Design of a Visual Alignment System for High-Concentrating Photovoltaic Panels

**Abstract**

Photovoltaic power generation is an effective approach to address energy challenges and achieve sustainable energy development. However, conventional photovoltaic technologies suffer from relatively low photoelectric conversion efficiency and high generation costs. Concentrating photovoltaic technology, regarded as the third generation of photovoltaic power generation, offers higher conversion efficiency and lower costs by concentrating sunlight onto small, high-efficiency solar cells. In concentrating photovoltaic modules manufactured using encapsulation integration technology, the photoelectric conversion efficiency largely depends on the alignment precision between the Fresnel lenses on the upper panel and the solar cell components on the lower panel of the photovoltaic module. To meet the requirement of precision alignment between the upper and lower panels of the photovoltaic module, this thesis investigates and designs a visual alignment system for a 750x concentrating photovoltaic panel. By leveraging machine vision technology, the system acquires the position, orientation, and relative deviation of the upper and lower panels, thereby guiding an alignment platform to perform correction tasks. The main contributions of this work are as follows: (1) A multi-camera array vision scheme was designed, the entire visual alignment system was modularized, and visual hardware was selected based on accuracy requirements and practical conditions; (2) After comparing several circular Mark point detection algorithms, I selected a shape-based template matching algorithm for localizing Mark points, and evaluated its stability and real-time performance; (3) I designed a calibration gauge suitable for calibrating the image coordinate systems of the cameras in this system and proposed a calibration method based on this gauge. I accomplished the calibration among the four camera image coordinate systems by developing dedicated software; (4) I first calibrated the alignment platform using a three-point calibration method with custom software. When the alignment accuracy remained unsatisfactory and errors were difficult to compensate, I completed the platform calibration through an experimental calibration method. Ultimately, the positioning algorithm and calibration data were integrated and embedded into the visual positioning system for the solar panels. The concentrating photovoltaic modules aligned using this system achieve the required alignment accuracy. The system has entered the trial production stage for concentrating photovoltaic modules.

Keywords: concentrating photovoltaic technology; visual alignment; Mark point positioning; multiple camera calibration; alignment platform calibration

Chapter 1 Introduction

1.1 Research Background and Significance

Energy drives the development of human society and the growth of the world economy, serving as the material foundation for human survival. Coal, petroleum, and natural gas are currently the primary energy sources consumed by humanity. However, these fossil fuels are non-renewable resources with finite reserves that cannot guarantee an unlimited supply. Their continued consumption will inevitably lead to energy depletion. Additionally, the extraction and utilization of fossil fuels cause a series of environmental pollution problems. For instance, coal mining loosens the earth’s surface, risking collapse; mine water discharge seriously contaminates groundwater resources and soil; and the direct combustion of fossil fuels produces large amounts of carbon dioxide and other greenhouse gases, leading to the greenhouse effect, global warming, and other severe consequences. These not only harm the balance of natural ecosystems but also threaten human survival. Therefore, given the current growth in energy demand and severe pollution from fossil fuels, developing new and clean energy sources and researching technologies for their utilization hold significant practical importance.

Solar energy, as a renewable energy source, continuously provides light and heat, is safe to use, and does not pollute the environment, demonstrating broad prospects for development and utilization. The primary method of utilizing solar energy is through solar power generation. Photovoltaic power generation collects sunlight on solar cells and utilizes the photovoltaic effect to convert light energy into electrical energy. With its good safety performance and high flexibility, photovoltaic power generation is currently the main method for generating electricity from solar energy.

Traditional photovoltaic technology uses large-area silicon-based cells for power generation, which has a low solar energy utilization rate. The extensive use of silicon raw materials makes it relatively expensive, and the cost of power generation is far higher than the market price of traditional power generation. Concentrating photovoltaic technology is the third-generation photovoltaic technology. It uses concentrating elements to gather large areas of sunlight onto small solar cells, increasing the incident light intensity per unit area of the solar cell and thus improving photoelectric conversion efficiency. The cost of concentrating elements is relatively low, and because the solar cell area is smaller, the reduced use of photovoltaic cell materials also greatly lowers the cost of concentrating photovoltaic power generation.

Concentrating photovoltaic systems are classified by concentration ratio into low-concentration systems (<100x), medium-concentration systems (100-300x), and high-concentration systems (>300x). A concentrating photovoltaic system primarily consists of a concentrator, solar cells, cooling components, and a tracking control system. The concentrator, which gathers sunlight onto the solar cells, is the most important component, determining the overall system performance. Concentrators can be classified as refractive or reflective based on optical principles.

The manufacturing trend for concentrating photovoltaic modules is to adopt encapsulation integration technology, encapsulating the concentrator, solar cells, and heat-dissipation substrate into a single module that is unaffected by external environmental conditions, thereby providing protection against rain, wind, and sand. Since the power generation efficiency of a concentrating photovoltaic system largely depends on the total amount and intensity of sunlight focused onto the solar cells, the manufacturing process imposes strict requirements on the installation accuracy of the concentrators and solar cells.

Currently, few domestic manufacturers independently develop production lines for concentrating photovoltaic modules; most rely on imported foreign equipment. Therefore, researching a precision solar panel visual alignment system to achieve precise alignment and installation of concentrators and solar cells in concentrating photovoltaic modules has important practical significance for the development of concentrating photovoltaic technology.

1.2 Domestic and International Research Status

1.2.1 Research Status of Machine Vision

Machine vision technology refers to the technology of using machines to replace human eyes for visual functions in industry. With the increasing demand for product quality records and traceability documentation, machine vision has become an indispensable key technology in industrial automation and intelligent processes. A machine vision system captures an image of a real object using light sources, lenses, and industrial cameras. The image is analyzed and processed using image processing algorithms on a computer or smart camera, and the extracted information is used to control and guide mechanical devices. Machine vision is a multidisciplinary technology involving optics, image processing, motion control, and other fields. Compared with computer vision, machine vision emphasizes solving practical industrial vision problems on production lines and requires significant engineering experience in vision projects. Machine vision systems must adapt to harsh industrial environments, with high stability, precision, fast processing speeds, and good real-time performance.

The adoption of machine vision for industrial applications is driven by several advantages: precision, as high-resolution image acquisition equipment far exceeds human visual accuracy; non-contact operation, avoiding impact or damage to target objects; high speed, through high-frame-rate cameras and high-performance processors; stability, avoiding quality fluctuations caused by human factors and enabling continuous long-duration operation; and extended vision, recognizing a broader spectral range than the human eye, including infrared, ultraviolet, and X-ray applications.

Machine vision has developed for over sixty years, driven by market demand and core technological advances. Currently, industrial fields applying machine vision technology include synthetic materials, optics and precision engineering, manufacturing, packaging, chemicals, semiconductors, healthcare, printing, new energy, wood, machinery, transportation, and more. The functions of machine vision can be categorized into recognition, positioning, inspection, and measurement.

Recognition refers to identifying different objects based on special features such as characters, barcodes, or shapes. Positioning involves obtaining specific positional information of a measured object to guide mechanical devices for subsequent processing or assembly. Inspection checks the integrity of an object or determines the presence of defects. Measurement measures geometric parameters of an object to ensure they remain within allowable tolerances.

1.2.2 Research Status of Alignment Systems

Alignment systems are not limited to solar panel alignment applications; they also play important roles in photovoltaic cell screen printing, LCD alignment and lamination, CD graphic printing, electronic component mounting, and other manufacturing processes. In alignment applications with high precision requirements, machine vision technology is used to obtain product position information and guide the alignment mechanism for correction.

For example, DEK’s Houyi series screen-printing platform uses a vision system equipped with 4 CCD cameras to achieve alignment by finding chip edges and substrate fiducial marks. The system handles substrates between 125 mm × 125 mm and 165 mm × 165 mm, with alignment accuracy up to 12.5 μm and productivity up to 1350 boards per hour. The EKRA SERIO 8000 series fully automatic screen-printing system supports large substrates up to 1000 mm × 610 mm. Its patented EVATM vision calibration system uses two high-resolution CCD cameras forming a camera module to capture images of the stencil and substrate, calculating alignment information from fiducial mark positions and spacing, with alignment accuracy up to 12.5 μm and a cycle time of approximately 15 seconds.

In recent years, numerous domestic experts and scholars have also studied alignment systems. Some have established error models for parallel platforms, applied Monte Carlo methods for accuracy synthesis, and analyzed systematic and random errors affecting image positioning, ultimately compensating for printing equipment accuracy. Others have designed automatic alignment systems for solar cell screen-printing equipment and successfully applied them. Some have analyzed the two main visual alignment methods used in LTCC printing machines, comparing them in terms of printing accuracy and manufacturing cost. Others have proposed calibration methods for FPC automatic feeding machines, developed vision inspection alignment systems, and achieved correction accuracy within ±20 μm. Some have developed LCD alignment lamination systems using LabVIEW to adjust and bond position deviations between tablet LCDs and battery housings.

1.3 Project Source

This project originates from the collaborative project “Solar Module Visual Lamination System” between South China University of Technology and an industrial robotics company in Guangdong Province.

1.4 Main Research Content

This paper focuses on achieving precise alignment between the Fresnel lenses on the upper panel and the solar cell components on the lower panel of concentrating photovoltaic panels to enhance photoelectric conversion efficiency. The work is organized into six chapters. Chapter 1 introduces the research background, significance, and domestic and international research status. Chapter 2 studies the alignment mechanism of the vision alignment system, including the concentrating photovoltaic module, the actuator (alignment platform), the overall system scheme, and the selection of machine vision hardware. Chapter 3 investigates the visual positioning algorithm for the solar panels, determining the shape-based template matching algorithm, extracting the geometric features of the Mark points, and evaluating the algorithm. Chapter 4 focuses on the calibration of the four camera image coordinate systems, including the design of a calibration gauge, the calibration algorithm among the cameras, and the calibration software. Chapter 5 covers the calibration of the alignment platform, including kinematic modeling, three-point mathematical calibration, and experimental calibration. Chapter 6 presents the integrated system operation, analysis of the results, and conclusions.

Chapter 2 Study of the Alignment Mechanism of the Visual Alignment System

2.1 Introduction to the Concentrating Photovoltaic Module

The aligned product in this research is a refractive-type concentrating photovoltaic module, as shown in the manuscript. The module consists of three parts: the upper panel, the side frame, and the lower panel. The upper panel is a refractive lens plate that primarily functions to concentrate sunlight. It contains multiple flat-plate point-focusing Fresnel lenses. The lower panel is a solar cell panel, with its main body made of tempered glass, on which the same number of solar cell components as the Fresnel lenses are distributed. Each solar cell component consists of a bare cell and a cell substrate, with the bare cell soldered at the center of the substrate. An optical rod is typically installed on each solar cell component to perform secondary concentration of the sunlight and to increase the acceptance angle, thereby reducing the tolerance required for the tracking control system.

The side frame is positioned between the upper and lower panels, serving protective and supportive functions. It provides an appropriate focal length for the Fresnel lenses and creates a sealed space to minimize interference from rain, wind, and sand during the concentration and photoelectric conversion processes. The Fresnel lenses in the upper panel have a concentration ratio of 750x, which classifies them as high-concentration concentrators. The upper panel dimensions are 830 mm × 630 mm × 4 mm, while the lower panel dimensions are 830 mm × 630 mm × 3.2 mm, with each panel weighing 3–5 kg.

The alignment objective is to ensure that the focal point of each Fresnel lens in the upper panel falls precisely onto the corresponding bare cell of the solar cell component in the lower panel. Since the upper panel is manufactured by molding, this method can only guarantee the dimensional accuracy of individual Fresnel lenses and the spacing between lenses, but cannot guarantee the dimensional accuracy of the outermost lenses relative to the upper panel border. Therefore, although the upper and lower panels have the same planar dimensions, aligning the edges of the panels does not guarantee that each lens focal point will be aligned with its corresponding bare cell. This would severely reduce the photoelectric conversion efficiency of the module, hence the introduction of a visual alignment system to accomplish this alignment process.

2.2 Introduction to the Actuator of the Visual Alignment System

2.2.1 Introduction to the Concentrating Photovoltaic Module Production Line

To improve production efficiency and product quality, concentrating photovoltaic modules are manufactured on an automated production line. The line primarily consists of industrial robots, conveyor belts, a dispensing machine, and an alignment lamination mechanism. Industrial robots and conveyor belts handle the loading and unloading of solar panels. The dispensing machine applies adhesive around the borders of the upper and lower panels. The alignment lamination mechanism completes the alignment of the panels and their lamination with the side frame. It is the most important part of the automated production line for concentrating photovoltaic modules, playing a decisive role in the final quality of the product.

The alignment lamination mechanism comprises a lamination table and an alignment platform. The lamination table is equipped with suction cups on its upper surface. When the upper panel is fed, it is held onto the lower surface of the lamination table by vacuum. The lower panel is placed directly onto the alignment platform when fed.

The production flow is as follows: (1) Two industrial robots take the upper and lower panels from wooden crates and place them onto their respective conveyor belts; (2) The conveyor belts transport the panels to the dispensing station, where adhesive is applied around the borders of both panels; (3) Two other robots remove the panels from the dispensing machine and simultaneously load them into the alignment lamination mechanism, with the lamination table holding the upper panel and the alignment platform carrying the lower panel; (4) After the robots retract, the vision alignment system calculates position deviations through image acquisition and processing, converts the deviations into motor pulse values via calibration algorithms, and drives the alignment platform to translate and rotate the lower panel for correction; (5) A robot places the side frame onto the lower panel; (6) The lamination table moves toward the alignment platform, pressing the upper panel, side frame, and lower panel together. Curing lights irradiate the adhesive to cure it. The robot then removes the laminated module and places it onto the finished product conveyor.

2.2.2 Analysis and Introduction of the Alignment Platform

The alignment platform, one of the primary research objects of this thesis, is the main actuator for the panel alignment process. The platform consists of a fixed platform and three actuator motor units. Each motor is a ball-screw-driven motor with a push rod attached. Opposite to the motors are spring-loaded pull-rod mechanisms with push rods. The fixed platform supports the lower panel during alignment. During alignment, a vacuum device on the fixed platform lifts the lower panel slightly to reduce friction. The push rods from the motors and the spring mechanisms fix the lower panel to prevent it from being blown off or drifting. The motors are then driven to move the push rods, which translate and rotate the lower panel.

The alignment platform must provide X-translation, Y-translation, and angular rotation θ, making it a planar three-degree-of-freedom mechanism. Planar three-DOF alignment mechanisms can be classified as serial or parallel types. Serial mechanisms are common, with independent motions controlled by separate motors, simplifying control and error compensation. However, serial structures tend to be bulky, causing error accumulation and instability during high-speed start-stop cycles. Additionally, ordinary motors struggle to achieve small rotation resolutions, and high-resolution motors increase cost. Parallel alignment mechanisms adopt a coplanar design philosophy, simplifying the structure and reducing platform thickness, thereby eliminating some errors and improving alignment accuracy. Parallel platforms can readily achieve high-resolution rotation and are widely used in precision alignment applications for planar products.

The alignment platform used in this project is essentially a parallel mechanism. Let the line connecting motors U and V be the X-axis, and the line through motor W perpendicular to the X-axis be the Y-direction. When motors U and V are stationary and motor W moves, the platform moves in the X direction. When motor W is stationary and motors U and V move by equal amounts, the platform moves in the Y direction. When all three motors move, with U and V having equal displacement, the platform translates in the XY plane. When U and V have unequal displacement, the platform rotates in the XY plane, regardless of whether W moves.

2.3 Overall Scheme of the Visual Alignment System

2.3.1 Vision Scheme

To achieve precise alignment between the upper and lower solar panels, a vision scheme that can acquire precise position information of both panels is required. Visual alignment typically relies on fiducial Mark points as alignment references. In this system, Mark points serve as references for lens and solar cell component positions, and their manufacturing precision must be high so that by acquiring and localizing the Mark points, the position and orientation of the panels can be derived, and their relative deviations calculated.

The position and orientation of each panel are determined primarily by two diagonally positioned Mark points. For the upper panel, the Mark points are the smallest concentric teeth within the first-row, eleventh-column and ninth-row, second-column Fresnel lenses. For the lower panel, the Mark points are circles printed inside black frames at the diagonal boundaries of the panel.

Because the panel dimensions are 830 mm × 630 mm, using a single industrial camera to image both Mark points simultaneously would require a large field of view, reducing Mark point resolution. To achieve high-precision positioning with a single camera would demand an ultra-high-resolution camera, which is cost-prohibitive. Considering the limited installation space and working distance constraints, a multi-camera array design for large field-of-view image acquisition was adopted. For each panel, two cameras image its two Mark points, resulting in a total of four industrial cameras organized into upper and lower camera groups for capturing the Mark point images.

2.3.2 Control Scheme

The visual alignment system operates within the alignment lamination mechanism, primarily performing position correction and calibration between the two solar panels. The final alignment deviation must be less than 0.15 mm. The system consists of motion control and machine vision components. The industrial control computer controls the camera groups for image acquisition, processes the images to compute panel position information, and then uses calibration algorithms to calculate motor pulse values via a motion control card, which drives the actuators for position correction. After the robots place the upper and lower panels, the vision system performs image acquisition and Processing steps to obtain the position deviation. The industrial computer then computes the motor pulses required for the alignment platform to correct the position of the lower panel, iterating until the desired alignment accuracy is achieved.

2.4 Machine Vision Hardware Selection

Machine vision hardware includes industrial cameras, lenses, and illumination devices. These components capture images for subsequent processing.

Industrial camera. The camera converts light focused on the sensor into an image. Industrial cameras feature superior image stability, transmission speed, and noise immunity. The sensor is the most critical component. CCD sensors offer advantages in sensitivity, resolution, and image quality, while CMOS sensors excel in cost, power consumption, and integration. Resolution determines the detail level in an image. The required camera resolution \( R_c \) is calculated as:

\[
R_c = \frac{FOV}{R_f / N_f}
\]

where \( FOV \) is the field of view, \( R_f \) is the feature resolution, and \( N_f \) is the number of pixels representing the feature resolution. In this system, the field of view is 8 mm × 6 mm, the visual precision requirement is 5 μm, and \( N_f = 1 \). The minimum resolution was calculated as 1600 × 1200 pixels.

Given the static image acquisition requirement, four Basler acA1600-20gm cameras with a resolution of 1626 × 1263 pixels, a frame rate of 20 fps, monochrome output, and Gigabit Ethernet interface were selected.

Lens. The lens gathers light onto the sensor. Among several lens types, telecentric lenses eliminate the perspective distortion inherent in standard fixed-focal-length lenses. Telecentric lenses maintain a constant magnification over a range of object distances, producing parallel projections essential for the multi-camera calibration in this system. After evaluating the field of view and installation space, a telecentric lens with 0.8x magnification and 65 mm working distance was chosen. Given the limited installation space below the platform, a right-angle prism was introduced to deflect the optical path by 90 degrees, enabling side-mounted camera installation. All four lenses are identical telecentric lenses to satisfy parallel-projection imaging requirements.

Illumination device. Proper illumination enhances the important features of the target while suppressing unwanted features, yielding high-contrast images. LED light sources are widely used because of their long lifetime, controllable brightness, and low power consumption. Initial testing used four white point light sources with front lighting. Although the upper panel Mark points showed clear contours, the lower panel Mark points suffered from strong specular reflection on the smooth glass surface, resulting in poor contrast. A more effective solution was achieved using two high-power red ring lights placed above the panels, illuminating downward. Red light exhibits the strongest penetration through the two stacked PV panels. The resulting images showed significantly improved contrast for both upper and lower Mark points, with clear contours.

Figure 2-21 in the original manuscript shows the installation positions of the machine vision hardware components within the alignment lamination mechanism.

Chapter 3 Research on Visual Positioning Algorithm for Solar Panels

3.1 Determination of the Positioning Algorithm

In solar panel visual alignment, the position information of the panel is determined by locating its Mark points. The Mark points in this project are circular. Various algorithms exist for locating circular Mark points, including Hough transform circle detection, edge-detection fitting, Radon transform circle detection, and template matching.

Hough transform circle detection is an extension of the Hough transform. It maps detection problems from image space to parameter space, where the parameters of the geometric shape are determined by finding accumulation points in the parameter space.

Edge-detection fitting primarily uses Blob analysis for coarse localization, searches for and labels Mark point regions based on connected component features, and then extracts edges and fits them to locate the Mark point.

Radon transform circle detection uses the Radon transform to detect lines in parameter space. The distance between any two parallel lines tangent to a circle equals the circle’s diameter. The line midway and parallel to these tangents passes through the circle’s center. By finding multiple such midlines and intersecting them, the circle’s center is obtained.

Template matching uses a template to search the image, computing similarity between the template and the image to achieve localization. It is broadly classified into intensity-based matching and shape-based matching. The former relies on image gray values as similarity measures, while the latter uses pixel point coordinates and direction vectors, edges and edge vectors, etc.

A critical aspect of this system is that Mark points are sometimes subject to contamination or occlusion by adhesives applied near the edges, and occasionally a Mark point may be partially absent when the panel is not fully within the field of view. These practical challenges demand a localization algorithm that is robust and precise. After evaluating the aforementioned algorithms, I selected the shape-based template matching algorithm for its robustness against illumination changes, occlusions, and deformations. All algorithms in this work were developed on the Halcon platform.

3.2 Geometric Feature Extraction of Mark Points

Before constructing the shape-based template, I extracted the geometric feature of the Mark point, i.e., its circular contour, from representative images with complete Mark points. The extraction process comprised region of interest (ROI) creation, image binarization, target region labeling, and edge fitting.

ROI creation. Because the Mark point occupies only a small portion of the image, creating an ROI containing only the Mark point reduces the amount of data, improving processing speed and accuracy. I manually created ROIs around the Mark points for both the upper and lower panel images.

Image binarization. The gray-level distribution between the Mark point and the background is distinct, allowing global thresholding. I employed Otsu’s method, which maximizes the inter-class variance to select the optimal threshold. Let the image size be \( M \times N \), and \( n_i \) be the number of pixels with gray level \( i \). The probability of gray level \( i \) is:

\[
p_i = \frac{n_i}{MN}
\]

The optimal threshold \( k \) separates the image into two classes \( T_1 \) (gray levels 0 to k) and \( T_2 \) (gray levels k+1 to 255). The probabilities of the two classes are:

\[
P_1(k) = \sum_{i=0}^{k} p_i, \quad P_2(k) = \sum_{i=k+1}^{255} p_i
\]

The class mean gray values are:

\[
f_1(k) = \frac{1}{P_1(k)} \sum_{i=0}^{k} i p_i, \quad f_2(k) = \frac{1}{P_2(k)} \sum_{i=k+1}^{255} i p_i
\]

The global mean gray value is:

\[
f_g = \sum_{i=0}^{255} i p_i = P_1(k) f_1(k) + P_2(k) f_2(k)
\]

The between-class variance is:

\[
\sigma^2 = P_1(k)(f_1 – f_g)^2 + P_2(k)(f_2 – f_g)^2
\]

Otsu’s algorithm selects the threshold \( k \) that maximizes \( \sigma^2 \). Application of this threshold produced binary images for both panels.

Target region labeling. After binarization, the image may contain interfering regions, and the Mark point region may contain holes. I first applied a hole-filling algorithm to eliminate internal pores. Then, using an 8-connected depth-first search, I labeled all connected components. The Mark point region has a relatively large area compared with interfering regions. Using area thresholds \( A_{min} \) and \( A_{max} \) estimated from the camera resolution, field of view, and actual Mark point diameter, I selected the Mark point region.

Edge fitting. After obtaining the Mark point region, morphological operations extracted its boundary. Dilation expands the region, while erosion shrinks it. The boundary is obtained by subtracting the eroded region from the dilated region:

\[
X \oplus B = \{ p : p = x + b, x \in X, b \in B \}
\]

\[
X \ominus B = \{ p : p = x + b, b \in B \}
\]

The boundary comprises numerous points; however, only the radius and center of the circular Mark point are needed. I performed circle fitting to the boundary points. The standard least-squares circle fitting minimizes the sum of squared distances from the boundary points to the fitted circle:

\[
\epsilon^2 = \sum_{i=1}^{n} \left( (r_i – \alpha)^2 + (c_i – \beta)^2 – \rho^2 \right)
\]

where \((\alpha, \beta)\) is the center, \(\rho\) is the radius, and \((r_i, c_i)\) are boundary points. Because boundary irregularities (convexities and concavities) can bias the fit, I introduced a Tukey weighting function to reduce the influence of outliers:

\[
\omega(\delta) =
\begin{cases}
\left(1 – \left(\frac{\delta}{\tau}\right)^2\right)^2, & |\delta| \le \tau \\
0, & |\delta| > \tau
\end{cases}
\]

where \(\tau\) is the clipping factor and \(\delta\) is the distance from a boundary point to the fitted circle. By iteratively reweighting the least-squares fit, a robust circular contour was extracted, coinciding well with the actual Mark point.

3.3 Shape-Based Template Matching Algorithm

After extracting the Mark point geometric features, I constructed a shape-based template. The shape template is defined as a point set \( p_i = (r_i, c_i)^T \) with direction vectors \( d_i = (t_i, u_i)^T \). The image is represented by a point set \( q = (r, c)^T \) with direction vectors \( e_{r,c} = (v_{r,c}, w_{r,c})^T \). Using the linear transformation model \( p_i’ = A p_i \) and \( d_i’ = (A^{-1})^T d_i \), the similarity measure is the normalized sum of dot products of direction vectors:

\[
s = \frac{1}{n} \sum_{i=1}^{n} \frac{d_i’^T e_{q+p_i’}}{\|d_i’\| \|e_{q+p_i’}\|} = \frac{1}{n} \sum_{i=1}^{n} \frac{t_i’ v_{r+r_i’, c+c_i’} + u_i’ w_{r+r_i’, c+c_i’}}{\sqrt{t_i’^2 + u_i’^2} \sqrt{v_{r+r_i’, c+c_i’}^2 + w_{r+r_i’, c+c_i’}^2}}
\]

Because the direction vectors are normalized, the similarity is unaffected by illumination intensity. However, various imaging conditions such as contrast reversal or partial occlusions require different similarity measures. For general robustness, I chose a similarity measure that tolerates local contrast reversals:

\[
s_3 = \frac{1}{n} \sum_{i=1}^{n} \frac{|d_i’^T e_{q+p_i’}|}{\|d_i’\| \|e_{q+p_i’}\|}
\]

A threshold \( s_{min} \) of 0.5 was used to terminate the search early for unlikely positions, improving speed. To accelerate the search, I used an image pyramid. The template and image are repeatedly reduced by a factor of 2 using a 2×2 mean filter, forming a pyramid structure. Search begins at the top (lowest resolution) layer to find potential matches and refines them at progressively higher-resolution layers, ultimately locating the object at full resolution. Each additional pyramid level provides up to a 16× speed improvement. However, too many levels degrade image information; I empirically set the pyramid to 5 levels because at level 6 the Mark point shape becomes too indistinct for reliable detection.

3.4 Evaluation of the Mark Point Positioning Algorithm

Stability. I tested the algorithm on various degraded images, including low-contrast images, partially missing Mark points, and images with interference and occlusion. In all cases, the algorithm successfully located the Mark point, demonstrating robustness. The figures in the manuscript show representative matching results under these challenging conditions.

Runtime. After constructing the shape templates, I saved them in .shm format. Table 3-1 lists the matching times for ten trials on both panels. The upper-panel Mark point matching averaged approximately 5 ms, while the lower-panel Mark point required approximately 20 ms due to its larger contour and hence greater number of template edge points. Including image acquisition time, the total localization time per Mark point is less than 100 ms, satisfying the real-time requirement.

Table 3-1 Operation times of the positioning algorithm

| Experiment No. | Upper panel Mark point [ms] | Lower panel Mark point [ms] |
| — | — | — |
| 1 | 4.760 | 19.174 |
| 2 | 5.190 | 19.588 |
| 3 | 5.131 | 21.173 |
| 4 | 5.025 | 20.343 |
| 5 | 4.867 | 20.314 |
| 6 | 5.083 | 19.706 |
| 7 | 5.035 | 21.230 |
| 8 | 4.943 | 21.696 |
| 9 | 4.895 | 19.755 |
| 10 | 4.380 | 21.129 |

Chapter 4 Calibration of Four Camera Image Coordinate Systems

4.1 Planar Coordinate System Calibration Principle

After completing Mark point localization, the position information is obtained in four independent camera image coordinate systems. To compute the relative deviation between the two solar panels, these discrete coordinate systems must be associated through calibration. Calibration computes the transformation from one coordinate system to another.

A coordinate system is described by position and orientation. The position is given by a position vector, and the orientation by a rotation matrix. For a planar coordinate system \( \{B\} \) relative to \( \{A\} \), the position vector and rotation matrix are:

\[
^A P_{BORG} = \begin{bmatrix} p_x \\ p_y \end{bmatrix}, \quad ^A R_B = \begin{bmatrix} r_{11} & r_{12} \\ r_{21} & r_{22} \end{bmatrix}
\]

When the origins of the two coordinate systems coincide and only rotation exists, a point \( ^B P \) in \( \{B\} \) is expressed in \( \{A\} \) as:

\[
^A P = {}^A R_B {}^B P
\]

In the general case with both rotation and translation, the transformation is:

\[
^A P = {}^A R_B {}^B P + {}^A P_{BORG}
\]

Expanding:

\[
\begin{bmatrix} X_A \\ Y_A \end{bmatrix} = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} X_B \\ Y_B \end{bmatrix} + \begin{bmatrix} q_x \\ q_y \end{bmatrix}
\]

where \( \theta \) is the rotation angle and \( q_x, q_y \) are the translation vector components. Planar coordinate system calibration thus requires determining \( \theta \) and the translation components. In this work, I used a calibration gauge with precisely fabricated feature points to establish the calibration relationship among camera coordinate systems.

4.2 Design of the Calibration Gauge

The calibration gauge must satisfy two requirements: it must contain feature points with precise physical dimensions, and it must have multiple feature points so that the rotation angle and translation between coordinate systems can be computed from their relationships.

Using the solar panel products themselves as calibration gauges is infeasible because each image contains only one Mark point, insufficient for angle computation. Standard calibration boards with circular dot patterns or checkerboards are designed for lens distortion correction and multi-camera calibration; however, in this system, the upper and lower cameras are separated by a significant height difference owing to the side frame height, so they cannot focus on the same plane simultaneously. Therefore, I designed a dedicated calibration gauge.

The gauge is designed with a thickness matching the side frame height so that both upper and lower cameras can focus on its feature points. The gauge comprises only the diagonal portions rather than a full planar panel, improving manufacturability while maintaining flatness. The feature points are positioned to correspond to the Mark point locations of the upper and lower panels so that they fall within the respective camera fields of view. To determine the angle accurately, each camera image must contain multiple feature points. Given manufacturing tolerances, I used three collinear feature points per camera group. Linear regression on these three points yields a line that best approximates the theoretical line, reducing angular error compared with using only two points.

Table 4-1 Calibration gauge feature point specifications

Figure 4-6 in the original manuscript shows the three-dimensional model and the physical calibration gauge.

4.3 Calibration Algorithm among Four Camera Image Coordinate Systems

4.3.1 Unifying Image Coordinate System Directions

The four cameras have distinct orientations due to their different mounting arrangements. I selected the upper-left camera image coordinate system as the reference. The upper-right coordinate system is rotated by 180°, the lower-left by -90°, and the lower-right by 90° to align all directions with the reference.

4.3.2 Calibration between Upper-Right and Upper-Left Camera Image Coordinate Systems

The upper-left and upper-right cameras simultaneously capture images of the calibration gauge. Each image yields three feature points, from top to bottom. Let their coordinates in the upper-left image be \( (X_1, Y_1), (X_2, Y_2), (X_3, Y_3) \) and in the upper-right image be \( (x_4, y_4), (x_5, y_5), (x_6, y_6) \).

Using the three points in each image, I performed linear regression to determine the best-fit line representing the theoretical common line of the three points. The regression line has the form \( y = kx + b \). The slope \( k \) is computed from the means \( \bar{X} \) and \( \bar{Y} \):

\[
\bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i, \quad \bar{Y} = \frac{1}{n} \sum_{i=1}^{n} Y_i
\]

\[
L_{XX} = \sum_{i=1}^{n} (X_i – \bar{X})^2, \quad L_{YY} = \sum_{i=1}^{n} (Y_i – \bar{Y})^2, \quad L_{XY} = \sum_{i=1}^{n} (X_i – \bar{X})(Y_i – \bar{Y})
\]

\[
k = \frac{L_{XY}}{L_{XX}}, \quad b = \bar{Y} – k\bar{X}
\]

The angle \( \alpha_1 \) of the regression line with the upper-left image coordinate system is:

\[
\alpha_1 = \arctan(k)
\]

Similarly, \( \alpha_2 \) is obtained from the upper-right image. Since the two groups of points lie on two parallel lines, the rotation angle \( \theta \) between the coordinate systems is:

\[
\theta = \alpha_2 – \alpha_1
\]

Next, using the middle points of each group, point 2 and point 5, the pixel distance \( L \) between them is computed as:

\[
L = K l
\]

where \( K \) is the pixel equivalent (mm per pixel) and \( l \) is the physical distance between points 2 and 5 on the calibration gauge. The coordinates of point 5 in the upper-left image coordinate system are \( (X_5, Y_5) \), computed geometrically:

\[
X_5 = X_2 + L \cos\alpha_1, \quad Y_5 = Y_2 – L \sin\alpha_1
\]

Using the planar coordinate transformation, point 5 can also be expressed from its coordinates in the upper-right image coordinate system:

\[
\begin{bmatrix} X_5 \\ Y_5 \end{bmatrix} = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} x_5 \\ y_5 \end{bmatrix} + \begin{bmatrix} T_X \\ T_Y \end{bmatrix}
\]

Solving the system yields the translation components:

\[
T_X = X_2 + L \cos\alpha_1 – x_5 \cos\theta – y_5 \sin\theta
\]

\[
T_Y = X_2 – L \sin\alpha_1 – x_5 \sin\theta + y_5 \cos\theta
\]

Thus, the calibration between the upper-right and upper-left camera image coordinate systems is completed.

4.3.3 Calibration between Lower-Left and Upper-Left Camera Image Coordinate Systems

The upper-left and lower-left cameras simultaneously capture the calibration gauge. The upper-left image yields points 1, 2, 3, and the lower-left image yields points 7, 8, 9. Linear regression on each group provides angles \( \alpha_1 \) and \( \alpha_3 \) with their respective coordinate systems.

According to the calibration gauge geometry, the two lines containing these groups intersect at a point \( O \) with an included angle \( \gamma \). The rotation angle \( \theta \) between the coordinate systems is:

\[
\theta = \alpha_3 – (\alpha_1 + \gamma)
\]

Using the middle points, point 2 and point 8, the pixel distances from point 2 to \( O \) and point 8 to \( O \) are:

\[
L_1 = K l_1, \quad L_2 = K l_2
\]

where \( l_1 \) and \( l_2 \) are the corresponding physical distances. The coordinates of point 8 in the upper-left image coordinate system are obtained geometrically:

\[
X_8 = X_2 + L_1 \cos\alpha_1 – L_2 \sin\beta, \quad Y_8 = Y_2 – L_1 \sin\alpha_1 – L_2 \cos\beta
\]

where \( \beta = \frac{\pi}{2} – \alpha_1 – \gamma \). Applying the coordinate transformation along with the lower-left coordinates of point 8, \( (x_8, y_8) \):

\[
\begin{bmatrix} X_8 \\ Y_8 \end{bmatrix} = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} x_8 \\ y_8 \end{bmatrix} + \begin{bmatrix} T_X \\ T_Y \end{bmatrix}
\]

Solving yields:

\[
T_X = X_2 + L_1 \cos\alpha_1 – L_2 \sin\beta – x_8 \cos\theta – y_8 \sin\theta
\]

\[
T_Y = Y_2 – L_1 \sin\alpha_1 – L_2 \cos\beta – x_8 \sin\theta + y_8 \cos\theta
\]

4.3.4 Calibration between Lower-Right and Upper-Left Camera Image Coordinate Systems

The lower-right and lower-left camera calibration is analogous to the upper-right and upper-left calibration because of the symmetry of the calibration gauge’s feature point distribution. Therefore, I first calibrated the lower-right with respect to the lower-left camera coordinate system using the same algorithm as in Section 4.3.2, and then combined this result with the lower-left-to-upper-left calibration to obtain the lower-right-to-upper-left transform.

4.4 Calibration Software for Four Camera Image Coordinate Systems

I implemented the calibration algorithms in a custom software program using C#. The software structure consists of four modules: capture, locate, calculate, and save. The calibration procedure is as follows:

1. Place the calibration gauge on the alignment lamination mechanism and move the lamination table to the lamination position. Fine-tune the gauge position so that the feature points are visible in all four camera fields of view.
2. Click the capture button to trigger simultaneous image acquisition by all four cameras.
3. Rotate the acquired images to unify coordinate directions: upper-left unchanged, upper-right rotated 180°, lower-left rotated -90°, lower-right rotated 90°.
4. Click the locate button. The software invokes the shape-based template matching algorithm to locate the three feature points in each rotated image. It then applies linear regression to compute the best-fit line angle for each image and displays the feature point coordinates and angle values.
5. Click the calculate button. The software invokes the three calibration algorithms (upper-right to upper-left, lower-right to lower-left, lower-left to upper-left) using the feature point coordinates, line angles, and physical dimensions of the calibration gauge to compute the calibration parameters.
6. Click the save button. The calibration data for all four camera image coordinate systems are saved in an .ini initialization file for subsequent retrieval and use.

The software interface displays the rotated images, feature point coordinates, angles, and calibration results, providing an intuitive and user-friendly experience.

Chapter 5 Calibration of the Solar Panel Alignment Platform

5.1 Kinematic Modeling of the Alignment Platform

After calibrating the four camera coordinate systems, all Mark point positions can be expressed in the upper-left camera image coordinate system, enabling the calculation of the deviation between the upper and lower solar panels. However, the panels are corrected on the alignment platform, so the deviation must be transformed into the alignment platform coordinate system to guide the platform.

This is an inverse kinematics problem: given the desired final position and orientation of the platform, compute the motor inputs. The platform model is shown in Figure 5-1. Coordinates \( xy \) represent the final platform position and orientation, while coordinates \( XY \) represent the initial state. The problem is to determine the motor inputs \( \Delta u, \Delta v, \Delta w \) required to move the platform from the initial state to the desired state, where \( L_1, L_2, L_3 \) are the distances from the motor axes to the platform origin.

From the geometric relationships:

\[
\Delta u = \Delta y – (L_1 – \Delta x) \tan\Delta\theta
\]

\[
\Delta v = \Delta y – (L_2 + \Delta x) \tan\Delta\theta
\]

\[
\Delta w = \Delta x – (L_3 – \Delta y) \tan\Delta\theta
\]

where \( \Delta x, \Delta y, \Delta\theta \) are the required platform coordinate corrections.

The deviation of the solar panel is not equal to the platform translation. Let \( (x_0, y_0) \) be the midpoint of the two Mark points of the lower panel in the platform coordinate system, and \( (x_1, y_1) \) be the midpoint of the upper panel Mark points. The angle deviation \( \Delta\theta \) is the same for both. The alignment process requires moving the lower panel so that \( (x_0, y_0) \) coincides with \( (x_1, y_1) \) and the platform rotates by \( \Delta\theta \).

Applying the planar coordinate transformation:

\[
\Delta x = x_1 – x_0 \cos\Delta\theta + y_0 \sin\Delta\theta
\]

\[
\Delta y = y_1 – y_0 \cos\Delta\theta – x_0 \sin\Delta\theta
\]

Substituting these into the motor equations yields the required motor movements.

5.2 Mathematical Calibration of the Alignment Platform

5.2.1 Theory of the Three-Point Calibration Method

The three-point calibration method computes the transformation between two coordinate systems using three non-collinear points. In this application, it establishes the relationship between the upper-left camera image coordinate system and the alignment platform coordinate system.

The coordinate transformation between the camera image coordinate system \( (x, y) \) and the platform coordinate system \( (X, Y) \) is:

\[
\begin{bmatrix} X \\ Y \end{bmatrix} = K \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} t_X \\ t_Y \end{bmatrix}
\]

where \( K \) is the scale factor converting pixels to motor pulses. Rewriting in a compact form:

\[
\begin{bmatrix} X \\ Y \end{bmatrix} = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix} E \\ F \end{bmatrix}
\]

Given three non-collinear points with coordinates \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) in the image coordinate system and \( (X_1, Y_1), (X_2, Y_2), (X_3, Y_3) \) in the platform coordinate system, substituting each point gives a system of equations. Subtracting the first equation from the second and third eliminates E and F, yielding:

\[
X_2 – X_1 = A(x_2 – x_1) + B(y_2 – y_1)
\]

\[
X_3 – X_1 = A(x_3 – x_1) + B(y_3 – y_1)
\]

and similarly for Y. Solving these 2×2 systems gives A, B, C, D. Then:

\[
E = X_1 – A x_1 – B y_1, \quad F = Y_1 – C x_1 – D y_1
\]

The explicit formulas for A and B are:

\[
A = \frac{(X_2 – X_1)(y_3 – y_1) – (X_3 – X_1)(y_2 – y_1)}{(x_2 – x_1)(y_3 – y_1) – (x_3 – x_1)(y_2 – y_1)}
\]

\[
B = \frac{(X_3 – X_1)(x_2 – x_1) – (X_2 – X_1)(x_3 – x_1)}{(x_2 – x_1)(y_3 – y_1) – (x_3 – x_1)(y_2 – y_1)}
\]

Table 5-1 Three-point calibration method parameters

| Parameter | Description |
| — | — |
| A | Scaled cosine term for X |
| B | Scaled sine term for X |
| C | Scaled sine term for Y |
| D | Scaled cosine term for Y |
| E | X translation offset (pulses) |
| F | Y translation offset (pulses) |

5.2.2 Calibration Software for the Alignment Platform

To find three points with coordinates in both the upper-left camera image coordinate system and the platform coordinate system, I used the solar panel itself. The procedure is:

1. Place the lower solar panel on the alignment platform, ensuring the Mark point is visible in the lower-left camera.
2. Record the motor pulse values and capture an image of the Mark point. The software rotates the image by -90°, locates the Mark point, and displays its coordinates along with the motor pulse values.
3. Move the platform by 400 pulses in one direction using the software’s micro-motion buttons. Capture the second Mark point image and record its position and the motor pulse values.
4. Move the platform by 400 pulses in a different direction to ensure the third point is non-collinear with the first two. Capture the third image and record the position and pulse values.
5. Click the calculate button. The software converts the lower-left camera coordinates to the upper-left camera coordinate system using the previously established calibration data, then applies the three-point calibration algorithm to compute the transformation between the upper-left camera image coordinate system and the platform coordinate system.
6. Save the platform calibration parameters to an .ini file.

The software interface resembles that of the camera calibration software and provides intuitive operation.

5.3 Experimental Calibration of the Alignment Platform

When I used the three-point calibration data to guide the alignment platform, the alignment error remained relatively large. The primary cause was the difference between the ideal mathematical model and the actual physical platform. Manufacturing and assembly tolerances cause the actual motor positions to differ from their ideal positions, so the motor pulse values cannot directly represent the platform coordinate system positions. Although improving machining and assembly accuracy could help, the improvement is limited. External measurement devices such as laser interferometers are expensive, and the numerous error sources make systematic measurement and compensation impractical.

Therefore, I calibrated the alignment platform experimentally. After the four-camera calibration, the deviations \( \Delta x, \Delta y, \Delta\theta \) between the two panels in the upper-left camera image coordinate system can be calculated. The system must determine the motor pulse increments \( \Delta u, \Delta v, \Delta w \). This is effectively a three-input, three-output model. The relationship is nonlinear, but for practical engineering purposes, I linearized it:

\[
\begin{bmatrix} \Delta u \\ \Delta v \\ \Delta w \end{bmatrix} = \begin{bmatrix} w_{11} & w_{12} & w_{13} \\ w_{21} & w_{22} & w_{23} \\ w_{31} & w_{32} & w_{33} \end{bmatrix} \begin{bmatrix} \Delta x \\ \Delta y \\ \Delta \theta \end{bmatrix} + \begin{bmatrix} m_1 \\ m_2 \\ m_3 \end{bmatrix}
\]

This model contains 12 unknown coefficients. Each set of input/output data provides three equations, so four sets of experiments are needed. I conducted multiple experiments by moving the motors by different amounts, recording the motor movements and the corresponding deviations measured through the vision system. I solved for the coefficients repeatedly. The coefficient calculations showed some fluctuation; for example, \( w_{11} \) varied within a range. Thus, I averaged the coefficients from multiple computations.

Using the resulting linear relationship, I evaluated the model on five additional datasets. The discrepancy between the actual motor pulse increments and the values predicted by the linear model was at most 10 pulses for the W motor and at most 40 pulses for the U and V motors. Given that the motor resolution is 400 pulses per millimeter, a 40-pulse error corresponds to 0.1 mm, which is within the 0.15 mm alignment accuracy requirement. Therefore, the linearized model was deemed acceptable.

Table 5-2 Comparison of actual and predicted motor pulses

| Experiment | Actual U | Predicted U | Actual V | Predicted V | Actual W | Predicted W |
| — | — | — | — | — | — | — |
| 1 | 2850 | 2821 | 1400 | 1437 | -220 | -214 |
| 2 | -2650 | -2688 | 1230 | 1268 | 180 | 174 |
| 3 | 1650 | 1684 | -2720 | -2682 | -140 | -133 |
| 4 | -1820 | -1791 | -1620 | -1589 | 260 | 266 |
| 5 | 2340 | 2372 | 2150 | 2118 | -310 | -301 |

Chapter 6 System Operation and Analysis

After completing the alignment platform calibration, the linear relationship model between the pixel deviations \( \Delta x, \Delta y, \Delta\theta \) in the upper-left camera image coordinate system and the motor pulse increments \( \Delta u, \Delta v, \Delta w \) was established. Since the computed pulse increments are fractional, they are rounded to integers. The linear relationship is an approximation of the actual nonlinear system, so a single correction may not achieve the required accuracy. I therefore introduced closed-loop control: the system performs multiple alignment cycles. After each correction, the panel deviations are recalculated; if they still exceed the tolerance, another correction is performed. The final integrated software interface displays the panel positions, deviations, motor pulses, and alignment status.

Figure 6-1 in the original manuscript shows the main interface of the developed solar panel visual alignment system.

Using this system, the satisfactory alignment accuracy is typically achieved after two correction cycles. To validate the system’s accuracy, I randomly sampled 10 aligned concentrating photovoltaic modules and measured the X and Y deviations and angular deviation between the upper and lower panels using a 3D CNC measuring machine.

Table 6-1 Measured deviations after alignment

| No. | X deviation [mm] | Y deviation [mm] | Angular deviation [°] |
| — | — | — | — |
| 1 | 0.0731 | 0.0823 | 0.0095 |
| 2 | 0.0716 | 0.0815 | 0.0139 |
| 3 | 0.0978 | 0.0642 | 0.0114 |
| 4 | 0.0791 | 0.0725 | 0.0131 |
| 5 | 0.0774 | 0.0893 | 0.0144 |
| 6 | 0.0815 | 0.0796 | 0.0104 |
| 7 | 0.0917 | 0.0634 | 0.0135 |
| 8 | 0.0818 | 0.0780 | 0.0124 |
| 9 | 0.0720 | 0.0829 | 0.0123 |
| 10 | 0.0637 | 0.0821 | 0.0118 |
| Mean | 0.0790 | 0.0776 | 0.0126 |
| Std. Dev. | 0.0100 | 0.0085 | 0.0012 |
| Range | 0.0341 | 0.0259 | 0.0040 |

The measured deviations are all below 0.12 mm, with standard deviations below 0.02 mm, satisfying the project requirement of 0.15 mm. The system has entered the trial production stage for concentrating photovoltaic modules, operating reliably in the production environment.

Table 6-2 Summary of system performance metrics

Conclusion and Outlook

In this thesis, I have conducted a systematic study on a visual alignment system for high-concentrating photovoltaic panels, addressing the critical requirement of precision alignment between the upper and lower solar panels. The main contributions of this work are:

(1) A multi-camera array vision scheme was designed based on the distribution and characteristics of the Mark points on the upper and lower solar panels. Four cameras image the Mark points on the panels. The entire visual alignment system was modularly designed into motion control and machine vision components. Based on the accuracy requirements and practical installation constraints, I selected appropriate industrial cameras, telecentric lenses, and a shared red ring-light illumination scheme that delivers high-contrast Mark point images for both panels.

(2) I compared various circular Mark point localization algorithms and selected the shape-based template matching algorithm as the positioning method, considering the actual image conditions with potential adhesive contamination and missing Mark points. The geometric features of the Mark points were extracted through ROI creation, image binarization, target region labeling, and robust edge fitting. The similarity measure was chosen to tolerate local contrast variations, and an image pyramid accelerated the search. The algorithm was evaluated in terms of stability and execution time, demonstrating robust performance suitable for real-time operation.

(3) A calibration gauge was designed specifically for calibrating the four camera image coordinate systems in this system. After unifying the coordinate directions, I derived calibration algorithms for the upper-right-to-upper-left, lower-left-to-upper-left, and lower-right-to-upper-left camera coordinate systems. The algorithms were implemented in custom software, providing an efficient and accurate calibration procedure.

(4) I modeled the kinematics of the alignment platform and initially calibrated it using a three-point method with custom software. When this approach proved insufficient due to manufacturing tolerances, I performed experimental calibration by linearizing the input-output relationship between panel deviations and motor pulses. The resulting linear model achieved acceptable accuracy within the required tolerance.

The integrated system successfully aligned the solar panels, with measured deviations below 0.12 mm, well within the specification. The system is currently in the trial production stage for concentrating photovoltaic modules.

Several avenues for future research remain:

(1) Although telecentric lenses eliminate perspective distortion, minor residual errors may still exist. Individual camera calibration could further reduce these errors.

(2) The dedicated calibration gauge is effective but costly due to high manufacturing precision requirements. More cost-effective calibration methods could be explored.

(3) The alignment platform calibration relied on a linearized model. More sophisticated approaches, such as artificial neural networks, could capture nonlinearities more accurately and improve alignment robustness.

I hope the methods and insights presented here contribute to the development of precision alignment systems for concentrating photovoltaic and related applications.