## 2 Dynamic Modeling of 6R Robot System
### Simulation Verification of Dynamic Parameter Identification Model
In this experiment, five sets of parameters are selected, respectively, taking the parameters at the five times of 0.3 s, 0.6 s, 0.9 s, 1.2 s and 1.5 s (other arbitrary times can also be randomly selected). The dynamic parameters of the 6R robot system are identified, as shown in Table 3.  
Among them, \(m_{i}(\mathbf{e}_{1}^{(0)})\),\(m_{i}(\mathbf{e}_{2}^{(0)})\),\(m_{i}(\mathbf{e}_{3}^{(0)})\) are the mass parameters of a rigid body \(B_{1}\) identified in the \(\mathbf{e}_{1}^{(0)}\mathbf{e}_{2}^{(0)}\mathbf{e}_{3}^{(0)}\) directions, respectively. Since rigid body \(B_{1}\) does not have acceleration in the \(\mathbf{e}_{2}^{(0)}\) direction, the mass cannot be identified in this direction. The absolute error between the dynamic parameters obtained by identifying rigid body \(B_{6}\), \(B_{5},\cdots,B_{1}\) from outside to inside and its true value is shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rigid Body \(\mathbf{B}_{i}\)** & \(\mathbf{B}_{1}\) & \(\mathbf{B}_{2}\) & \(\mathbf{B}_{3}\) & \(\mathbf{B}_{4}\) & \(\mathbf{B}_{5}\) & \(\mathbf{B}_{6}\) \\ \hline \(m_{i}(\mathbf{e}_{1}^{(0)})\)(kg) & 6402.6000 & 2746.0720 & 1186.1658 & 308.7958 & 284.2875 & 661.7041 \\ \(m_{i}(\mathbf{e}_{2}^{(0)})\)(kg) & — & 2746.0723 & 1186.1661 & 308.7955 & 284.2875 & 661.7043 \\ \(m_{i}(\mathbf{e}_{3}^{(0)})\)(kg) & 6402.5942 & 2746.0723 & 1186.1660 & 308.7955 & 284.2877 & 661.7042 \\ \(f_{i_{1}}^{(i)}\)(kg\(\cdot\) m\({}^{2}\)) & 800.3252 & 123.6157 & 23.7206 & 6.1761 & 5.6856 & 29.7769 \\ \(f_{i_{2}}^{(i)}\)(kg\(\cdot\) m\({}^{2}\)) & 982.8120 & 416.4683 & 156.5821 & 5.6412 & 4.8348 & 19.8511 \\ \(f_{i_{3}}^{(i)}\)(kg\(\cdot\) m\({}^{2}\)) & 982.8120 & 416.5109 & 156.5722 & 5.4619 & 4.8353 & 19.8514 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Identified 6R robot system dynamic parameters. Figure 10: The termination posture of the KR500 robot ADAMS simulation. There are two reasons for the error: 1. The dynamics identification model is a complex system. To obtain the final result, many calculations are required. The result of each calculation will cause absolute errors due to only taking part of the significant digits. Therefore, the greater the number of calculations, the bigger the absolute error accumulated. 2. Since the data measured by ADAMS software retains seven significant digits and the counting rules cannot be changed, the larger the measured number, the more digits of the integer and the fewer digits of the decimals, then the greater the absolute error produced. It can be seen from Table 4 that the absolute error of the identified mass \(m_{i}\) is very small. This is because the number of calculations for the identified mass is less. The absolute error of \(m_{1}\) is larger than that of other \(m_{i}\)\((i=2,3,\cdots,6)\). This is because the force and moment of rigid body \(B_{1}\) is larger than that of other \(B_{i}\)\((i=2,3,\cdots,6)\). The reduction in the number of decimal places of relevant data increases the absolute error. The absolute error of the principal moment of inertia \(J_{i_{11}}^{(i)},J_{i_{22}}^{(i)},J_{i_{33}}^{(i)}\) of rigid body \(B_{6},B_{5},\cdots,B_{2}\) is larger than that of mass \(m_{i}\). This is because the principal moment of inertia \(J_{i_{11}}^{(i)},J_{i_{22}}^{(i)},J_{i_{33}}^{(i)}\) is identified in the rigid body joint base \((O_{i},\ e^{(i)})\). The calculation process involves the coordinate transformation of parameters such as angular velocity \(\omega_{i}\) and angular acceleration \(\dot{\omega}_{i}\), and more calculation times cause the accumulation of absolute errors. The absolute error of the principal moment of inertia \(J_{i_{11}}^{(1)},J_{i_{22}}^{(1)},J_{i_{33}}^{(1)}\) of \(B_{1}\) is smaller than that of \(J_{i_{11}}^{(i)},J_{i_{22}}^{(i)},J_{i_{33}}^{(i)}\)\((i=2,3,\cdots,6)\).