# 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 Load  
When applying the derived dynamic parameters identification method of load for a serial robot, it was necessary to set the joints other than the active joints to a pulse-free input state. This was the consideration of the actual control situation of the system platform. Each arm of the dual-arm robot SDA5F has a total of seven rotating joints, with the last joint being the axial degree of freedom of the end flange. The installation position of the six-dimensional force sensor needed to be changed from the coordinate system of the end flange, which was installed on the end-effector of the arm. The coordinate system of the six-dimensional force sensor needed to be set at a certain offset distance along the axial direction of the end flange first, and then it should rotate around the axial direction of the end flange by a certain angle. Figure 4: Difference in the identification results of the linkages. Figure 5: Average elapse in ten iterations in simulation. In actual identification experiments, the initial pose of the robotic arm was set to the extended state of the arm, and the sixth joint was used as the active joint, without inputting motion commands to the remaining joints, while keeping the robotic arm in the motion form of a single joint. Furthermore, the active joint moved at a constant speed or acceleration, which is the exciting trajectory for short, and the control system has to collect the data of the robot and the six-dimensional force sensor. Figure 6 shows the installation status of the load and the six-dimensional force sensor during the procedure of identifying the dynamic parameters of the load. The six-dimensional force sensor used in the experiments was an ATI mini-45, and the estimated weight of the load before the experiments did not exceed the range of the six-dimensional force sensor. The load was connected to the end flange of the arm by the six-dimensional force sensor. When the robot joints were moving, the six-dimensional force sensor could obtain the change data of the force and torque transmitted by the load. During the identification procedure, the motion angular velocity and angular acceleration information of the sixth joint are obtained from the dual-arm robot system. The force and torque data obtained by the six-dimensional force sensor do not directly affect the equivalent force at the active joint, so it is necessary to convert the velocity and acceleration of the active joint to the equivalent form in the six-dimensional force sensor coordinate system. \[\hat{\mathbf{q}}_{6}^{sen}=\hat{\mathbf{q}}_{robot}^{sen}*\hat{\mathbf{q}}_{6}^{robot}* \overline{\hat{\mathbf{q}}_{robot}^{sen}}^{*} \tag{29}\]  
where \(\hat{\mathbf{q}}_{6}^{sen}\) is the dual quaternion representation of the coordinate system transformation of the sixth joint with respect to the force sensor, \(\hat{\mathbf{q}}_{robot}^{sen}\) is the dual quaternion transformation of the robot coordinate system with respect to the force sensor coordinate system, \(\hat{\mathbf{q}}_{6}^{robot}\) is the dual quaternion transformation of the sixth joint with respect to the robot coordinate system. Furthermore, during the experiment, within the rotation angle range of \([-\pi/2,-\pi/2]\), it was necessary to collect the velocity and acceleration information of the sixth joint of the arm during the procedure of the motion control, so that it could obtain the corresponding six-dimensional force sensor data for further procedure of identification. In addition, acceleration information included the positive and negative values of acceleration, and the negative acceleration is deceleration. During the procedure of identification, in order to achieve better results of the experiment, multiple sets of data have been collected, and then the datasets were stacked to obtain a combined sample matrix.