CN118342520A - Mechanical arm calibration method and device, intelligent equipment and storage medium - Google Patents

Abstract

The application relates to a mechanical arm calibration method, a mechanical arm calibration device, intelligent equipment and a storage medium. The method comprises the following steps: determining a calibration parameter value and an offset error based on the plurality of sets of moving end positions and moving image positions, and the plurality of sets of rotating end positions and rotating image positions; the position of the moving tail end is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm moves, and the position of the moving image is the position of the calibration object in the shot image after the mechanical arm moves; the rotating tail end position is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm rotates, and the rotating image position is the position of the calibration object in the photographed image after the mechanical arm rotates; acquiring a target image position of an object to be operated, and determining a conversion position corresponding to the object to be operated based on the target image position and a calibration parameter value; and obtaining a target operation position corresponding to the object to be operated based on the conversion position and the offset error. By adopting the method, the accuracy of the operation position can be improved.

Description

Robot arm calibration method, device, intelligent device and storage medium

Technical Field

The present application relates to the field of artificial intelligence technology, and in particular to a robot arm calibration method, apparatus, intelligent device and storage medium.

Background technique

With the development of artificial intelligence technology, robotic arms are being used in more and more fields, such as automated production, work manufacturing, medical and smart home fields. The use of robotic arms has improved the automation level of smart devices and laid the foundation for smart devices to perform more complex and intelligent tasks.

In the conventional technology, when using a robotic arm, a nine-point calibration method is used to determine calibration parameter values, and then the operation position corresponding to the object to be operated is determined according to the calibration parameter values, resulting in low accuracy of the operation position.

Summary of the invention

Based on this, it is necessary to provide a robotic arm calibration method, apparatus, intelligent device and computer-readable storage medium that can improve the accuracy of the operating position in response to the above technical problems.

In a first aspect, the present application provides a robotic arm calibration method. The method comprises:

Based on multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions, the calibration parameter values and offset errors are determined; the moving end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm moves, and the moving image position is the position of the calibration object in the captured image after the robotic arm moves; the rotating end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm rotates, and the rotating image position is the position of the calibration object in the captured image after the robotic arm rotates;

Acquire a target image position of the object to be operated, and determine a conversion position corresponding to the object to be operated based on the target image position and the calibration parameter value;

Based on the conversion position and the offset error, a target operation position corresponding to the object to be operated is obtained.

In a second aspect, the present application also provides a robot arm calibration device. The device comprises:

A determination module, used to determine the calibration parameter value and the offset error based on multiple sets of mobile end positions and mobile image positions, and multiple sets of rotational end positions and rotational image positions; the mobile end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm moves, and the mobile image position is the position of the calibration object in the captured image after the robotic arm moves; the rotational end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm rotates, and the rotational image position is the position of the calibration object in the captured image after the robotic arm rotates;

An acquisition module, used for acquiring a target image position of an object to be operated, and determining a conversion position corresponding to the object to be operated based on the target image position and the calibration parameter value;

A correction module is used to obtain a target operation position corresponding to the object to be operated based on the conversion position and the offset error.

In a third aspect, the present application further provides an intelligent device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any one of the methods described in the first aspect when executing the computer program.

In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of any one of the methods described in the first aspect.

In a fifth aspect, the present application further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of any one of the methods described in the first aspect.

The above-mentioned robot arm calibration method, device, intelligent device, storage medium and computer program product determine the calibration parameter value and offset error based on multiple sets of moving end positions and moving image positions, as well as multiple sets of rotating end positions and rotating image positions; the moving end position is the position of the robot arm end in the base coordinate system after the robot arm moves, and the moving image position is the position of the calibration object in the captured image after the robot arm moves; the rotating end position is the position of the robot arm end in the base coordinate system after the robot arm rotates, and the rotating image position is the position of the calibration object in the captured image after the robot arm rotates; the target image position of the object to be operated is obtained, and the conversion position corresponding to the object to be operated is determined based on the target image position and the calibration parameter value; based on the conversion position and the offset error, the target operation position corresponding to the object to be operated is obtained. Before determining the target operation position of the object to be operated, calibration parameter values and offset errors are determined through multiple sets of mobile end positions and mobile image positions, as well as multiple sets of rotational end positions and rotational image positions. Compared with determining the calibration parameter values only through multiple sets of mobile end positions and mobile image positions, multiple sets of mobile end positions and mobile image positions, as well as multiple sets of rotational end positions and rotational image positions are used to determine the calibration parameter values, and multiple sets of data of the movement of the robotic arm and multiple sets of data of the rotation of the robotic arm are combined, thereby improving the accuracy of the calibration parameter values; in the process of determining the target operation position of the object to be operated, the calibration parameter values with higher accuracy are used to determine the conversion position corresponding to the object to be operated, thereby improving the accuracy of the conversion position, and then the determined offset error is used to correct the conversion position to obtain the target operation position corresponding to the object to be operated, thereby further improving the accuracy of the operation position.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

FIG1 is a schematic diagram of a flow chart of a robot arm calibration method in one embodiment;

FIG2 is a schematic flow chart of steps for determining calibration parameter values and offset errors in one embodiment;

FIG3 is a schematic flow chart of an offset error determination step in one embodiment;

FIG4 is a flow chart of steps for determining calibration parameter values and offset errors in another embodiment;

FIG5 is a schematic flow chart of an offset error determination step according to another embodiment;

FIG6 is a schematic flow diagram of the steps of determining and using a plane transformation relationship in one embodiment;

FIG7 is a block diagram of a mechanical arm calibration device according to an embodiment;

FIG. 8 is a diagram showing the internal structure of a smart device in one embodiment.

Detailed ways

In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

In one embodiment, as shown in FIG1 , a robot arm calibration method is provided, and the method is applied to an intelligent device as an example for explanation. The intelligent device may be, but is not limited to, various intelligent robots, household intelligent devices, education and scientific research intelligent devices, intelligent manufacturing equipment, and environmental detection and maintenance intelligent devices, etc. The intelligent robot may be an industrial robot, a service robot, a medical robot, and an agricultural robot, etc. The intelligent device includes a robot arm and a camera, which can be divided into two cases: eyes on the hand and eyes outside the hand. The eyes on the hand refer to the camera (eye) being directly installed at the end of the robot arm (hand), and the eyes outside the hand refer to the camera being installed at a certain position outside the robot arm. The camera may be fixed at other positions in the work scene, for example, the camera is fixed on a bracket or ceiling on a production line. Before the intelligent device controls the robot arm to operate the object to be operated, it is necessary to determine the operation position corresponding to the object to be operated, and then control the robot arm to operate the object to be operated according to the operation position corresponding to the operation object. In this embodiment, the robot arm calibration method includes steps 102 to 106, wherein:

Step 102, based on multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions, determine the calibration parameter values and offset errors; the moving end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm moves, and the moving image position is the position of the calibration object in the captured image after the robotic arm moves; the rotating end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm rotates, and the rotating image position is the position of the calibration object in the captured image after the robotic arm rotates.

Among them, the mobile end position refers to the position of the end of the robot arm in the base coordinate system after the robot arm moves. The mobile end position can be expressed in two-dimensional coordinates. The base coordinate system refers to the base coordinate system of the robot arm, and the base coordinate system generally takes the fixed point of the robot arm as the coordinate origin. The mobile image position refers to the position of the calibration object in the captured image after the robot arm moves. It can be understood that the position coordinates of the calibration object in the captured image taken by the camera, and the mobile image position can be expressed in two-dimensional coordinates of pixel points. The rotation end position refers to the position of the end of the robot arm in the base coordinate system after the robot arm rotates. The rotation image position refers to the position of the calibration object in the captured image after the robot arm rotates. The multiple sets of mobile end positions and mobile image positions can be at least 9 sets of mobile end positions and mobile image positions, and the multiple sets of rotation end positions and rotation image positions can be at least 5 sets of rotation end positions and rotation image positions.

The calibration parameter value refers to the parameter used to transform the target image position of the object to be operated. It can be understood that the calibration parameter value is a conversion parameter for determining the operating position of the object to be operated. When the height of the robotic arm is fixed, the calibration parameter value includes a rotation and translation matrix; when the height of the robotic arm is variable, the calibration parameter value includes a rotation and translation matrix and a projection distortion matrix; the rotation and translation matrix represents the geometric relationship between the camera and the end of the robotic arm, and the projection distortion matrix represents the perspective projection of the captured image and the influence of lens distortion. The offset error refers to the value used to correct the initial operating position. It can be understood that the initial operating position of the object to be operated is determined according to the target image position corresponding to the object to be operated and the calibration parameter value, and the initial operating position is corrected using the offset error to obtain the target operating position of the object to be operated.

Exemplarily, in the case where the smart device needs to perform hand-eye calibration, the smart device controls the mechanical arm to move on the calibration plane with the calibration object, and for each movement, the smart device obtains a set of mobile terminal positions and mobile image positions, and after multiple movements, multiple sets of mobile terminal positions and mobile image positions are obtained; the smart device controls the mechanical arm to rotate multiple times, and for each rotation, the smart device obtains a set of rotation terminal positions and rotation image positions, and after multiple movements, multiple sets of rotation terminal positions and rotation image positions are obtained. The smart device determines the calibration parameter value based on the multiple sets of mobile terminal positions and mobile image positions, and the multiple sets of rotation terminal positions and rotation image positions; and then determines the offset error based on the multiple sets of rotation terminal positions and rotation image positions, and the calibration parameter value. In the case where the smart device needs to perform hand-eye calibration, it can be before determining the target operation position of the object to be operated, that is, before the smart device determines the target operation position of the object to be operated, the hand-eye calibration is performed first; or, in the case where the smart device needs to perform hand-eye calibration, it can also be every preset time period, that is, the smart device performs hand-eye calibration every preset time period.

Step 104 , obtaining the target image position of the object to be operated, and determining the conversion position corresponding to the object to be operated based on the target image position and the calibration parameter value.

The object to be operated refers to the object that needs to be operated by the robot arm, and the object to be operated is located in the operation plane of the robot arm. The target image position refers to the position coordinates of the object to be operated in the image taken by the camera. The converted position refers to the position coordinates obtained by converting the target image position according to the calibration parameter value.

Exemplarily, after the smart device determines the calibration parameter value and the offset error, when it is necessary to control the robotic arm to operate the object to be operated, the smart device obtains the target image position of the object to be operated in the operation plane through the camera corresponding to the robotic arm; when the calibration parameter value includes a rotation and translation matrix, the projection distortion matrix is obtained, and the product of the target image position, the calibration parameter value and the projection distortion matrix is determined as the transformation position corresponding to the object to be operated; when the calibration parameter value includes a rotation and translation matrix and a projection distortion matrix, the product of the target image position and the calibration parameter value is determined as the transformation position corresponding to the object to be operated.

Step 106: Obtain a target operation position corresponding to the object to be operated based on the conversion position and the offset error.

Exemplarily, when the working plane of the robotic arm and the calibration plane are in the same plane, the intelligent device adds the offset error to the conversion position corresponding to the object to be operated to obtain the target operation position corresponding to the object to be operated; when the working plane of the robotic arm and the calibration plane are not in the same plane, the intelligent device adds the offset error to the conversion position corresponding to the object to be operated to obtain the initial operation position corresponding to the object to be operated, and determines the target operation position corresponding to the object to be operated based on the initial operation position.

The above-mentioned robot arm calibration method determines the calibration parameter value and the offset error through multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions, before determining the target operation position of the object to be operated. Compared with determining the calibration parameter value only through multiple sets of moving end positions and moving image positions, multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions are used to determine the calibration parameter value, and multiple sets of data of the robot arm movement and multiple sets of data of the robot arm rotation are combined, thereby improving the accuracy of the calibration parameter value; in the process of determining the target operation position of the object to be operated, the calibration parameter value with higher accuracy is used to determine the conversion position corresponding to the object to be operated, thereby improving the accuracy of the conversion position, and then the determined offset error is used to correct the conversion position to obtain the target operation position corresponding to the object to be operated, thereby further improving the accuracy of the operation position.

In one embodiment, as shown in FIG2 , when the camera is located on a robotic arm, the calibration parameter values and the offset errors are determined based on multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions, including:

Step 202, averaging multiple groups of mobile terminal positions to obtain an average position.

The average position refers to the position coordinates obtained by averaging multiple groups of mobile terminal positions.

Exemplarily, when the camera is located on a robotic arm, that is, when the eye is on the hand, the smart device averages multiple groups of mobile terminal positions to obtain an average position.

Step 204, determining the movement difference position between the movement end position and the average position, and the rotation difference position between the rotation end position and the average position.

The moving difference position refers to the position coordinate obtained by subtracting the average position from the moving end position, and the rotation difference position refers to the position coordinate obtained by subtracting the average position from the rotation end position.

Exemplarily, for each mobile terminal position, the smart device subtracts the average position from the mobile terminal position to obtain a mobile difference position; and for each rotational difference position, the smart device subtracts the average position from the rotational difference position to obtain a rotational difference position.

Step 206 : determining calibration parameter values based on the multiple sets of movement difference positions and movement image positions, and the multiple sets of rotation difference positions and rotation image positions.

Exemplarily, the smart device performs straight-line fitting on multiple sets of movement difference positions and movement image positions, and multiple sets of rotation difference positions and rotation image positions to obtain calibration parameter values.

In one embodiment, the smart device performs straight-line fitting on multiple sets of movement difference positions and movement image positions, and multiple sets of rotation difference positions and rotation image positions to obtain calibration parameter values. The straight-line fitting method includes but is not limited to least squares method, robust regression, regularized regression, Bayesian regression, etc. The straight-line fitting formula is as follows:

Formula 1)

in, is the average position, is the X-axis coordinate value in the average position, is the Y-axis coordinate value in the average position; is the nth moving end position or rotation end position; is the nth moving image position or rotating image position; is the rotation and translation matrix; P is the projection distortion matrix.

Step 208, determining the offset error based on the calibration parameter value and the average position.

Exemplarily, the intelligent device determines the offset error based on the first set of rotational end positions and rotational image positions, the calibration parameter values and the average position; the rotation angle corresponding to the first set of rotational end positions and rotational image positions is zero, that is, when the robotic arm rotates for the first time, the rotation angle of the robotic arm is zero, the position of the robotic arm end in the base coordinate system is the rotational end position, and the position of the calibration object in the captured image is the rotational image position.

In the present embodiment, when the photographing device is located on the robotic arm, that is, when the eye is on the hand, calibration parameter values are determined by multiple sets of moving difference positions and moving image positions, as well as multiple sets of rotational difference positions and rotated image positions. Compared with determining the calibration parameter values only by multiple sets of moving end positions and moving image positions, multiple sets of moving difference positions and moving image positions, as well as multiple sets of rotational difference positions and rotated image positions are used to determine the calibration parameter values, which combines multiple sets of data of the movement of the robotic arm and multiple sets of data of the rotation of the robotic arm, thereby improving the accuracy of the calibration parameter values; then, the offset error is determined based on the calibration parameter value, providing basic data for subsequent correction of the initial operation position.

In one embodiment, as shown in FIG3 , based on the calibration parameter value and the average position, determining the offset error includes:

Step 302 : for each rotated image position, based on the rotated image position and the calibration parameter value, obtain the first image position corresponding to the rotated image position in the terminal coordinate system.

The end coordinate system refers to the coordinate system of the end effector of the robot arm, and the end coordinate system usually takes the center of the end effector of the robot arm as the coordinate origin.

Exemplarily, for each rotated image position, the smart device multiplies the rotated image position by the calibration parameter value to obtain a first image position corresponding to the rotated image position in the terminal coordinate system.

Step 304: Perform curve fitting on the multiple first image positions to obtain the fitting circle center position.

The curve fitting refers to the process of fitting multiple points into a circle. The fitting center position refers to the position coordinates of the center of the circle obtained by the curve fitting.

Exemplarily, the smart device performs curve fitting on the multiple first image positions to obtain a fitting circle, and determines the position coordinates of the center point of the fitting circle as the center position of the fitting circle.

Step 306 , determining an offset error based on a set of rotation end positions and rotation image positions, a fitting circle center position and an average position.

Exemplarily, the smart device determines a first difference value between the rotation end position and the average position, and a second difference value between the rotation image position in the same group as the rotation end position and the fitting circle center position, and adds the first difference value to the second difference value to obtain an offset error.

In one embodiment, the offset error diff is as follows:

Formula (2)

Among them, _{Protational end position} refers to the coordinates of the rotational end position, _{Protational image position} refers to the coordinates of the rotational image position, _{Protational end position} and _{Protational image position} are a group of rotational end positions and rotational image positions, and generally the first group of rotational end positions and rotational image positions are used, and the rotation angle of the robotic arm corresponding to the first group of rotational end positions and rotational image positions is zero; _{Paverage position} refers to averaging multiple groups of mobile end positions to obtain the coordinates of the average position; _{Pfitted circle center position} refers to curve fitting of multiple first image positions to obtain the coordinates of the fitted circle center position.

In this embodiment, when the camera is located on the robotic arm, that is, when the eye is on the hand, if the calibration parameter values determined in the above steps 202 to 206 are directly used to calculate the target operation position of the object to be operated, the calculated target operation position is offset from the actual operation position by two distances, one of which is the distance from the rotated image position to the rotation center position of the robotic arm, and the other is the distance from the rotation midline position of the robotic arm to the average position. The fitted center position determined by the above steps 302 and 304 is the rotation center position of the robotic arm. The offset error is determined by a set of rotation end positions and rotation image positions, the fitted center position and the average position, which provides basic data for subsequent correction of the initial operation position.

In one embodiment, as shown in FIG4 , when the camera is located outside the robot arm, the calibration parameter value and the offset error are determined based on multiple sets of mobile end positions and mobile image positions, and multiple sets of rotation end positions and rotation image positions, including:

Step 402 : determining calibration parameter values based on multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions.

For example, when the camera is outside the robot arm, that is, the eye is outside the hand, the smart device performs linear fitting on multiple sets of mobile end positions and mobile image positions, and multiple sets of rotation end positions and rotation image positions to obtain calibration parameter values. The linear fitting method includes but is not limited to least squares method, robust regression, regularized regression, Bayesian regression, etc.

In one embodiment, the straight line fitting formula is as follows:

Formula (3)

in, is the nth moving end position or rotation end position; is the nth moving image position or rotating image position; is the rotation and translation matrix; P is the projection distortion matrix.

Step 404 : for each rotated image position, based on the rotated image position and the calibration parameter value, obtain a second image position corresponding to the rotated image position in the base coordinate system.

Exemplarily, for each rotated image position, the smart device multiplies the rotated image position by the calibration parameter value to obtain a second image position corresponding to the rotated image position in the base coordinate system.

Step 406: Perform curve fitting on the multiple second image positions to obtain the fitting circle center position and fitting radius.

The center position of the fitting circle refers to the center position of the fitting circle obtained by performing curve fitting on the multiple second image positions. The fitting radius refers to the radius of the fitting circle obtained by performing curve fitting on the multiple second image positions.

Exemplarily, the smart device performs curve fitting on the multiple second image positions to obtain a fitting circle, determines the position coordinates of the center of the fitting circle as the fitting center position, and determines the radius of the fitting circle as the fitting radius.

Step 408 , determining an offset error based on a set of rotation end positions and rotation image positions, a fitting circle center position, and a fitting radius.

Exemplarily, the smart device calculates a set of rotation end positions and rotation image positions, a fitting circle center position and a fitting radius to obtain an offset error.

In the present embodiment, when the photographing device is located outside the robotic arm, that is, when the eye is outside the hand, the calibration parameter value is determined by multiple sets of moving end positions and moving image positions, as well as multiple sets of rotating end positions and rotating image positions. Compared with determining the calibration parameter value only by multiple sets of moving end positions and moving image positions, the calibration parameter value is determined by using multiple sets of moving end positions and moving image positions, as well as multiple sets of rotating end positions and rotating image positions, which combines multiple sets of data of the movement of the robotic arm and multiple sets of data of the rotation of the robotic arm, thereby improving the accuracy of the calibration parameter value; then, the offset error is determined based on the calibration parameter value, providing basic data for subsequent correction of the initial operation position.

In one embodiment, as shown in FIG5 , based on a set of rotation end positions and rotation image positions, a fitting center position and a fitting radius, determining the offset error includes:

Step 502: Based on the rotation end position and the fitting circle center position, determine the inclination angle of the straight line where the rotation end position and the fitting circle center position are located.

The tilt angle refers to the angle between the straight line where the rotation end position and the fitting circle center position are located and the positive direction of the Y axis.

Exemplarily, the smart device determines the X-axis difference value between the X-axis coordinate value of the rotation end position and the X-axis coordinate value of the fitting center position, determines the Y-axis difference value between the Y-axis coordinate value of the rotation end position and the Y-axis coordinate value of the fitting center position, determines the difference ratio between the X-axis difference value and the Y-axis difference value, performs an inverse tangent operation on the difference ratio, and obtains the inclination angle of the straight line where the rotation end position and the fitting center position are located.

In one embodiment, the tilt angle As follows:

Formula (4)

Among them, (x ₁ ,y ₁ ) is the rotation end position. Generally, the first set of rotation end position and rotation image position are used. The rotation angle of the robot arm corresponding to the first set of rotation end position and rotation image position is zero; (x _circle ,y _circle ) is the fitting circle center position.

Step 504: Obtain an offset error based on the sine value of the tilt angle, the cosine value of the tilt angle, and the fitting radius.

Exemplarily, the smart device multiplies the sine value of the tilt angle by the fitting radius to obtain a sine error, multiplies the cosine value of the tilt angle by the fitting radius to obtain a cosine error, and obtains an offset error based on the sine error and the cosine error.

In one embodiment, the offset error diff is as follows:

Formula (5)

Among them, circle_r is the fitting radius; is the cosine of the tilt angle; is the sine of the tilt angle.

In this embodiment, when the camera is located outside the robotic arm, that is, the eye is outside the hand, the offset error is determined through a set of rotation end positions and rotation image positions, fitting circle center positions and fitting radius, providing basic data for subsequent correction of the initial operation position.

In one embodiment, as shown in FIG6 , when the calibration object is located on the calibration plane, and the calibration plane and the working plane are located on different planes, before obtaining the target operation position corresponding to the object to be operated based on the conversion position and the offset error, and obtaining the target operation position corresponding to the object to be operated based on the conversion position and the offset error, includes:

Step 602, obtain multiple sets of corrected end positions and corrected image positions; the corrected end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm moves to the corrected calibration object located on the working plane; the corrected image position is the position of the corrected calibration object in the captured image.

Among them, the correction end position refers to the position of the end of the manipulator in the base coordinate system after the manipulator moves to the correction calibration object located on the working plane. The calibration plane refers to the plane where the calibration object is located, which can be understood as the plane used to determine the calibration parameter value. The working plane refers to the plane on which the manipulator performs operations, which can be understood as the working plane of the manipulator. The correction calibration object refers to the calibration object located on the working plane used to determine the plane transformation relationship between the calibration plane and the working plane. The correction image position refers to the position of the correction calibration object in the captured image.

Exemplarily, when the calibration object is located on the calibration plane, and the calibration plane and the working plane are located on different planes, after the intelligent device determines the calibration parameter value and before determining the target operation position corresponding to the object to be operated, the intelligent object controls the robotic arm to move to the corrected calibration object located on the working plane, and obtains a set of corrected end positions and corrected image positions. After multiple movements, multiple sets of corrected end positions and corrected image positions are obtained.

Step 604: Determine a corrected conversion position corresponding to the corrected image position based on the corrected image position and the calibration parameter value.

Exemplarily, for each corrected image position, the smart device multiplies the corrected image position by the calibration parameter value to obtain a corrected transformation position corresponding to the corrected image position.

Step 606: Determine a plane transformation relationship between the calibration plane and the working plane based on the multiple sets of corrected end positions and corrected transformation positions.

Among them, the plane transformation relationship refers to the transformation parameter value of transforming the position coordinates located on the calibration plane to the working plane. The plane transformation relationship includes a scaling matrix and a translation matrix; the scaling matrix may include a first scaling parameter value and a second scaling parameter value, the first scaling parameter value represents the scaling factor on the X axis, and the second scaling parameter value represents the scaling factor on the Y axis; the translation matrix may include a first translation parameter value and a second translation parameter value, the first translation parameter value represents the translation distance on the X axis, and the second translation parameter value represents the translation distance on the Y axis.

Exemplarily, the intelligent device fits multiple sets of corrected end positions and corrected transformation positions to obtain a plane transformation relationship between the calibration plane and the working plane.

In one embodiment, the fitting formula for fitting multiple sets of corrected end positions and corrected conversion positions is as follows:

Formula (6)

in, Transform position for the nth correction; is the nth corrected end position; scale_x is the scaling factor corresponding to the X axis, i.e. the first scaling parameter; scale_y is the scaling factor corresponding to the Y axis, i.e. the second scaling parameter; original_x is the translation distance of the X axis, i.e. the first translation parameter; origin_y is the translation distance of the Y axis, i.e. the second translation parameter.

Step 608: Based on the conversion position and the offset error, an initial operation position corresponding to the object to be operated is obtained.

Exemplarily, the smart device adds an offset error to the conversion position corresponding to the object to be operated to obtain an initial operation position corresponding to the object to be operated.

Step 610: Based on the initial operation position and the plane transformation relationship, a target operation position corresponding to the object to be operated is obtained.

Exemplarily, the smart device subtracts the translation matrix in the plane transformation relationship from the initial operation position to obtain a translation difference position, and multiplies the translation difference position by the scaling matrix in the plane transformation relationship to obtain a target operation position corresponding to the object to be operated.

In this embodiment, when the calibration object is located on the calibration plane, and the calibration plane and the working plane are located on different planes, the plane transformation relationship between the calibration plane and the working plane is determined according to multiple sets of corrected end positions and corrected transformation positions, and then the plane transformation relationship is used to transform the initial operation position located on the calibration plane to the target operation position located on the operating plane, thereby ensuring that the target operation position is located on the working plane of the robot arm, thereby improving the accuracy of the target operation position.

In an exemplary embodiment, a method for calibrating a robotic arm of an object to be operated is provided, which is divided into two cases: eyes on the hand and eyes outside the hand, respectively:

1. Eyes on the Hands

If alignment is required and the calibration plane and the operation plane are on the same plane, the following steps are included:

1. Move the robotic arm to the corresponding calibration object and record the moving end position (x, y) of the calibration object in the base coordinate system;

2. Move the robotic arm to ensure that the calibration object is in the field of view of the camera, record the current mobile end position ( _xn , _yn ) and the corresponding mobile image position ( _ximagen , _yimagen ) of the robotic arm in the base coordinate system, repeat the above steps nine times to obtain nine sets of mobile end positions ( _xn , _yn ) and mobile image positions ( _ximagen , _yimagen );

3. Based on the nine sets of mobile terminal positions ( _xn , _yn ) and mobile image positions ( _ximagen , _yimagen ), fit formula (7) to obtain the rotation and translation matrix And the projection distortion matrix P.

Formula (7)

4. Obtain the target terminal position and target image position corresponding to the object to be operated, multiply the target image position by the rotation translation matrix and the projection distortion matrix to obtain the transformed position of the object to be operated in the terminal coordinate system, add the transformed position to the target terminal position to obtain the target operation position of the object to be operated in the base coordinate system.

If alignment is not required and the calibration plane and the operation plane are on the same plane, the following steps are included:

1. Move the robotic arm to ensure that the calibration object is in the field of view of the camera, record the current mobile end position ( _xn , _yn ) of the robotic arm in the base coordinate system and the corresponding mobile image position ( _ximagen , _yimagen ), repeat the above steps nine times to obtain nine sets of mobile end positions ( _xn , _yn ) and mobile image positions ( _ximagen , _yimagen );

2. Rotate the robotic arm to ensure that the calibration object is in the field of view of the camera, record the current rotation end position (x _m , y _m ) and the corresponding rotation image position (ximage _m , yimage _m ) of the robotic arm end in the base coordinate system, repeat the above steps five times to obtain five sets of rotation end positions (x _m , y _m ) and rotation image positions (ximage _m , yimage _m ); the angle of the first rotation of the robotic arm is zero;

3. Average the positions of multiple mobile terminals to get the average position ;

4. Based on average position , nine sets of moving end positions ( _xn , _yn ) and moving image positions ( _ximagen , _yimagen ), and five sets of rotating end positions ( _xm , _ym ) and rotating image positions ( _ximagem , _yimagem ), fit formula (1) and obtain the rotation and translation matrix and the projection distortion matrix P;

5. For each rotation image position, the intelligent device multiplies the rotation image position by the calibration parameter value to obtain the first image position corresponding to the rotation image position in the terminal coordinate system; curve fitting is performed on the five first image positions to obtain a fitting circle, and the position coordinates of the center point of the fitting circle are determined as the fitting circle center position; the first set of rotation terminal positions and rotation image positions, fitting circle center positions and average positions are substituted into formula (2) to obtain the offset error;

6. Obtain the target image position corresponding to the object to be operated, multiply the target image position by the rotation and translation matrix and the projection distortion matrix to obtain the transformed position of the object to be operated in the terminal coordinate system, add the offset error to the transformed position, and obtain the target operation position of the object to be operated in the base coordinate system.

2. Eyes outside the hands

If alignment is required and the calibration plane and the operation plane are on the same plane, the following steps are included:

1. Place nine calibration objects on the calibration plane, move the robotic arm to correspond to the previous target calibration object, record the moving end position (x, y) of the target calibration object in the base coordinate system, and the moving image positions (ximage _n , yimage _n ) corresponding to the nine calibration objects respectively;

2. Based on the mobile terminal position (x, y) and the nine mobile image positions (ximage _n , yimage _n ), fit formula (8) to obtain the rotation and translation matrix And the projection distortion matrix P.

Formula (8)

3. Obtain the target image position corresponding to the object to be operated, multiply the target image position by the rotation and translation matrix and the projection distortion matrix to obtain the target operation position of the object to be operated in the base coordinate system.

If alignment is not required and the calibration plane and the operation plane are on the same plane, the following steps are included:

1. Move the robotic arm to ensure that the calibration object is in the field of view of the camera, record the current mobile end position ( _xn , _yn ) of the robotic arm in the base coordinate system and the corresponding mobile image position ( _ximagen , _yimagen ), repeat the above steps nine times to obtain nine sets of mobile end positions ( _xn , _yn ) and mobile image positions ( _ximagen , _yimagen );

2. Rotate the robotic arm to ensure that the calibration object is in the field of view of the camera, record the current rotation end position (x _m , y _m ) and the corresponding rotation image position (ximage _m , yimage _m ) of the robotic arm end in the base coordinate system, repeat the above steps five times to obtain five sets of rotation end positions (x _m , y _m ) and rotation image positions (ximage _m , yimage _m ); the angle of the first rotation of the robotic arm is zero;

3. Based on nine sets of moving end positions ( _xn , _yn ) and moving image positions ( _ximagen , _yimagen ), and five sets of rotating end positions ( _xm , _ym ) and rotating image positions ( _ximagem , _yimagem ), formula (8) is fitted to obtain the rotation and translation matrix And the projection distortion matrix P.

4. For each rotated image position, multiply the rotated image position by the calibration parameter value to obtain the second image position corresponding to the rotated image position in the base coordinate system; perform curve fitting on the multiple second image positions to obtain a fitting circle, determine the position coordinate of the center of the fitting circle as the fitting center position, and determine the radius of the fitting circle as the fitting radius;

5. Substitute the first rotation end position and the fitting center position into formula (4) to obtain the inclination angle of the straight line where the rotation end position and the fitting center position are located; substitute the fitting radius and the inclination angle into formula (5) to obtain the offset error;

6. Obtain the target image position corresponding to the object to be operated, multiply the target image position by the rotation and translation matrix and the projection distortion matrix to obtain the transformed position of the object to be operated in the terminal coordinate system, add the offset error to the transformed position, and obtain the target operation position of the object to be operated in the base coordinate system.

In the above method for determining the operation position, the calibration object is located on the calibration plane, and the calibration plane and the working plane are in the same plane. If the calibration object is located on the calibration plane, and the calibration plane and the working plane are not in the same plane, after the intelligent device determines the calibration parameter value and before determining the target operation position corresponding to the object to be operated, the intelligent object controls the robot arm to move to the corrected calibration object located on the working plane to obtain a set of corrected end positions and corrected image positions. After multiple movements, multiple sets of corrected end positions and corrected image positions are obtained; for each corrected image position, the intelligent device multiplies the corrected image position by the calibration parameter value to obtain a corrected transformation position corresponding to the corrected image position; based on the multiple sets of corrected end positions and corrected transformation positions, formula (6) is fitted to obtain a plane transformation relationship between the calibration plane and the working plane, and the plane transformation relationship includes a scaling matrix and a translation matrix.

After determining the plane transformation relationship, obtain the determined rotation translation matrix and projection distortion matrix, as well as the target image position corresponding to the object to be operated, multiply the target image position by the rotation translation matrix and the projection distortion matrix to obtain the transformation position of the object to be operated in the terminal coordinate system, add the offset error to the transformation position to obtain the initial operation position of the object to be operated in the base coordinate system; subtract the translation matrix in the plane transformation relationship from the initial operation position to obtain the translation difference position, multiply the translation difference position by the scaling matrix in the plane transformation relationship to obtain the target operation position corresponding to the object to be operated.

The above-mentioned robot arm calibration method determines the calibration parameter value and the offset error through multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions, before determining the target operation position of the object to be operated. Compared with determining the calibration parameter value only through multiple sets of moving end positions and moving image positions, multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions are used to determine the calibration parameter value, and multiple sets of data of the robot arm movement and multiple sets of data of the robot arm rotation are combined, thereby improving the accuracy of the calibration parameter value; in the process of determining the target operation position of the object to be operated, the calibration parameter value with higher accuracy is used to determine the conversion position corresponding to the object to be operated, thereby improving the accuracy of the conversion position, and then the determined offset error is used to correct the conversion position to obtain the target operation position corresponding to the object to be operated, thereby further improving the accuracy of the operation position. When the calibration object is located on the calibration plane, and the calibration plane and the working plane are located on different planes, the plane transformation relationship between the calibration plane and the working plane is determined according to multiple sets of corrected end positions and corrected transformation positions, and then the plane transformation relationship is used to transform the initial operation position located on the calibration plane to the target operation position located on the operating plane, thereby ensuring that the target operation position is located on the working plane of the robot arm, thereby improving the accuracy of the target operation position.

It should be understood that, although the steps in the flowcharts involved in the above embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

Based on the same inventive concept, the embodiment of the present application also provides a robot arm calibration device for implementing the robot arm calibration method involved above. The implementation solution provided by the device to solve the problem is similar to the implementation solution recorded in the above method, so the specific limitations in one or more robot arm calibration device embodiments provided below can refer to the limitations of the robot arm calibration method above, and will not be repeated here.

In one embodiment, as shown in FIG. 7 , a robot arm calibration device is provided, including: a determination module 702 , an acquisition module 704 , and a correction module 706 , wherein:

The determination module 702 is used to determine the calibration parameter value and the offset error based on multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotating image positions; the moving end position is the position of the end of the manipulator in the base coordinate system after the manipulator moves, and the moving image position is the position of the calibration object in the captured image after the manipulator moves; the rotating end position is the position of the end of the manipulator in the base coordinate system after the manipulator rotates, and the rotating image position is the position of the calibration object in the captured image after the manipulator rotates;

An acquisition module 704 is used to acquire a target image position of the object to be operated, and determine a conversion position corresponding to the object to be operated based on the target image position and the calibration parameter value;

The correction module 706 is used to obtain a target operation position corresponding to the object to be operated based on the conversion position and the offset error.

In one embodiment, the determination module 702 is also used to: average multiple groups of moving end positions to obtain an average position; determine the moving difference position between the moving end position and the average position, and the rotational difference position between the rotating end position and the average position; determine calibration parameter values based on multiple groups of moving difference positions and moving image positions, and multiple groups of rotational difference positions and rotated image positions; determine the offset error based on the calibration parameter values and the average position.

In one embodiment, the determination module 702 is also used to: for each rotated image position, based on the rotated image position and the calibration parameter value, obtain the first image position corresponding to the rotated image position in the terminal coordinate system; perform curve fitting on multiple first image positions to obtain the fitted center position; and determine the offset error based on a set of rotational end positions and rotated image positions, the fitted center position and the average position.

In one embodiment, the determination module 702 is also used to: determine calibration parameter values based on multiple sets of moving end positions and moving image positions, and multiple sets of rotating end positions and rotated image positions; for each rotated image position, based on the rotated image position and the calibration parameter values, obtain the second image position corresponding to the rotated image position in the base coordinate system; perform curve fitting on multiple second image positions to obtain the fitting center position and the fitting radius; determine the offset error based on a set of rotating end positions and rotating image positions, the fitting center position and the fitting radius.

In one embodiment, the determination module 702 is also used to: determine the inclination angle of the straight line where the rotation end position and the fitting center position are located based on the rotation end position and the fitting center position; and obtain the offset error based on the sine value of the inclination angle, the cosine value of the inclination angle and the fitting radius.

In one embodiment, the correction module 706 is also used to: obtain multiple sets of corrected end positions and corrected image positions; the corrected end position is the position of the end of the robotic arm in the base coordinate system after the robotic arm moves to the corrected calibration object located on the working plane; the corrected image position is the position of the corrected calibration object in the captured image; based on the corrected image position and the calibration parameter value, determine the corrected transformation position corresponding to the corrected image position; based on multiple sets of corrected end positions and corrected transformation positions, determine the plane transformation relationship between the calibration plane and the working plane; based on the transformation position and the offset error, obtain the initial operation position corresponding to the object to be operated; based on the initial operation position and the plane transformation relationship, obtain the target operation position corresponding to the object to be operated.

Each module in the above-mentioned robot arm calibration device can be implemented in whole or in part by software, hardware and their combination. Each of the above-mentioned modules can be embedded in or independent of the processor in the smart device in the form of hardware, or can be stored in the memory of the smart device in the form of software, so that the processor can call and execute the corresponding operations of each of the above modules.

In one embodiment, a smart device is provided, which can be a terminal, and its internal structure diagram can be shown in Figure 8. The smart device includes a processor, a memory, an input/output interface, a communication interface, a display unit and an input device. The processor, the memory and the input/output interface are connected through a system bus, and the communication interface, the display unit and the input device are connected to the system bus through the input/output interface. The processor of the smart device is used to provide computing and control capabilities. The memory of the smart device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input/output interface of the smart device is used to exchange information between the processor and an external device. The communication interface of the smart device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be implemented through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a method for calibrating a robotic arm is implemented. The display unit of the smart device is used to form a visually visible picture, which can be a display screen, a projection device or a virtual reality imaging device. The display screen can be a liquid crystal display screen or an electronic ink display screen, and the input device of the smart device can be a touch layer covering the display screen, or a button, trackball or touchpad set on the smart device shell, or an external keyboard, touchpad or mouse.

Those skilled in the art will understand that the structure shown in FIG. 8 is merely a block diagram of a partial structure related to the scheme of the present application, and does not constitute a limitation on the smart device to which the scheme of the present application is applied. A specific smart device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

In one embodiment, a smart device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims (10)

1. The mechanical arm calibration method is characterized by comprising the following steps of:

Determining a calibration parameter value and an offset error based on the plurality of sets of moving end positions and moving image positions, and the plurality of sets of rotating end positions and rotating image positions; the position of the moving tail end is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm moves, and the position of the moving image is the position of the calibration object in the shot image after the mechanical arm moves; the rotating tail end position is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm rotates, and the rotating image position is the position of the calibration object in the shot image after the mechanical arm rotates;

Acquiring a target image position of an object to be operated, and determining a conversion position corresponding to the object to be operated based on the target image position and the calibration parameter value;

And obtaining a target operation position corresponding to the object to be operated based on the conversion position and the offset error.

2. The method of claim 1, wherein the determining calibration parameter values and offset errors based on the plurality of sets of moving end positions and moving image positions, and the plurality of sets of rotating end positions and rotating image positions with the camera on the robotic arm comprises:

averaging a plurality of groups of mobile terminal positions to obtain an average position;

Determining a movement difference position between the movement end position and the average position, and a rotation difference position between the rotation end position and the average position;

determining a calibration parameter value based on a plurality of sets of the movement difference position and the movement image position, and a plurality of sets of the rotation difference position and the rotation image position;

the offset error is determined based on the calibration parameter value and the average position.

3. The method of claim 2, wherein the determining the offset error based on the calibration parameter value and the average position comprises:

For each rotated image position, obtaining a first image position corresponding to the rotated image position under an end coordinate system based on the rotated image position and the calibration parameter value;

Performing curve fitting on a plurality of first image positions to obtain fitted circle center positions;

The offset error is determined based on a set of the rotational end position and rotational image position, the fitting center position, and the average position.

4. The method of claim 1, wherein the determining calibration parameter values and offset errors based on the plurality of sets of moving end positions and moving image positions, and the plurality of sets of rotating end positions and rotating image positions, with the camera located outside the robotic arm, comprises:

determining calibration parameter values based on the plurality of sets of mobile end positions and mobile image positions, and the plurality of sets of rotating end positions and rotating image positions;

For each rotated image position, obtaining a second image position corresponding to the rotated image position under a base coordinate system based on the rotated image position and the calibration parameter value;

Performing curve fitting on a plurality of second image positions to obtain fitting circle center positions and fitting radiuses;

The offset error is determined based on a set of the rotational end position and rotational image position, the fitting center position, and the fitting radius.

5. The method of claim 4, wherein said determining said offset error based on a set of said rotational end position and rotational image position, said fitting center position, and said fitting radius comprises:

determining the inclination angle of a straight line where the rotating tail end position and the fitting circle center position are located based on the rotating tail end position and the fitting circle center position;

And obtaining the offset error based on the sine value of the inclination angle, the cosine value of the inclination angle and the fitting radius.

6. The method according to claim 1, wherein, in a case where the calibration object is located on a calibration plane and the working plane are located on different planes, before the obtaining the target operation position corresponding to the object to be operated based on the conversion position and the offset error, the method further comprises:

acquiring a plurality of groups of corrected tail end positions and corrected image positions; the position of the corrected tail end is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm moves to the corrected calibration object positioned on the working plane; the corrected image position is the position of the corrected calibration object in the shot image;

Determining a corrected conversion position corresponding to the corrected image position based on the corrected image position and the calibration parameter value;

determining a plane conversion relationship between the calibration plane and the working plane based on a plurality of groups of the corrected end positions and the corrected conversion positions;

The obtaining, based on the conversion position and the offset error, a target operation position corresponding to the object to be operated includes:

The initial operation position corresponding to the object to be operated is obtained based on the conversion position and the offset error;

And obtaining a target operation position corresponding to the object to be operated based on the initial operation position and the plane conversion relation.

7. A robotic arm calibration apparatus, the apparatus comprising:

a determining module for determining a calibration parameter value and an offset error based on the plurality of sets of moving end positions and moving image positions, and the plurality of sets of rotating end positions and rotating image positions; the position of the moving tail end is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm moves, and the position of the moving image is the position of the calibration object in the shot image after the mechanical arm moves; the rotating tail end position is the position of the tail end of the mechanical arm in the base coordinate system after the mechanical arm rotates, and the rotating image position is the position of the calibration object in the shot image after the mechanical arm rotates;

the acquisition module is used for acquiring a target image position of an object to be operated and determining a conversion position corresponding to the object to be operated based on the target image position and the calibration parameter value;

And the correction module is used for obtaining a target operation position corresponding to the object to be operated based on the conversion position and the offset error.

8. A smart device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any one of claims 1 to 6 when the computer program is executed.

9. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 6.

10. A computer program product comprising a computer program, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 6.