## 5 Proposed Methods
### Transforming the Model
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** & **Units** \\ \hline \(\ell_{1s}\) & \(\mathrm{Thigh}\) length & \(24.05\,\%\times h=0.4209\) & m \\ \(\ell_{2s}\) & \(\mathrm{Shank}\) length & \(24.85\,\%\times h=0.4349\) & m \\ \(\ell_{3s}\) & \(\mathrm{Foot}\) length & \(13.15\,\%\times h=0.2301\) & m \\ \(\ell_{1r}\) & \(\mathrm{Robot}\)’s link 1 length & \(0.4209\) & m \\ \(\ell_{2r}\) & \(\mathrm{Robot}\)’s link 2 length & \(0.4349\) & m \\ \(\ell_{3r}\) & \(\mathrm{Robot}\)’s link 3 length & \(0.2301\) & m \\ \(\ell_{1}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s link 1 length & \(0.4209\) & m \\ \(\ell_{2}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s link 2 length & \(0.4349\) & m \\ \(\ell_{3}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s link 3 length & \(0.2301\) & m \\ \(m_{1s}\) & \(\mathrm{Thigh}\) weight & \(14.47\,\%\times m=10.8525\) & kg \\ \(m_{2s}\) & \(\mathrm{Shank}\) weight & \(4.57\,\%\times m=3.4275\) & kg \\ \(m_{3s}\) & \(\mathrm{Foot}\) weight & \(1.33\,\%\times m=0.9975\) & kg \\ \(m_{1r}\) & \(\mathrm{Robot}\)’s link 1 weight & \(19\) & kg \\ \(m_{2r}\) & \(\mathrm{Robot}\)’s link 2 weight & \(9\) & kg \\ \(m_{3s}\) & \(\mathrm{Robot}\)’s link 3 weight & \(11\) & kg \\ \(m_{1}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s weight of link 1 & \(29.8525\) & kg \\ \(m_{2}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s weight of link 2 & \(12.4275\) & kg \\ \(m_{3}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s weight of link 3 & \(11.9975\) & kg \\ \(b_{1}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s CoM of link 1 & \(38.53\,\%\times\ell_{1}=0.1622\) & m \\ \(b_{2}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s CoM of link 2 & \(44.37\,\%\times\ell_{2}=0.193\) & m \\ \(b_{3}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s CoM of link 3 & \(42.14\,\%\times\ell_{3}=0.1382\) & m \\ \(l_{c1,2z}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s Inertia of link 1 & \(\frac{1}{3}m_{1}(2b_{1})^{2}=1.047\) & kg m\({}^{2}\) \\ \(l_{c2,2z}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s Inertia of link 2 & \(\frac{1}{3}m_{2}(2b_{2})^{2}=0.6171\) & kg m\({}^{2}\) \\ \(l_{c3,2z}\) & \(\mathrm{Robot}\) + \(\mathrm{Subject}\)’s Inertia of link 3 & \(\frac{1}{3}m_{3}(2b_{3})^{2}=0.3053\) & kg m\({}^{2}\) \\ \(v_{1}\) & Viscous Friction in hip joint & \(100\) & \(\frac{\mathrm{Num}}{\mathrm{Num}}\)s \\ \(v_{2}\) & Viscous Friction in knee joint & \(100\) & \(\frac{\mathrm{Num}}{\mathrm{Num}}\)s \\ \(v_{3}\) & Viscous Friction in ankle joint & \(60\) & \(\frac{\mathrm{Num}}{\mathrm{Num}}\)s \\ \(g_{0}\) & Gravity & \(9.8\) & \(\frac{\mathrm{Num}}{\mathrm{Num}}\)s \\ \(K_{p}\) & Proportional gain & \(150\) & \(\frac{\mathrm{Num}}{\mathrm{Num}}\)s \\ \(T_{i}\) & Integral time & \(0\) & s \\ \(T_{4}\) & Derivative time & \(0.1\) & s \\ \(sat_{1}\) & \(\mathrm{Motor}\) 1 saturation & \(768.458\) & N m \\ \(sat_{2}\) & \(\mathrm{Motor}\) 2 saturation & \(371.377\) & N m \\ \(sat_{3}\) & \(\mathrm{Motor}\) 3 saturation & \(102.689\) & N m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: LLRR parameters for simulation including a subject of \(h=1.75\,\)m height and \(m=75\,\)kg weight.