop parameter P into its own file " / current loop parameter / cross-axis current loop.bin".

[0080] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0081] Parts not described in detail in the present invention belong to common knowledge of those skilled in the art.

Claims

1. An on-orbit heterogeneous management system for motion parameters of a space manipulator, characterized by: Including the main and backup joint controllers and joint controller FPGA and the robot arm central controller in cold backup relationship; The manipulator central controller communicates with the spacecraft central processing unit via an external bus to save a copy of motion parameters; the motion parameters are parameters required for calculating the joint control motor; The master and backup joint controllers communicate with the central controller via the robot control bus; the master and backup joint controllers and the master joint controller FPGA are respectively used to store a copy of motion parameters, which are used for master and backup control respectively; the master or backup joint controller loads the motion parameters from the corresponding joint controller memory into the corresponding FPGA for calculation; The joint controller FPGA performs parameter calculation and motor control; The robot arm central controller and the main backup joint controller use the ROMFS file system to store motion parameters. Several groups of motion parameters constitute a file. The parameter format is a floating point number. A group of motion parameters is the external input parameters required by the joint controller FPGA to run the joint motion control algorithm. Each group of parameters includes the parameter name, parameter value, storage address of the parameter in the FPGA, parameter type and decimal places, and is stored in a table. The primary or backup joint controller loads the motion parameters from the corresponding joint controller memory into the corresponding FPGA for calculation including: S1, the joint controller inquires the value of each set of motion parameters by sending the parameter name to the central controller; S2, the central controller finds the corresponding file from its memory according to the received parameter name, reads the parameter name, parameter value, storage address, type and decimal places of the parameter in FPGA from the file, and sends the checksum to the joint controller through the bus; S3. After confirming that the checksum is correct, the joint controller writes the read content into its corresponding parameter name file to complete the recovery of the data content; otherwise, no writing is performed; S4, the joint controller reads the parameter value from the written parameter name file and determines whether the parameter is a valid parameter. If it is a valid parameter, the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address; if it is invalid, the default value of the parameter is read, and the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address; S5. The corresponding joint controller FPGA obtains the corresponding parameter value from the storage address for corresponding control signal calculation.

2. The system according to claim 1, characterized in that: Each set of motion parameters is saved in triplicate for two-out-of-three processing.

3. The system according to claim 1, characterized in that: The joint controller reloads the parameters according to the processing in S4 at a preset time interval to avoid parameter errors caused by single particle time.

4. The system according to claim 1, characterized in that: In the operation of converting a floating-point number to an integer, it is assumed that the floating-point data is a and is required to be converted to a 16-bit signed fixed-point number. If there is 1 sign bit, m1 integer bits, and m2 decimal bits in the 16 bits, the conversion formula is as follows: 。 5. A method for on-orbit heterogeneous management of motion parameters of a space manipulator implemented by the system of claim 1, characterized in that Each time the joint controller is started, the joint motion parameters are loaded into the corresponding FPGA, including: S1, the joint controller inquires the value of each set of motion parameters by sending the parameter name to the central controller; S2, the central controller finds the corresponding file from its memory according to the received parameter name, reads the parameter name, parameter value, storage address, type and decimal places of the parameter in FPGA from the file, and sends the checksum to the joint controller through the bus; S3. After confirming that the checksum is correct, the joint controller writes the read content into its corresponding parameter name file to complete the recovery of the data content; otherwise, no writing is performed; S4, the joint controller reads the parameter value from the written parameter name file and determines whether the parameter is a valid parameter. If it is a valid parameter, the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address; if it is invalid, the default value of the parameter is read, and the floating point number is converted to an integer, and the converted integer value is loaded into the corresponding FPGA storage address; S5. The corresponding joint controller FPGA obtains the corresponding parameter value from the storage address for corresponding control signal calculation.

6. The method according to claim 5, characterized in that: The update of the motion parameters of the space manipulator includes the external update initiated by the ground operation and control center and the internal update caused by the autonomous change of parameters on the FPGA.

7. The method according to claim 5, characterized in that: The external update process includes: The joint controller receives the remote control command with motion parameters sent from the ground and forwarded by the central controller, and updates the motion parameters in the local memory after parsing; The joint controller detects changes in local parameters, reads the set of motion parameters stored in its own memory, calculates the checksum, and sends it to the central controller; The central controller checks whether the checksum is correct. If it is correct, the motion parameters are written into its own memory, otherwise, they are not written; The joint controller reads the FPGA address and decimal value corresponding to the parameter value from the local memory, converts the floating point number into an integer, and then loads it into the FPGA to complete the motion parameter update.

8. The method according to claim 6, characterized in that: The internal update process includes: The joint controller periodically reads the motion parameters stored on the FPGA. When a set of parameters changes, the joint controller performs the inverse operation of converting floating-point numbers to integers to calculate the floating-point values ​​of the parameters. The joint controller finds the storage path of the parameter in the joint controller memory according to the FPGA address and updates the corresponding value; When the joint controller detects that the local parameters have changed, it reads the motion parameters saved in its own memory, calculates the checksum, and sends it to the central controller; The central controller checks whether the checksum is correct. If it is correct, the motion parameters are written into its own memory, otherwise they are not written.

Images