Woolfrey / software_robot_library

Custom classes for robot control.
GNU General Public License v3.0
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Solve joint trajectory tracking as QP #118

Open Woolfrey opened 6 months ago

Woolfrey commented 6 months ago

We could solve the trajectory tracking control problem using QP:

\begin{align}
\min_\mathbf{\ddot{q}} \| \mathbf{\ddot{q}}_\mathrm{r} - \mathbf{\ddot{q}}\|^2_\mathrm{M}  \\
\begin{bmatrix}
\mathbf{\ddot{q}}_\mathrm{min} \\
\boldsymbol{\tau}_\mathrm{min}
\end{bmatrix}
\le
\begin{bmatrix}
\mathbf{\ddot{q}} \\
\mathbf{M\ddot{q}}
\end{bmatrix}
\le
\begin{bmatrix}
\mathbf{\ddot{q}}_\mathrm{max} \\
\boldsymbol{\tau}_\mathrm{max}
\end{bmatrix}
\end{align}

So that the resulting joint acceleration satisfied both kinematic and dynamic limits.