Marine seat framework welding track real-time correction system based on machine vision and mechanical feedback

Abstract

The invention discloses a marine seat framework welding track real-time correction system based on machine vision and mechanical feedback. The marine seat framework welding track real-time correction system comprises a robot control unit, a welding unit, a vision sensing unit, a force sensing unit and a track correction module running on the robot control unit. The visual sensing unit is installed on an end effector of the robot and used for collecting image data including a to-be-welded weld joint and a peripheral area of the to-be-welded weld joint in real time. The force sensing unit is installed between a robot end effector and a welding gun and used for detecting six-dimensional force and torque signals between the welding gun and a workpiece in the welding process in real time. The core of the track correction module is a real-time correction algorithm based on multi-sensor information fusion, and the track correction module receives image data from the visual sensing unit and mechanical data from the force sensing unit. The sensing limitation of a single sensor is overcome, the vision provides macroscopic position deviation, the force sensing provides microcosmic contact and attitude information, and more comprehensive environment sensing is realized through complementation of the vision and the force sensing.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of marine mechanical processing, and particularly relates to a marine seat framework welding track real-time correction system based on machine vision and mechanical feedback. BACKGROUND

[0002] The marine seat framework structure is complex, and is usually welded by various specifications of pipes and profiles. In actual welding operation, due to factors such as incoming material tolerance, clamping error, and welding thermal deformation, the actual position and shape of the workpiece deviate from the preset theoretical model (CAD model). The traditional teaching programming or offline programming welding robot strictly operates according to the preset track and cannot adapt to such dynamic changes, which easily leads to the welding gun deviating from the welding seam, resulting in welding quality defects such as welding deviation, undercut, and incomplete fusion.

[0003] In the prior art, there is a system that uses a laser vision sensor to track the welding seam, but it mainly compensates for the two-dimensional position of the welding seam (such as the transverse and height deviation of the butt joint welding seam and the fillet welding seam), and lacks comprehensive sensing and processing capability for the overall structure deformation caused by thermal deformation and the change of the contact force between the welding gun and the workpiece during the welding process. Especially in the marine seat framework structure with multiple joints and complex spatial angles, a single visual feedback cannot fully guarantee the accurate matching of the welding gun posture and the welding seam position, and cannot avoid the unintended contact force between the welding gun and the workpiece caused by the deformation of the workpiece, affecting the stability of the welding process. SUMMARY

[0004] To solve the problems raised in the background, the present application provides a marine seat framework welding track real-time correction system and method based on machine vision and mechanical feedback. The system fuses visual spatial deviation and mechanical contact information, uses a core correction algorithm to generate a track correction amount of the robot end (welding gun) in real time, realizes dynamic and adaptive adjustment of the welding path, and improves the welding precision and quality stability of complex workpieces under dynamic deformation.

[0005] To achieve the above purpose, the present application provides the following technical solutions: A marine seat framework welding track real-time correction system based on machine vision and mechanical feedback, comprising: a robot control unit, a welding unit, a vision sensing unit, a force sensing unit, and a track correction module running on the robot control unit; The vision sensing unit is installed on the robot end effector and is used to collect image data containing the to-be-welded welding seam and its surrounding area in real time; The force sensing unit is installed between the robot end effector and the welding gun and is used to detect six-dimensional force and torque signals between the welding gun and the workpiece in real time during the welding process; The trajectory correction module, whose core is a real-time correction algorithm based on multi-sensor information fusion, receives image data from the visual sensing unit and mechanical data from the force sensing unit, and performs the following processing flow: S1: Visual feature extraction and deviation calculation: process the real-time image, extract the actual image coordinates [u_actual, v_actual]^T of the weld feature points, and compare them with the theoretical image coordinates [u_nominal, v_nominal]^T obtained based on the preset theoretical trajectory and camera model projection, and calculate the image plane deviation Δp_image: Δp_image = [u_actual - u_nominal, v_actual - u_nominal]^T Subsequently, through the camera calibration parameters and the hand-eye calibration matrix, the image plane deviation Δp_image is converted to the three-dimensional space position deviation ΔP_visual = [Δx_v, Δy_v, Δz_v]^T in the robot base coordinate system; Δx_v: position deviation in the X-axis direction of the robot base coordinate system (unit: millimeter).

[0006] Δy_v: position deviation in the Y-axis direction of the robot base coordinate system (unit: millimeter).

[0007] Δz_v: position deviation in the Z-axis direction of the robot base coordinate system (unit: millimeter).

[0008] S2: Force feedback information processing and deviation extraction: read the original signal F_raw = [Fx, Fy, Fz, Mx, My, Mz]^T of the force sensing unit, after low-pass filtering and gravity compensation, obtain the net force / torque F_contact caused by contact. By constructing a virtual spring-damper model, the contact force is mapped to the "embedded" depth or attitude deviation of the welding torch end in the contact normal direction. For example, for the contact force F_n perpendicular to the weld direction, an equivalent position compensation amount Δd_force can be calculated: Δd_force = K_f * F_n (when |F_n| > F_threshold) Where K_f is the force compliance coefficient (adjustable parameter matrix), and F_threshold is the force perception threshold. This compensation amount Δd_force, combined with the current welding torch attitude, can be further decomposed into position and attitude deviations ΔP_force and ΔO_force in the robot base coordinate system; S3: Multi-information fusion and trajectory correction quantity generation (core algorithm): An adaptive weighted fusion function is designed to fuse the visual deviation ΔP_visual and force feedback deviation ΔP_force, ΔO_force to generate the final robot end pose correction quantity ΔX_correct. The fusion function not only considers the size of the deviation, but also considers the current welding stage (such as arc striking, normal welding, and arc collecting) and sensor confidence. The mathematical expression is as follows: ΔX_correct = W_v(t, σ_v) · Φ(ΔP_visual) + W_f(t, σ_f) · Ψ(ΔP_force, ΔO_force) Where: Φ(·) and Ψ(·) are pre-processing functions for visual and force deviations (such as amplitude limiting and smoothing).

[0009] W_v and W_f are time-varying, sensor confidence related adaptive weight coefficients, satisfying W_v + W_f = I (identity matrix). σ_v and σ_f are the clarity index of the current time visual feature point extraction and the noise level index of the force signal.

[0010] t represents time or welding progress. In the welding seam tracking dominant stage (such as clear features), W_v increases; in the contact force sensing sensitive stage (such as large local deformation of the workpiece), W_f increases.

[0011] S4: Real-time trajectory superposition and execution: The calculated correction quantity ΔX_correct is superimposed on the current execution of the preset theoretical trajectory X_nominal(t) of the robot at a high control frequency (such as ≥100Hz) to generate the real-time corrected target trajectory X_target(t): X_target(t) = X_nominal(t) + ΔX_correct(t) The robot control unit drives the welding robot to track X_target(t), while the corrected trajectory data is fed back to the S1 step for updating the theoretical image coordinate calculation at the next time, forming a closed-loop control.

[0012] Preferably, in the step S1, the visual feature extraction uses a deep learning based weld seam feature point detection network, which is trained for typical joint forms of ship seat skeletons and can resist the interference of welding arc light, splashes and smoke.

[0013] Preferably, the calculation of adaptive weight coefficients W_v and W_f in step S3 uses a method based on fuzzy logic or neural network, which dynamically adjusts according to σ_v, σ_f and preset process rules (such as "strong contact, prefer to follow force feedback").

[0014] Preferably, the system further comprises a trajectory prediction unit, which makes a short-term prediction of the possible deformation trend of the workpiece based on historical correction data and the current welding speed, and pre-adds the predicted slight offset to ΔX_correct to enhance the response smoothness and foresight of the system.

[0015] Compared with the prior art, the present application has the following beneficial effects: (1) Overcomes the limitations of single sensor perception, vision provides macro position deviation, force sensing provides micro contact and posture information, both complementary, realize more comprehensive environmental perception.

[0016] (2) Through the high-frequency closed-loop control algorithm, the position and shape of the workpiece can be responded to within milliseconds during the welding process, significantly reducing defects such as welding deviation and welding discontinuity.

[0017] (3) The core fusion algorithm has self-adaptive weight adjustment capability, which can automatically adjust the dependence degree according to the welding working condition and sensor signal quality, improving the robustness and intelligent level of the system.

[0018] (4) Guarantees the welding precision of complex structural parts under dynamic deformation, reduces the rework caused by unqualified welding, improves the production efficiency and first pass rate, and is especially suitable for small-batch, multi-variety, high-quality welding scenes such as ship seat skeletons. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The logic principle of the present application; Figure 2 is a ΔP_visual acquisition step diagram. DETAILED DESCRIPTION

[0020] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0021] Please refer to Figure 1 , the present application provides the following technical solutions: A ship seat skeleton welding trajectory real-time correction system based on machine vision and mechanical feedback, comprising an industrial robot, a robot control unit (containing a trajectory correction module software), a welding unit (containing a welding gun), a six-dimensional force and torque sensor (installed between the robot wrist and the welding gun), and a structured light or laser vision sensor (installed in front of the welding gun).

[0022] Both vision sensor and force sensor communicate with robot controller through high-speed bus. Vision sensor is used to capture image data containing the weld seam and its surrounding area in real time. Six-axis force and moment sensor is used to detect six-axis force and moment signals between welding torch and workpiece in real time during welding process.

[0023] The trajectory correction module, whose core is a real-time correction algorithm based on multi-sensor information fusion, receives image data from the vision sensor and mechanical data from the force sensor, and performs the following processing flow: S1: Vision thread: capture images at a frequency of 50Hz, call the trained deep learning model (such as lightweight U-Net variant) to segment the weld area and locate key feature points (such as groove center, fillet toe), and convert pixel deviation to ΔP_visual in robot base coordinate system according to calibration data. The specific steps are as follows: Process real-time images to extract the actual image coordinates of the weld feature points, [u_actual, v_actual]^T, and compare them with the theoretical image coordinates [u_nominal, v_nominal]^T based on the pre-set theoretical trajectory and camera model projection, to calculate the image plane deviation Δp_image: Δp_image=[u_actual-u_nominal, v_actual-u_nominal]^T Then, through camera calibration parameters and hand-eye calibration matrix, the image plane deviation Δp_image is converted to the three-dimensional space position deviation ΔP_visual=[Δx_v, Δy_v, Δz_v]^T in the robot base coordinate system.

[0024] Δx_v: position deviation in X-axis direction of robot base coordinate system (unit: millimeter).

[0025] Δy_v: position deviation in Y-axis direction of robot base coordinate system (unit: millimeter).

[0026] Δz_v: position deviation in Z-axis direction of robot base coordinate system (unit: millimeter).

[0027] Wherein, the step of converting the image plane deviation Δp_image to the three-dimensional space position deviation ΔP_visual in the robot base coordinate system specifically includes: Step one: back-projection calculation based on depth information: Based on the feature point depth value Z_c measured by the vision sensor and the camera intrinsic parameter matrix K, the image plane deviation Δp_image = [Δu, Δv]^T is mapped to the three-dimensional position deviation ΔP_cam in the camera coordinate system. The mapping relationship is approximately expressed as: ΔX_c≈(Δu*Z_c) / fx, ΔY_c≈(Δv*Z_c) / fy Here, ΔZ_c serves as a bridge connecting 2D and 3D. For structured light / laser sensors, Z_c is the depth of the feature point relative to the camera's optical axis, obtained through direct measurement. For monocular systems, it needs to be estimated indirectly through prior models (such as known weld cross-sectional geometry) or motion parallax.

[0028] The camera intrinsic parameter matrix K is obtained through calibration. K=[fx,0,cx;0,fy,cy;0,0,1], (cx,cy) are principal points, fx=f / dx, fy =f / dy (f is the focal length, dx, dy are the pixel size).

[0029] Step 2: Hand-eye coordinate transformation: Using the rotation component R_base_cam in the pre-calibrated hand-eye transformation matrix H_cam_base, the deviation ΔP_cam in the camera coordinate system is transformed to the robot base coordinate system to obtain the initial three-dimensional spatial deviation ΔP_visual_base: ΔP_visual_base=R_base_cam*ΔP_cam The specific method is as follows: 1. Calculate the normalized planar coordinate transformation of feature points in the camera coordinate system: Based on the pinhole camera model, the relationship between the projection of a 3D point P_c=[X_c, Y_c, Z_c]^T onto pixel coordinates p=[u,v]^T is as follows: s*[u,v,1]^T=K*[X_c,Y_c,Z_c]^T Where s is the scaling factor (usually Z_c). Expanding it and ignoring the homogeneous terms, we get: u = fx * (X_c / Z_c) + cx v=fy*(Y_c / Z_c)+cy 2. By differentiating or calculating the deviation of the above formula, the relationship between Δp_image and ΔP_cam can be established: Δu = fx * (ΔX_c / Z_c - X_c * ΔZ_c / Z_c²) ≈ fx * (ΔX_c / Z_c) / / Assuming the influence of depth change ΔZ_c is small or treated separately Av = fy * (AY_c / Z_c - Y_c * AZ_c / Z_c2) ~ fy * (AY_c / Z_c) This is a common first order approximation. From which we can solve the offsets in X and Y directions in camera coordinate system: AX_c ~ (Au * Z_c) / fx AY_c ~ (Av * Z_c) / fy 3. Handle the depth direction offset (AZ_c): For seam tracking, the depth change AZ_c is also important. It cannot be directly obtained from Au, Av of a single frame image. Common methods are: Geometric model method: for V groove, there is a certain triangular relationship between the change of groove width in image AW_image and the depth change AZ_c.

[0030] Structured light / laser method: directly measure the depth value change between two frames.

[0031] Multi-feature point method: estimate by image motion of multiple feature points.

[0032] Suppose we get AZ_c through some method (denoted as function g (Ap_image, model parameters)).

[0033] Finally, we get the three-dimensional offset vector in the camera coordinate system: AP_cam = [AX_c, AY_c, AZ_c]T Through hand-eye calibration, we get the rigid transformation matrix H_cam_base from the camera coordinate system to the robot base coordinate system.

[0034] [R_base_cam t_base_cam] Where R_base_cam is a 3x3 rotation matrix, and t_base_cam is a 3x1 translation vector.

[0035] Convert the offset AP_cam in the camera coordinate system to the base coordinate system: Since AP_cam is a free vector (representing the direction and size of the offset, not the position of a point), it is only affected by rotation, not translation. Therefore, the conversion formula is: AP_visual_base = R_base_cam * AP_cam At this point, AP_visual_base is a three-dimensional offset vector expressed in the robot base coordinate system.

[0036] Step three: tool coordinate system direction compensation: To further improve the accuracy of the welding gun posture adjustment, the direction decomposition and synthesis of ΔP_visual_base are performed in combination with the rotation matrix R_nominal of the current theoretical pose of the robot, and the three-dimensional spatial position deviation ΔP_visual=[Δx_v,Δy_v,Δz_v]^T used for trajectory correction is finally output.

[0037] S2: Force sensing thread: read force sensor data at a frequency of 500 Hz, after filtering and compensation, calculate the force deviation ΔP_force and ΔO_force that need to be compliant according to the preset force control direction (such as the welding gun axial and radial direction). The specific method is: Read the original signal F_raw = [Fx,Fy,Fz,Mx,My,Mz]^T of the force sensing unit, after low-pass filtering and gravity compensation, get the net force / torque F_contact caused by contact. By constructing a virtual spring damping model, the contact force is mapped to the "embedding" depth or posture deviation of the welding gun end in the contact normal direction. For example, for the contact force F_n perpendicular to the weld direction, an equivalent position compensation amount Δd_force can be calculated: Δd_force = K_f * F_n (when |F_n|>F_threshold) Where K_f is the force compliance coefficient (adjustable parameter matrix), and F_threshold is the force perception threshold. The compensation amount Δd_force combined with the current welding gun posture can be further decomposed into position and attitude deviation ΔP_force and ΔO_force in the robot base coordinate system. For example, set the radial contact force threshold F_threshold=5N, when the radial force is detected to exceed this threshold, calculate a yield offset according to the compliance coefficient.

[0038] S3: Fusion decision thread (core): runs at a frequency of 100 Hz. Get the latest ΔP_visual, ΔP_force, ΔO_force. Calculate the contrast of the current image features as σ_v, and calculate the variance of the force signal in the last 100 ms as σ_f. A simple fuzzy inference decides W_v and W_f: if σ_v is low (feature blur), reduce W_v; if |F_contact| is large and continuous, increase W_f. Substitute the fusion formula to calculate ΔX_correct. The specific method is: An adaptive weighted fusion function is designed to fuse the visual deviation ΔP_visual and force feedback deviation ΔP_force, ΔO_force to generate the final robot end pose correction amount ΔX_correct. The fusion function not only considers the size of the deviation amount, but also considers the current welding stage (such as arc striking, normal welding, and arc collecting) and sensor confidence. The mathematical expression is as follows: ΔX_correct=W_v(t,σ_v)·Φ(ΔP_visual)+W_f(t,σ_f)·Ψ(ΔP_force, ΔO_force) Wherein: Φ(·) and Ψ(·) are respectively the pre-processing functions of visual and force deviation (such as amplitude limiting and smoothing).

[0039] W_v and W_f are time-varying, adaptive weight coefficients related to sensor confidence, satisfying W_v+ W_f=I (unit matrix). σ_v and σ_f are respectively the clarity index of the visual feature point extraction at the current time and the noise level index of the force signal.

[0040] t represents time or welding progress. In the seam tracking dominant stage (such as clear features), W_v increases; in the contact force sensing sensitive stage (such as large local deformation of the workpiece), W_f increases.

[0041] S4: Real-time trajectory superposition and execution: superimpose the calculated correction amount ΔX_correct on the current preset theoretical trajectory X_nominal(t) executed by the robot at a high control frequency (such as ≥100Hz) to generate the real-time corrected target trajectory X_target(t): X_target(t) =X_nominal(t) +ΔX_correct(t) Through the servo interface of the robot controller, it is issued to the joint drive of the robot. The robot control unit drives the welding robot to track X_target(t), and the corrected trajectory data is fed back to the S1 step for updating the theoretical image coordinate calculation at the next time, forming a closed-loop control.

[0042] Wherein, X_nominal(t) is the theoretical motion trajectory of the preset robot end effector (welding torch). It is a function of time t or progress s, which completely describes the position (x, y, z) and attitude (Rx, Ry, Rz, usually represented by Euler angles or quaternions) of the robot welding torch in three-dimensional space in order to complete a weld seam in ideal conditions (i.e. the workpiece completely conforms to the CAD model, clamping zero error, no welding deformation).

[0043] Mathematical expression: X_nominal(t) = [x_nom(t), y_nom(t), z_nom(t), a_nom(t), b_nom(t), g_nom(t)]T Where the first three components are positions, and the last three components are attitude angles.

[0044] The preset theoretical trajectory X_nominal(t) is generated by the following steps: 1. Offline programming: Based on the CAD three-dimensional model of the marine seat skeleton, the initial trajectory program X_program(t) of the welding gun moving along all the weld center lines is planned in the robot offline programming software, and the welding parameters of each point are determined.

[0045] 2. Actual workpiece calibration: On the welding station, the actual object is scanned by a high-precision laser scanner installed at the end of the robot, and the actual point cloud data is obtained. Through the point cloud registration algorithm (such as ICP algorithm), the space transformation matrix T_correction between the actual workpiece coordinate system and the CAD model coordinate system is calculated.

[0046] 3. Trajectory preset: The space transformation matrix T_correction is applied to the initial trajectory program X_program(t), and the coordinate transformation of all path points is performed, so as to obtain the preset theoretical trajectory X_nominal(t) for the current specific workpiece, which has compensated the initial static error, and download it to the robot controller.

[0047] After the above preset is completed, the welding and subsequent real-time correction process can be started. The real-time correction system of the present application is based on the high-precision preset trajectory X_nominal(t), and the dynamic error caused by thermal deformation, arc force, and small amplitude motion during welding is compensated in a secondary closed loop, so as to realize high-precision welding throughout the process.

[0048] Although embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and alterations can be made thereto without departing from the principles and spirit of the present application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A real-time correction system for welding trajectory of marine seat skeleton based on machine vision and mechanical feedback, characterized in that, Comprising: a robot control unit, a welding unit, a vision sensing unit, a force sensing unit, and a trajectory correction module; the vision sensing unit and the force sensing unit are mounted on the robot end effector, respectively used for collecting weld seam image data and force and torque data between the welding torch and the workpiece; the trajectory correction module runs on the robot control unit, configured to perform the following steps: a vision processing step: extracting the actual image coordinates of the weld seam feature points from the real-time image, comparing with the theoretical image coordinates to obtain the image plane deviation, and converting it to the first spatial position deviation ΔP_visual in the robot base coordinate system; a force signal processing step: processing the signals of the force and torque sensors to obtain the net force and torque caused by contact, and calculating the second spatial position deviation ΔP_force and attitude deviation ΔO_force according to the force compliance model; a fusion correction step: through an adaptive weighted fusion function, the first spatial position deviation ΔP_visual and the second spatial position deviation ΔP_force and attitude deviation ΔO_force are fused to generate the real-time trajectory correction amount ΔX_correct of the robot end effector; the adaptive weighted fusion function is: ΔX_correct=W_v(t,σ_v)·Φ(ΔP_visual)+W_f(t,σ_f)·Ψ(ΔP_force, ΔO_force) where W_v and W_f are time-varying adaptive weight coefficients, and W_v + W_f = I, I is the unit matrix; σ_v and σ_f are the visual feature clarity index and the force signal noise level index respectively; Φ(·) and Ψ(·) are pre-processing functions; a trajectory execution step: superimposing the real-time trajectory correction amount ΔX_correct on the preset theoretical trajectory X_nominal(t) to obtain the real-time target trajectory X_target(t) and driving the robot to execute.

2. The real-time correction system for welding trajectory of marine seat framework based on machine vision and mechanical feedback according to claim 1, characterized in that: In the vision processing step, a deep learning-based image processing model is used to extract weld seam feature points, and the model is trained for the joint form of the marine seat skeleton.

3. The system of claim 1, wherein, In the force signal processing step, the force compliance model is expressed as: Δd_force = K_f * F_n, where K_f is the force compliance coefficient matrix, F_n is the normal contact force, and Δd_force is the equivalent position compensation.

4. The system of claim 1, wherein, The adaptive weight coefficients W_v and W_f are dynamically adjusted by a fuzzy logic controller or a neural network model, and the basis for adjustment at least includes σ_v, σ_f, and a preset process rule.

5. The system of claim 4, wherein, The preset process rule includes: when the absolute value of the net force and torque exceeds a set threshold, the weight of W_f is increased; when the visual feature clarity is lower than a set threshold, the weight of W_v is reduced.

6. The system of claim 1, wherein, The trajectory correction module further includes a trajectory prediction unit for predicting the workpiece deformation trend based on historical correction data and pre-adding the predicted offset to the real-time trajectory correction amount ΔX_correct.

7. A method for real-time correction of a trajectory for welding of a marine seat framework, characterized in that, The method is applied to the system as claimed in any one of claims 1-6, comprising: The real-time image of the weld seam area is acquired by the visual sensing unit, and the real-time force and torque signals between the welding torch and the workpiece are acquired by the force sensing unit; The real-time image is processed to obtain a first spatial position deviation ΔP_visual; The real-time force and torque signals are processed to obtain a second spatial position deviation ΔP_force and an attitude deviation ΔO_force; An adaptive weighted fusion algorithm is used to fuse ΔP_visual, ΔP_force and ΔO_force, and to calculate a real-time trajectory correction amount ΔX_correct; The current welding trajectory of the robot is adjusted according to the real-time trajectory correction amount ΔX_correct.

8. The method of claim 7, wherein, The adaptive weighted fusion algorithm is represented as: ΔX_correct = W_v(t, σ_v)·Φ(ΔP_visual) + W_f(t, σ_f)·Ψ(ΔP_force, ΔO_force) Wherein, W_v and W_f are weight coefficients dynamically adjusted according to the sensor confidence and the welding stage.

9. The method according to claim 7 or 8, characterized in that, When adjusting the welding trajectory, the real-time trajectory correction amount ΔX_correct is superimposed on the preset theoretical trajectory at a control frequency of no less than 100 Hz.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by the processor, implements the steps of the method of any one of claims 7-9. The program, when executed by the processor, implements the steps of the method of any one of claims 7-9.

Images