Commit 7f9cbf9b authored by Florent Lamiraux's avatar Florent Lamiraux Committed by Florent Lamiraux florent@laas.fr
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[slides] Add a figure about relative poses.

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......@@ -781,18 +781,30 @@ Manipulation RRT is initialized with $\conf_{init}$, $\conf_{goal}$.
\begin {frame} {Relative positions as numerical constraints}
Let $T_1 = T_{(R_1,t_1)}$ and $T_2 = T_{(R_2,t_2)}$ be two rigid-body transformations. The relative transformation $T_{2/1} = T_1^{-1}\circ T_2$ can be represented by a vector of dimension 6:
$$
\left(\begin{array}{c} \mathbf{u} \\ \mathbf {v}\end{array}\right)
$$
where
\begin {columns}
\column {.5\textwidth}
$$
\mathbf{u} = R_1^T (t_2-t_1)
$$
\column {.5\textwidth}
$R_1^T R_2$ is the matrix of the rotation around axis $\mathbf{v}/\|\mathbf {v}\|$ and of angles $\|\mathbf {v}\|$.
\end {columns}
\centerline{
\parbox{.5\linewidth}{
\begin{itemize}
\item $T_1 = T_{(R_1,t_1)}\in SE(3)$, $T_2 = T_{(R_2,t_2)}\in SE(3)$.
\item $T_{2/1} = T_1^{-1}\circ T_2$ can be represented by a vector of dimension 6:
$$
\left(\begin{array}{c} \mathbf{u} \\ \mathbf {v}\end{array}\right)
$$
where
$$
\mathbf{u} = R_1^T (t_2-t_1)
$$
$R_1^T R_2$ matrix of the rotation around axis $\mathbf{v}/\|\mathbf {v}\|$ and of angles $\|\mathbf {v}\|$.
\end{itemize}
}
\parbox{.5\linewidth}{
\centerline {
\def\svgwidth {\linewidth}
{\tiny
\graphicspath{{./figures/}}
\input {figures/relative-pose.pdf_tex}
}
}
}
}
\end {frame}
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