# 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  
In order to obtain better identification results, in the procedure of identifying the dynamic parameters of linkages of the dual-arm robot, the arms of the robot system were set as a single joint motion based on the proposed combination steps of the identification method. The exciting trajectory has been considered in the experiment, which was a constant speed or acceleration state of the active joint. First, the initial poses of the arms were still set to the extended state, and the active joint, which is one of 15 joints, was limited from high-speed motion. Then, the active joint was moved at a constant speed or acceleration state. At every step of the experiment, the adjacent joints and linkages of each arm were considered as a combination. The six-dimensional force sensor and the seventh joint of the corresponding arm were considered as a combination, and then controlling the corresponding single joint to move followed the preset motion. Otherwise, the dual-arm robot system used two joint-biased arms and adjacent joint axes perpendicular to each other, so it was flexible to some extent. When the arm was in a straight and extended state, the first and third joint axes of the arm were close to overlapping, and the fifth and seventh  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**No. **} & \multirow{2}{*}{ \begin{tabular}{c} **Mass** \\ \(\mathbf{m}(\mathbf{kg})\) \\ \end{tabular}  } & \multicolumn{4}{c}{**Centroid** (\(\mathbf{mm}\))} & \multicolumn{4}{c}{**Inertia** (\(\mathbf{kgm^{2}}\))} \\ \cline{3-11}  & & & \(\mathbf{p_{x}}\) & \(\mathbf{p_{y}}\) & \(\mathbf{p_{z}}\) & \(\mathbf{I_{xx}}\) & \(\mathbf{I_{xy}}\) & \(\mathbf{I_{xz}}\) & \(\mathbf{I_{yy}}\) & \(\mathbf{I_{yz}}\)  
joint axes were approximately overlapping. The procedure of the experiment followed Algorithm 1 below. ```
Input: Data obtained by the six-dimensional force sensor include the force \(\mathbf{f}\) and torque \(\tau\); the pose data of end-effector \(\mathbf{q}\); the corresponding format of dual quaternions: \(\mathbf{f}_{\mathbf{I}}^{t}\), \(\tau_{\mathbf{I}}^{t}\), \(\mathbf{q}_{\mathbf{I}+1}^{t}\). 1: Under the motion state of the robot to obtain different pose data of the end-effector \(\mathbf{q}\), the six-dimensional force sensor is used to obtain the force and torque data of the load, and the dynamic parameters of the load are identified using the least-squares method based on Equations (14) and (19). 2: Identify the combination of the load and the \(\mathbf{n}\)-th connecting linkage, and obtain the dynamic parameters of the \(\mathbf{n}\)-th connecting linkage by combining them with known dynamic parameters of the load based on Equation (25). 3: Identify the combination of the \(\mathbf{n}-1\)-th to the \(\mathbf{n}\)-th connecting linkages and the load, and obtain the dynamic parameters of the combination by combining the known dynamic parameters of the combination of the \(\mathbf{n}\)-th linkage and the load. 4. Repeat step 2 to identify the dynamic parameters of the remaining linkages. Output: \(\mathbf{M}(\mathbf{I}_{\mathbf{I}})\leftarrow\mathbf{M}(\mathbf{I})\)
```  
**Algorithm 1**Dynamic parameters identification of a serial robot based on dual quaternion (DPDQ)  
Therefore, in the procedure of the identification experiment using the concept of combination, first, the first joint to the third joint of the robotic arm was identified as a combination part, and from the fifth joint to the seventh joint was identified as another combination part. When obtaining the initial state of the experimental data for these two combination parts separately, set the third joint axis near the end direction to be perpendicular to the first joint axis, basically, and set the seventh joint axis to be perpendicular to the fifth joint axis, basically.