## 1 Introduction  
Because of the advantages of 6-DOF industrial robots, such as high DOFs and open structure, the use of 6-degrees of freedom (DOF) robots for complex workpiece surface milling has become one of the popular topics in industrial robots in recent years [1; 2; 3; 4; 5]. In surface milling, only five DOFs need to be restricted, of which three are used to locate the tool's tip and the other two are used to determine the tool axis vector. Therefore, there will be a redundant DOF, i.e., the rotation around the tool axis, when using a 6-DOF robot for surface machining. This redundant DOF results in one tool pose corresponding to infinite robot postures. When planning the motion of the 6-DOF robot to perform the ball-end milling task, the redundant DOF can lead to trouble in solving the inverse kinematics, but it also provides an opportunity to optimize the robot posture for a given tool posture. Therefore, in the trajectory plan of robot milling, the main concern is the elimination of the redundant DOF, i.e., optimizing the robot posture according to a specific index [6; 7; 8; 9; 10; 11]. In the process of robot milling, it is essential for the tool point at the end of the robot to accurately reach the trajectory points specified in the task space. However, due to the existence of the redundant DOF, the motion of the robot joints between the trajectory points is free. Therefore, how to make a reasonable plan for the robot posture of the milling task has become a problem. In order to solve this robot machining problem, scholars have proposed different optimization objectives. [PERSON] et al. utilized the Jacobi condition number as the optimization objective of flexible optimization, leveraging redundant degrees of freedom to obtain smoother joint-rate time history [12]. In order to improve the milling accuracy of the robot and achieve the best machining performance, [PERSON] et al. proposed the evaluation index of the end deformation and the main stiffness index of the robot [13]. [PERSON] et al. selected the ultimate cutting depth of regenerative chatter in robot milling as the optimization objective to prevent regenerative chatter during robot milling and enhance the quality and efficiency of machining [14]. [PERSON] et al. proposed the minimum energy deformation index based on the static deformation energy generated by machining forces and optimized the robot attitude and workpiece position [15]. [PERSON] et al. used the relationship between average absolute machining error and joint parameter error to reduce machining error and improve stiffness [16]. [PERSON] et al. considered the deformation caused by the weight of the spindle and the deformation caused by the cutting force and proposed a comprehensive deformation index to evaluate the stiffness performance of robot milling [17]. [PERSON] et al. combined joint constraint, stiffness performance index, and dexterity performance index as optimization objectives to conduct comprehensive optimization of redundant robot posture [18]. [PERSON] et al. considered the relationship between the translational displacement of the machine-effector of the robot and the applied force and established an optimization model using the volume of the flexibility ellipsoid as the stiffness performance index [19]. However, the redundant robot posture optimization related to the joint trajectory and joint loads has not been published. This paper argues that the robot joint trajectory should be minimized when eliminating the redundant DOF in the milling process. Meanwhile, the joint load coefficients are introduced into each joint to reduce the trajectory of the joints which have large loads. At present, there are many optimization algorithms for the robot redundant DOF, including genetic algorithm [20; 21; 22; 23; 24], particle swarm optimization [25] and so on. However, these algorithms still have some limitations and defects in different application scenarios and problems.