# A Method of Estimating an Object's Parameters Based on Simplication with Momentum for a Manipulator
## 4 Parameter Estimation Simulation
### Comparison with Previous Studies
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Joints** & \multicolumn{2}{c}{**0.1**} & \multicolumn{2}{c}{**0.05**} & \multicolumn{2}{c}{**0.025**} \\ \cline{3-8}  & & **Linear** & **Angular** & **Linear** & **Angular** & **Linear** & **Angular** \\ \hline \multirow{6}{*}{Range of joint motion (rad)} & \(q_{1}\) & 2.44 \(\times 10^{-1}\) & 2.41 \(\times 10^{-2}\) & 1.13 \(\times 10^{-1}\) & 1.21 \(\times 10^{-2}\) & 5.43 \(\times 10^{-2}\) & 6.10 \(\times 10^{-3}\) \\ \cline{2-8}  & \(q_{2}\) & 6.51 \(\times 10^{-2}\) & 2.61 \(\times 10^{-2}\) & 5.03 \(\times 10^{-2}\) & 1.26 \(\times 10^{-2}\) & 2.94 \(\times 10^{-2}\) & 6.20 \(\times 10^{-3}\) \\ \cline{2-8}  & \(q_{3}\) & 2.20 \(\times 10^{-1}\) & 5.80 \(\times 10^{-2}\) & 9.08 \(\times 10^{-2}\) & 2.89 \(\times 10^{-2}\) & 4.07 \(\times 10^{-2}\) & 1.44 \(\times 10^{-2}\) \\ \cline{2-8}  & \(q_{4}\) & 2.84 \(\times 10^{-1}\) & 1.31 \(\times 10^{-1}\) & 1.41 \(\times 10^{-1}\) & 6.64 \(\times 10^{-2}\) & 7.01 \(\times 10^{-2}\) & 3.33 \(\times 10^{-2}\) \\ \cline{2-8}  & \(q_{5}\) & 6.60 \(\times 10^{-4}\) & 9.99 \(\times 10^{-2}\) & 3.37 \(\times 10^{-4}\) & 5.00 \(\times 10^{-2}\) & 1.62 \(\times 10^{-4}\) & 2.50 \(\times 10^{-2}\) \\ \cline{2-8}  & \(q_{6}\) & 2.44 \(\times 10^{-1}\) & 1.24 \(\times 10^{-1}\) & 1.13 \(\times 10^{-1}\) & 6.22 \(\times 10^{-2}\) & 5.43 \(\times 10^{-2}\) & 3.11 \(\times 10^{-2}\) \\ \hline \multirow{6}{*}{Maximum joint velocity (rad/s)} & \(q_{1}\) & \(4.64\times 10^{-1}\) & \(4.54\times 10^{-2}\) & \(2.14\times 10^{-1}\) & \(2.28\times 10^{-2}\) & \(1.02\times 10^{-1}\) & 1.14 \(\times 10^{-2}\) \\ \cline{2-8}  & \(q_{2}\) & \(1.62\times 10^{-1}\) & \(4.90\times 10^{-2}\) & \(1.74\times 10^{-1}\) & \(2.37\times 10^{-2}\) & \(5.58\times 10^{-2}\) & \(1.17\times 10^{-2}\) \\ \cline{2-8}  & \(q_{3}\) & \(4.32\times 10^{-1}\) & \(1.09\times 10^{-1}\) & 9.08 \(\times 10^{-2}\) & \(5.42\times 10^{-2}\) & \(7.69\times 10^{-2}\) & \(2.71\times 10^{-2}\) \\ \cline{2-8}  & \(q_{4}\) & \(5.34\times 10^{-1}\) & \(2.48\times 10^{-1}\) & \(2.65\times 10^{-1}\) & \(1.24\times 10^{-1}\) & \(1.31\times 10^{-1}\) & \(6.23\times 10^{-2}\) \\ \cline{2-8}  & \(q_{5}\) & \(1.30\times 10^{-3}\) & \(1.87\times 10^{-1}\) & \(6.06\times 10^{-4}\) & \(9.37\times 10^{-2}\) & \(2.92\times 10^{-4}\) & \(4.69\times 10^{-2}\) \\ \cline{2-8}  & \(q_{6}\) & \(4.63\times 10^{-1}\) & \(1.87\times 10^{-1}\) & \(2.13\times 10^{-1}\) & \(9.37\times 10^{-2}\) & \(1.02\times 10^{-1}\) & \(4.69\times 10^{-2}\) \\ \hline \multirow{6}{*}{Maximum joint acceleration} & \(q_{1}\) & \(1.67\times 10^{0}\) & \(1.54\times 10^{-1}\) & \(7.46\times 10^{-1}\) & \(7.71\times 10^{-1}\) & \(3.51\times 10^{-1}\) & \(3.86\times 10^{-2}\) \\ \cline{2-8}  & \(q_{2}\) & \(7.00\times 10^{-1}\) & \(1.59\times 10^{-1}\) & \(3.67\times 10^{-1}\) & \(7.81\times 10^{-1}\) & \(1.90\times 10^{-1}\) & \(3.88\times 10^{-2}\) \\ \cline{2-8}  & \(q_{3}\) & \(1.60\times 10^{0}\) & \(3.36\times 10^{-1}\) & \(6.03\times 10^{-1}\) & \(1.67\times 10^{-1}\) & \(2.54\times 10^{-1}\) & \(8.35\times 10^{-2}\) \\ \cline{2-8}  & \(q_{4}\) & \(1.66\times 10^{0}\) & \(7.67\times 10^{-1}\) & \(8.22\times 10^{-1}\) & \(3.82\times 10^{-1}\) & \(4.07\times 10^{-1}\) & \(1.92\times 10^{-1}\) \\ \cline{2-8}  & \(q_{5}\) & \(2.97\times 10^{-2}\) & \(5.78\times 10^{-1}\) & \(1.29\times 10^{-2}\) & \(2.89\times 10^{-1}\) & \(6.30\times 10^{-3}\) & \(1.45\times 10^{-1}\) \\ \cline{2-8}  & \(q_{6}\) & \(1.55\times 10^{0}\) & \(5.77\times 10^{-1}\) & \(6.88\times 10^{-1}\) & \(2.89\times 10^{-1}\) & \(3.22\times 10^{-1}\) & \(1.43\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Range of joint angles and maximum joint velocity and acceleration during the estimation by each motion range. The estimation motions are summarized in Tables 7 and 8. Table 7 shows the range of linear and angular displacements of the robot's end-effector, along with the maximum velocities and accelerations observed during the estimation process in previous studies and in this study with a motion range of 0.1.