Abstract: This paper uses theoretical knowledge and computer simulation of mirror design to realize the rapid and effective design of mirrors for the panoramic vision system of medium-sized soccer competition robots. A simulation design system for mirror contour design was independently developed, and a mirror with a special curve that meets the requirements of the robot task was designed and manufactured. Practice shows that the modern design method based on knowledge and computer simulation has greatly improved the quality and efficiency of mirror design, can grasp the rationality of the design as a whole, avoid design errors and product rework, save manufacturing costs, and make the design results meet the expected task requirements. Keywords: panoramic vision, computer simulation, mirror contour design 0 Introduction The panoramic vision system consists of an upward-facing camera and a mirror. The camera obtains images in a 360-degree range through the mirror. Due to its wide field of view, soccer competition robots usually use panoramic vision systems to obtain information about the entire field. The mirror is an important factor affecting the image effect and observation range of panoramic vision. Simon Baker and Shree K. Nayar et al. of Columbia University in the United States have conducted a careful study and analysis on the geometric characteristics of panoramic vision systems and proposed the problem of "single viewpoint" [1]. A curved surface that conforms to a single viewpoint, after all the light rays that are directed toward the focal point are reflected, they are directed toward another focal point or parallel to the axis of symmetry, rather than scattered. Studies have shown that different mirror surfaces are suitable for different observation needs. Commonly used curved mirror surfaces (such as parabolic surfaces, conical surfaces, etc.) often cannot simultaneously meet the multiple observation needs of robots performing special tasks. Therefore, some scholars have proposed to reverse-engineer the curved surface of the mirror based on the observation needs or the assumed imaging effect [2], so as to design a mirror profile that meets the needs of special tasks. The mirror design process in this paper is to obtain the curved surface profile based on the reverse-engineering algorithm, and to establish a corresponding model to simulate the pre-observation imaging effect, compare it with the expected imaging, optimize the parameters based on certain evaluation and analysis, and complete a large number of calculation processes and quantitative analysis by computer. This design method can efficiently design mirrors with good performance and low cost. 1 Mirror design principle and development of imaging simulation system 1.1 Mirror design principle and method To predict the imaging effect after mirror reflection, it is necessary to know the mapping relationship between the mirror curve and the imaging point (imaging unit on CCD) after mirror reflection and the real space point. Using the pinhole imaging model as the imaging model of the camera, since the mirror is a rotationally symmetric structure, only the two-dimensional mirror profile curve needs to be studied. As shown in Figure 2, according to the light reflection theorem and the pinhole imaging rule, the following relationship can be obtained: (1) In the above formula, F(t) is the curve equation. For the specific derivation of the relationship, please refer to [4]. [align=center] Figure 1 Mirror imaging principle[/align] If the mirror curve equation is unknown, but the correspondence between the real point and the image point is given, then it is necessary to reverse the mirror contour line. There are two methods for reversely obtaining the mirror curve: analytical solution [2] and numerical solution [3]. This paper adopts the algorithm for obtaining the numerical solution because it has low computational complexity and is easy to implement in programming. The main implementation process is shown in Figure 2: [align=center] Figure 2 Flowchart of Mirror Contour Design[/align] 1.2 Imaging Simulation To make the mirror curve design more intuitive and easier to adjust parameters, simulation preview of the mirror imaging effect can make the design application more user-friendly, while improving efficiency and design quality, avoiding large discrepancies between the design and the expected effect, thus avoiding waste of time and cost. The simulation system uses Matlab as the development platform because Matlab has powerful mathematical calculation functions and image processing libraries, which can provide convenient function calls and shorten the development time of the simulation system. The imaging graphics are simulated based on the mapping relationship between the obtained image and the actual spatial vector. First, it is necessary to obtain the environment for mirror imaging. The environment used for simulation in this paper is the soccer robot's playing field (including the white lines, goals, goalposts, etc. on the field) and the ball used in the game. The object information on the field is a simple regular geometric body. After determining the global coordinate system, the spatial expression of each object, that is, their mathematical model, can be obtained. Assuming the center of the field is the origin of the global coordinate system, according to the right-hand rule, the length direction is the x-axis (pointing to the yellow goal), the width direction is the y-axis, and the z-axis is perpendicular to the ground and upwards. The mathematical model of the main object is as follows (the unit of calculation is mm): Ball: (where r=110) Yellow goal: Blue goal: Let the position of the robot in the field be (dx,dy,θ)T, where dx and dy are the planar coordinate positions and θ is the robot's facing angle. The mathematical model of the object (x,y,θ)T and the expression (x',y',z')T under the local coordinates with the robot's vision system as the origin have the following relationship: (2) Since the mirror is a rotationally symmetric mirror, in order to simplify the calculation of the simulation imaging, θ=0 is taken. Thus, the transformation matrix is ​​simplified to: (3) Based on the previously calculated relationship between pixels and spatial vectors (points on the object model must pass through a certain spatial vector), the imaging effect of the designed virtual environment can be obtained. Then, the parameters are modified according to the imaging effect, and the desired effect is quickly achieved through imaging simulation, and the final mirror processing parameters can be obtained. 2. Experiments and Results The designed mirror for the soccer robot needs to meet the following requirements: 1) When the robot is in the middle of the field, it needs to see the goal to distinguish between its own goal and the opponent's goal and determine the direction of movement. 2) The distance of the ball seen should have relatively accurate directional information. 3) The distance of the ball seen should have relatively accurate directional and distance information, that is, the close-range observation resolution needs to meet certain requirements. 4) Minimize the amount of information seen about the robot itself (useless information) to obtain more information about the robot's surrounding environment. Based on the above requirements, the mirror can be designed in two parts: one part is used to observe the area within 1m of the robot, and the other part observes information beyond 1m and the goal. The implementation process is as follows: The distribution of the observation area of ​​the entire image is considered in advance according to the needs, and the resolution of different distance intervals is allocated. Then, the simulation program is run to obtain the mirror curve and imaging effect (see Figure 3), and the coordinates of each point of the mirror curve are saved as a data file for easy data extraction in subsequent CNC lathe machining. The actual mirror imaging effect is shown in Figure 4. [align=center]Figure 3. Cross-sectional view and imaging effect of the mirror[/align] [align=center]Figure 4. Finished reflective mirror and actual mirror image[/align] 3. Summary Through computer-aided design methods using virtual simulation and mirror inverse calculation algorithms, reflective mirrors for panoramic vision systems can be designed conveniently and effectively, meeting the pre-defined task requirements and performing well in soccer robot applications. With the help of computer-aided design and simulation methods, product design not only improves efficiency but also enhances design quality, allowing the design to focus on innovation rather than tedious calculations and parameter refinement. References: [1] Simon Baker and Shree K. Nayar, A Theory of Catadioptric Image Formation[C], Computer Vision, 1998 Sixth International Conference, Published in Jan. 1998 on Page 35-48. [2] José Gaspar, Claudia Décor, Jun Okamoto Jr etc., Constant Resolution Omnidirectional Cameras[C], In Proceedings of the Third Workshop on Omnidirectional Vision (OMNIVIS.02) IEEE, 2002. [3] Fabio M. Marchese, and Domenico. G. Sorrenti, Mirror Design of a Prescribed Accuracy Omni-directional Vision System[C], In Proceedings of the Third Workshop on Omnidirectional Vision (OMNIVIS.02) IEEE, 2002. [4] Xu Chengshen, Jiang Ping. Target Localization of Soccer Games Robot Based on Full-Dimensional Vision [J]. Microcomputer Information, 2005, 8-3: 85-87. Innovative Viewpoint: A mirror design simulation system was developed, capable of designing mirror contours of arbitrary requirements (including traditional mirrors with a certain surface equation and mirrors with on-demand input range imaging resolution). Furthermore, a special curved mirror (different from other existing curved surfaces) meeting specific task requirements was designed and manufactured based on this simulation system. Author Biographies: Zhuang Huimin (1981), female, from Fujian Province, postgraduate student at the Robotics Institute, Department of Mechanical and Electronic Engineering, Shanghai Jiao Tong University, major research direction: panoramic vision navigation for intelligent robots. Cao Qixin (1960), male, from Wenzhou, Zhejiang Province, professor, doctoral supervisor, major research areas: robot vision, network-based intelligent robot control. Downloadable materials on panoramic vision mirror design based on computer simulation.