## 5 Optimization Result
### Problem Data
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Link** & \(I_{xx}\left(\mathbf{kgm}^{2}\right)\) & \(I_{xy}\left(\mathbf{kgm}^{2}\right)\) & \(I_{xx}\left(\mathbf{kgm}^{2}\right)\) & \(I_{yy}\left(\mathbf{kgm}^{2}\right)\) & \(I_{yz}\left(\mathbf{kgm}^{2}\right)\) & \(I_{zz}\left(\mathbf{kgm}^{2}\right)\) \\ \hline
**1** & \(1.035\times 10^{0}\) & \(1.615\times 10^{-2}\) & \(-4.038\times 10^{-1}\) & \(1.749\times 10^{0}\) & \(6.423\times 10^{-3}\) & \(1.704\times 10^{0}\) \\
**2** & \(6.968\times 10^{-2}\) & \(4.534\times 10^{-3}\) & \(3.603\times 10^{-2}\) & \(1.064\times 10^{0}\) & \(-3.916\times 10^{-3}\) & \(1.095\times 10^{0}\) \\
**3** & \(2.853\times 10^{-2}\) & \(-1.836\times 10^{-3}\) & \(-3.915\times 10^{-3}\) & \(3.356\times 10^{-2}\) & \(-5.231\times 10^{-3}\) & \(3.721\times 10^{-2}\) \\
**4** & \(2.602\times 10^{-1}\) & \(-1.805\times 10^{-7}\) & \(2.179\times 10^{-4}\) & \(2.563\times 10^{-1}\) & \(-2.879\times 10^{-4}\) & \(2.102\times 10^{-2}\) \\
**5** & \(1.250\times 10^{-3}\) & \(1.078\times 10^{-5}\) & \(4.926\times 10^{-8}\) & \(1.699\times 10^{-3}\) & \(0\times 10^{0}\) & \(2.103\times 10^{-3}\) \\
**6** & \(2.935\times 10^{-4}\) & \(0\times 10^{0}\) & \(0\times 10^{0}\) & \(2.935\times 10^{-4}\) & \(0\times 10^{0}\) & \(4.615\times 10^{-4}\) \\
**7** & \(1.577\times 10^{-2}\) & \(0\times 10^{0}\) & \(5.550\times 10^{-3}\) & \(2.324\times 10^{-2}\) & \(0\times 10^{0}\) & \(1.279\times 10^{-2}\) \\ \hline
**Link** & \(r_{x}\left(\mathbf{m}\right)\) & \(r_{y}\left(\mathbf{m}\right)\) & \(r_{z}\left(\mathbf{m}\right)\) & \(\mathbf{m}\left(\mathbf{kg}\right)\) & & \\ \hline
**1** & \(4.969\times 10^{-2}\) & \(2.218\times 10^{-2}\) & \(1.757\times 10^{-1}\) & \(7.147\times 10^{1}\) & & \\
**2** & \(2.675\times 10^{-1}\) & \(1.557\times 10^{-2}\) & \(-3.977\times 10^{-3}\) & \(2.468\times 10^{1}\) & & \\
**3** & \(2.386\times 10^{-2}\) & \(1.063\times 10^{-1}\) & \(1.526\times 10^{-3}\) & \(2.592\times 10^{0}\) & & \\
**4** & \(-5.593\times 10^{-5}\) & \(4.071\times 10^{-4}\) & \(-2.620\times 10^{-1}\) & \(7.889\times 10^{0}\) & & \\
**5** & \(1.490\times 10^{-2}\) & \(-2.619\times 10^{-4}\) & \(3.226\times 10^{-6}\) & \(1.029\times 10^{0}\) & & \\
**6** & \(0\times 10^{0}\) & \(0\times 10^{0}\) & \(-1.775\times 10^{-2}\) & \(4.183\times 10^{-1}\) & & \\
**7** & \(-4.213\times 10^{-2}\) & \(0\times 10^{0}\) & \(6.046\times 10^{-2}\) & \(5.785\times 10^{0}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inertial parameters for the 6-DoF robot. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Joint** & \(q_{min}\) (\({}^{\circ}\)) & \(q_{max}\) (\({}^{\circ}\)) & \(\dot{q}_{max}\) (\(\mathbf{rpm}\)) & \(\dot{q}_{rate}\) (\(\mathbf{rpm}\)) & \(\tau_{max}\) (\(\mathbf{Nm}\)) \\ \hline
**1** & \(-172\) & \(172\) & \(38\) & \(15\) & \(412\) \\
**2** & \(-180\) & \(78\) & \(38\) & \(15\) & \(412\) \\
**3** & \(-82\) & \(180\) & \(38\) & \(15\) & \(245\) \\
**4** & \(-180\) & \(180\) & \(72\) & \(40\) & \(25\) \\
**5** & \(-135\) & \(135\) & \(72\) & \(40\) & \(16\) \\
**6** & \(-360\) & \(360\) & \(107\) & \(40\) & \(16\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Limit on joint displacement, speed and torque.