# Joint Stiffness Identification Based on Robot Configuration Optimization Away from Singularities
## 1 Introduction  
Recently, industrial robots are mostly used in many operations such as palletizing, painting, deburring, and welding. Such operations do not require good pose repeatability and global pose accuracy (ISO 9283). Industrial robots have advantages of dexterity, low price, and large operating range in milling, drilling, and grinding compared with traditional machine tools. In the fields of automotive parts manufacturing, shipbuilding, and aerospace industry [1; 2], industrial robots can complete low-cost and high value-added machining tasks in the processing of parts with large dimensions and complex structures. However, industrial robots have disadvantages such as poor absolute position accuracy, poor stiffness performance, and poor compliance due to the open-chain and serial structure. The following topics have been considered in many studies: (i) path optimization [3; 4; 5; 6], (ii) stiffness characteristic analysis [7; 8; 9; 10; 11], (iii) determination of robot machining performance indices [12; 13; 14], and (iv) tool chatter avoidance [15; 16; 17]. To improve the stiffness and dynamic properties in robot machining, the following methods are investigated by scholars: (i) optimize the compliance of the spindle holder in the machining robot by controlling the position and orientation of the spindle at the end-effector [18], (ii) increase the systematical stiffness of the machining robot by using serial-parallel hybrid structures [19], and (iii) optimize the robot machining stiffness by determining robot performance indices based on stiffness model 13. The third method does not require a complex structure of an end-effector that would limit the end degrees of freedom compared to the first one and does not require a complex new structure of robot compared to the second one and can make full use of the end load to optimize the machining stiffness and improve the machining accuracy and performance. Currently, the most widely used static robot stiffness model is the cartesian stiffness and joint stiffness transformation. On this basis, [PERSON] et al. [20] introduced an enhanced stiffness model by considering the external force vector acting on the endpoint of the manipulator and the variation of the manipulator configuration and proposed the complementary stiffness matrix (CoSM). [PERSON] et al. [21] introduced the effective stiffness matrix Kg, takinginto consideration the robot links deformation. The effective stiffness matrix Kg was based on the conservative congruence transformation (CCT). Many scholars have studied the identification methods of robot joint stiffness. For example, [PERSON] et al. [22] proposed a new method for robot joint stiffness identification. The sensitiveness of the experimental results to errors in measurement and the number of tests was analyzed. [PERSON] et al. [23] presented a pose optimization method using static and dynamic robot stiffness models in robotic machining. [PERSON] et al. [24] introduced the 6-DOF robot stiffness model. The two-dimensional manifold was improved by two stiffness-oriented performance indices. [PERSON] et al. [25] introduced the stiffness model and proposed a pose optimization method to increase the robot stiffness in robotic machining applications. [PERSON] et al. [26] used laser displacement sensors to identify joint stiffness, providing a new robot joint stiffness identification method. The joint stiffness identification method introduced by [PERSON] et al. [26] requires multiple experiments and takes a long time, although the experiments are not complicated. [PERSON] et al. [22] presented a highly robust and highly accurate method, but the experiments are complex and require an expensive laser tracker. Therefore, it is necessary to propose a low-cost method to simplify the experiment and reduce the number of tests. In this paper, a new robot joint stiffness identification method is presented, which applies to any 6R serial robot. In Section 2, the robot kinematic and stiffness models are set up.