# Dynamic Parameters Identification of Serial Robot Based on Dual Quaternion
## 5 Experiments of Dynamic Parameters Identification of Load and Linkages for a Serial Robot
### Experiment of Dynamic Parameters Identification of Linkages
According to the actual usage characteristics of the dual-arm robot SDA5F system, it was necessary to obtain joint torque data of the active single joint during the acceleration stage of the movement. Furthermore, when processing actual samples, data near the start and last state time slices were removed in order to obtain effective theoretical calculation values and identification results. Similarly, during the procedure of dealing with experimental data, it was necessary to convert the obtained information on velocity and acceleration of the active joint into a unified coordinate system for calculation. Therefore, the equivalent form of pose and velocity variables can be directly calculated in the coordinate system of the active joint, and the convert equation is  
\[\mathbf{\hat{q}}_{\mathbf{I}}^{t}=\mathbf{\hat{q}}_{robot}^{t}*\mathbf{\hat{q}}_{\mathbf{I}}^{robot }*\mathbf{\hat{q}}_{robot}^{t}* \tag{30}\]  
where \(\mathbf{\hat{q}}_{\mathbf{I}}^{t}\) is the dual quaternion representation of the \(i\)-th joint coordinate system, \(\mathbf{\hat{q}}_{robot}^{t}\) is the dual quaternion representation of the transformation of the robot coordinate system with respect to the \(i\)-th joint coordinate system, \(\mathbf{\hat{q}}_{\mathbf{I}}^{robot}\) is the dual quaternion transformation of the \(i\)-th joint coordinate system with respect to the robot coordinate system. During the experiment of the identification, as shown in Figures 6 and 7, six-dimensional force sensors were installed at the end flange of the left and right arms, and the loads were connected to the measuring faces of two six-dimensional force sensors. Combining the method proposed above, it was necessary to control the corresponding joint movements of two arms separately, while obtaining the information of joint angular velocity and angular acceleration. Figure 8 shows the dynamic identification of R2 with the load of the dual-arm robot SDA5F. Similarly, it was necessary to consider the kinematic parameters of a seven-degree-of-freedom arm in conjunction with the robot system platform, and use the positional offset of each joint along the \(z\)-axis direction in the corresponding coordinate system, which could be used as the reference for the calculation data for setting. During the experiment, in order to obtain better theoretical results of identification, the data of the six-dimensional force sensor and each joint were sampled multiple times. After removing some data from the starting and stopping stages, a combination matrix was constructed to obtain the results of identification. The dynamic parameters of load and linkage for the serial robot were obtained and processed in the experiments. The results of the dynamic parameters identification of linkages of R1 arm are shown in Table 1 from joint 1 to joint 7, and the results of the dynamic parameters identification of linkages of R2 arm are shown in Table 1, as well. As can be seen from the identification process in Table 1, the errors of the dynamic parameters are different at different times of the calculation, but the results can be applied to the corresponding dynamic model. This means the method proposed in this paper can identify the dynamic parameters of linkages for a serial robot, and the calculation amount of the identification model is relatively small. Figure 8: Manipulator R2 with load of dual-arm robot SDASF. Figure 7: Manipulator R1 with load of dual-arm robot SDASF. Furthermore, the effective set of dynamic parameters of linkages satisfying the corresponding dynamics model can be obtained. Furthermore, the RBFNN-based method was also used in the experiment of identifying the dynamic parameters of the load and linkages of the robot SDA5F. The strategy of using RBFNN should also depend on the actual platform and the setup of the data processing. The average elapse is recorded in Figure 9, and the figure shows that the proposed DQ-based method in this paper has the advantage of lower cost compared with the RBFNN-based method.