Optimization Vector¶
The optimization vector in the quadratic problem is written as follows :
\[\begin{split}X =
\begin{pmatrix}
\dot{\nu}^{fb}\\
\dot{\nu}^{j}\\
\tau^{fb}\\
\tau^{j}\\
^{e}w_{0}\\
\vdots\\
^{e}w_{n}\\
\end{pmatrix}\end{split}\]
- \(\dot{\nu}^{fb}\) : Floating base joint acceleration (\(6 \times 1\))
- \(\dot{\nu}^{j}\) : Joint space acceleration (\(n_{dof} \times 1\))
- \(\tau^{fb}\) : Floating base joint torque (\(6 \times 1\))
- \(\tau^{j}\) : Joint space joint torque (\(n_{dof} \times 1\))
- \(^{e}w_n\) : External wrench (\(6 \times 1\))
- \(\tau^{fb}\) : Floating base joint torque (\(6 \times 1\))
- \(\tau^{j}\) : Joint space joint torque (\(n_{dof} \times 1\))
- \(^{e}w_n\) : External wrench (\(6 \times 1\))
In ORCA those are called Control variables and should be used to define every task and constraint. In addition to those necessary variables, you can specify also a combination :
- \(\dot{\nu}\) : Generalised joint acceleration, concatenation of \(\dot{\nu}^{fb}\) and \(\dot{\nu}^{j}\) (\(6+n_{dof} \times 1\))
- \(\tau\) : Generalised joint torque, concatenation of \(\tau^{fb}\) and \(\tau^{j}\) (\(6+n_{dof} \times 1\))
- \(X\) : The whole optimization vector (\(6 + n_{dof} + 6 + n_{dof} + n_{wrenches}6 \times 1\))
- \(^{e}w\) : External wrenches (\(n_{wrenche} 6 \times 1\))
- \(X\) : The whole optimization vector (\(6 + n_{dof} + 6 + n_{dof} + n_{wrenches}6 \times 1\))
- \(^{e}w\) : External wrenches (\(n_{wrenche} 6 \times 1\))