# Shape Design Optimization of a Robot Arm Using a Surrogate-Based Evolutionary Approach
## 1 Introduction  
Nowadays, facing the megatrend for smart factories of the future, industrial robots play a greatly important role not only in traditional pick-and-place tasks but also in many of the precision applications such as assembly, welding, and machining. These robots, in order to satisfy the requirements of new applications, must be designed to meet high end/performance requirements, i.e., high accuracy and high efficiency. The design process of an industrial robot arm with high speed performance is still challenging due to the interconnecting roles of adjacent joints, which may significantly impact the efficiency and stability of the robot arm. For example, the deformation and residual vibration of the robot arm will cause its positioning accuracy to decrease, and the robot arm mass and moment of inertia will affect its dynamic behavior, such as controllability and efficiency; moreover, these factors generally are in conflict with each other. Therefore, design optimization of robot arms is becoming increasingly important. With the advance of digital twins in smart factories, the use of simulation technologies to address computation-expensive and multi-objective optimization issues has become an important research topic. Design optimization is the process of establishing the right combination of product parameters that satisfy project requirements [1]. Structural optimization can be separated into three main categories: size, shape, and topology optimization [2]. In a structural design process, a topology optimization is first performed to obtain an initial sketch of the optimal configuration of the structure; the suggested configuration is interpreted to draw an engineering design, and this design is then optimized using detailed sizing and shape optimization methods together with realistic design constraints. These methods are not only able to optimize the robot arm but can also be extended to the design of the whole robot system. For the purpose of improving the performance of industrial robots, a number of research works have been carried out with respect to the related topics in recent years. Some works focused on the selection criteria of the servo motor and gearbox for optimizing the servo drive system [3; 4]. A few reports studied new control algorithms to obtain high speed performance, such as residual vibration suppression [5]. Certain researchers used the finite element method (FEM) to optimize robot structure. [PERSON] et al. used the finite element method to design a high-performance robot arm and reported experimental structural data to support the design of the robot arm [6]. [PERSON] and [PERSON] studied the design optimization of the mechanical structure and control of a two-link robot for which the weight and inertia of the robot arm were minimized to attain high-speed positioning [7]. [PERSON] and [PERSON] used the FEM of the ANSYS workbench to optimize the performance of a six-axis industrial robot via stress, modal, and dynamic behavior analyses [8; 9; 10]. [PERSON] et al. also used an FEM-based optimization technique to study the influence of the static and dynamic behaviors on the positioning accuracy of robots [11]. [PERSON] et al. analyzed the static strength and stiffness of a two-link robot and then used a topology optimization method to design the structure for quality improvement [12]. In the above studies, it was revealed that CAE together with FEM-based design optimization can be an important tool for attaining structural performance improvement in real-world engineering applications. However, for cases with large design space or the requirement of attaining numerous design samples, the high computational effort of analysis may hinder the implementation of the conventional FEM-based design optimization methods in the design optimization process. On the other hand, only a few researchers have studied the multi-objective and computational inefficiency problems related to the design optimization of industrial robots.