# Optimization of Redundant Degrees of Freedom in Robotic Flat-End Milling Based on Dynamic Response
## 1 Introduction
[22] employed the shortest path algorithm to calculate a sequence of posture variations with maximum smoothness along the feeding trajectory. However, under high stiffness requirements, obtaining machining trajectories with fine smoothness became challenging due to limitations in the range of available postures. [PERSON] et al. [23] focused on optimizing robot posture by improving stiffness performance in the direction of the cutting force during planar milling. [PERSON] et al. [24] optimized the redundant degrees of freedom by minimizing the deformation in the orientation required for machining accuracy in order to reduce machining errors. Considering the limitation of robot kinematics and the conventional toolpath pattern, [PERSON] et al. [25] proposed a region-based toolpath generation method to improve robot stiffness for robotic milling of freeform surfaces. For the evaluation of robot posture stiffness, [PERSON] et al. [26] introduced a comprehensive deformation index, considering both spindle weight-induced and cutting force-induced deformations. [PERSON] et al. [27] proposed a deformation energy model for a stiffness evaluation, emphasizing that simultaneous optimization of robot posture and workpiece position could significantly improve machining quality. However, these stiffness performance indexes mainly considered static stiffness properties. Several recent studies have proposed dynamic performance indexes to improve the dynamic characteristics of robotic milling systems. In their experimental research, [PERSON] et al. [28] investigated the chatter stability in robotic milling with respect to robot posture, revealing a significant impact on chatter suppression. [PERSON] et al. [29] proposed an energy optimal index for robot assembly path planning, considering the dynamic characteristics of robots. [PERSON] et al. [30] optimized robot machining postures based on the cutting depth limit index, aiming to enhance the stability of robotic milling. [PERSON] et al. [31] used the eigenvalues of the frequency response matrix as a dynamic index, demonstrating its effectiveness by comparing the index values at different frequencies. [PERSON] et al. [32] employed the maximum transient vibration amplitude during the machining process as a dynamic performance index. The optimized path reduced the vibration amplitude, demonstrating the superiority of the dynamic performance index over the static stiffness index. [PERSON] et al. [33] developed an optimization model of redundant degrees of freedom in robotic milling, considering chatter stability and the constraints of robot motion performance. [PERSON] et al. [34] proposed a posture optimization method based on the surface location error, which improved machining accuracy and surface quality by optimizing the functional redundant degrees of freedom in robotic milling. Through control of the robot redundant angle, the dynamic performance of the robot is enhanced, which improves the machining stability and surface quality. These performance optimization indicators do not effectively address machining accuracy, leading to difficulties in achieving acceptable dimensional tolerances and surface quality in the produced parts. Many studies on robotic milling processes simplify the analysis, neglecting the impact of dynamic characteristics on machining accuracy. On the other hand, the few studies concentrating on dynamic features tend to emphasize vibration amplitudes and chatter stability, neglecting machining accuracy in the process. Consequently, challenges persist in achieving parts with acceptable dimensional tolerances and surface quality. To address this, our article proposes a posture optimization model utilizing a dynamic response index. This model integrates posture-dependent robot dynamic performance with machining errors. By calibrating and conducting modal tests in the robot workspace, we first investigate the dynamic behavior of the robotic milling system.