## 1 Introduction  
The development of robust, compact, and low-cost optical, mechanical, and electronic components makes it possible to build accurate and reliable 3D scanning systems. In particular, in the textile industry, surface digitization allows for the assessment of textile surface quality, such as changes in appearance or the detection of fabric defects [1; 2]. Internationally, the automation and optimization of the scanning process has been considered through different variants using diverse methods such as:  
* Mounting a handheld 3D scanner on a machine tool for which inverse kinematics was performed in order to perform automated scanning [3; 4; 5];
* Mounting a handheld 3D scanner on a robot [6];
* Mounting a handheld 3D scanner on a tripod, the object to be scanned being positioned on a rotating table [7]. When performing 3D scanning with structured light while using a robotic arm, it is not necessary to pulverize the surface with special spray for antireflection (as in the case of laser scanning). Three-dimensional scanning of sneakers using a robotic arm is faster compared to other methods such as photogrammetry or laser scanning along a line and point (which takes more time). The robotic arm together with a 3D handle scanner can be quickly guided around the object, which allows flexibility in scanning complex surfaces or objects with uneven geometry. Compared to the above-mentioned methods, the authors of the paper propose a technical and economical solution that is much more advantageous compared to the existing variants on the market. The research in this paper also aims to optimize the scanning process based on a mathematical model for generating a 3D scanning trajectory of sports shoes used by handball players. However, few works have dealt with the generation of scanning trajectories on shoes used for indoor sports. Manual scanning performed by several people is different even if the procedures are standardized, and in applications requiring a high degree of accuracy and repeatability, this leads to measurement variations. In order to scan more sports shoes, automation minimizes a lot of repetitive work performed by the human factor (i.e., manually performing the scanning procedures, which can become tiring for the human factor) [8,9]. Consistent results and reduced errors compared to the manual scanning process can be achieved by automating the 3D scanning process by using a robotic arm, leading to long-term cost savings, and thus minimizing the need for additional human resources for important tasks and system control [10]. Kinematic and reverse analysis has been performed internationally for prismatic and other shaped parts made of solid materials, but has not been performed for products made of flexible materials such as the sneakers used for indoor sport analyzed in this paper. This paper uses inverse kinematics to automate 3d scanning for footwear used for indoor sport with the help of a robotic arm for which the minimum and maximum trajectory was simulated. The robotic arm proposed with a low investment and maintenance cost for automated 3D scanning is composed of three actuated joints with three degrees of mobility which can be controlled by a simple and non-expansive controller based on Arduino or Raspberry Pi. Sustainability is increasingly important in the footwear industry as consumers look for environmentally-friendly and sustainable options [11]. The use of a handheld 3D hand scanner contributes to increased sustainability by creating scanned models (databases) that are processed using specialized software to generate a 3D digital model of the feet for custom footwear design purposes, resulting in the production of only the exact amount of material required for each pair of shoes. By 3D scanning the existing shoes used for indoor sports before a new product is made, this design can be checked and adjusted to reduce material loss and minimize energy consumption.