diff --git a/doc/images/ergodicControl-fromCrudetoPrecise01.jpg b/doc/images/ergodicControl-fromCrudetoPrecise01.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..0f67c875f160f9ac79cc62e5560c3e287441d920
Binary files /dev/null and b/doc/images/ergodicControl-fromCrudetoPrecise01.jpg differ
diff --git a/doc/images/f_ee01.png b/doc/images/f_ee01.png
index 89d70336229a315f739ceb16126c5551354a40dc..8b4792a35fd7da2b67870c24df5b58633e8acfa9 100755
Binary files a/doc/images/f_ee01.png and b/doc/images/f_ee01.png differ
diff --git a/doc/images/iLQR_objectBoundaries01.png b/doc/images/iLQR_objectBoundaries01.png
new file mode 100755
index 0000000000000000000000000000000000000000..8b855c268999f7291ccc7a204b30235ace41b1fa
Binary files /dev/null and b/doc/images/iLQR_objectBoundaries01.png differ
diff --git a/doc/images/transformations01.jpg b/doc/images/transformations01.jpg
deleted file mode 100644
index c493bfb2f2bdf3233b1687cb1c678f3157dbcc0c..0000000000000000000000000000000000000000
Binary files a/doc/images/transformations01.jpg and /dev/null differ
diff --git a/doc/images/transformations01.png b/doc/images/transformations01.png
new file mode 100755
index 0000000000000000000000000000000000000000..f408379b082d37ff57e41febfcaa284d31448ccb
Binary files /dev/null and b/doc/images/transformations01.png differ
diff --git a/doc/rcfs.pdf b/doc/rcfs.pdf
index c61f486fad35a89c1ddabb8eb46155ed1555dd85..3e34e0ee14b7f55711941b31da3520780957987e 100644
Binary files a/doc/rcfs.pdf and b/doc/rcfs.pdf differ
diff --git a/doc/rcfs.tex b/doc/rcfs.tex
index 1664acca51b3270d1eba27ba73f76765d18e1bae..8ad68ae82b7e22201b6fa7bfc858f3a4df1a3a53 100644
--- a/doc/rcfs.tex
+++ b/doc/rcfs.tex
@@ -573,7 +573,7 @@ f = np.array([L @ np.diag(l) @ np.cos(L @ x), L @ np.diag(l) @ np.sin(L @ x)]) #
 
 \begin{figure}
 \centering
-\includegraphics[width=.5\columnwidth]{images/transformations01.jpg}
+\includegraphics[width=.5\columnwidth]{images/transformations01.png}
 \caption{\footnotesize
 Typical transformations involved in a manipulation task involving a robot, a vision system, a visual marker on the object, and a desired grasping location on the object.  
 }
@@ -601,12 +601,12 @@ where $\bm{J}\in\mathbb{R}^{R\times D}$ is the Jacobian matrix of $\bm{f}\in\mat
 
 For the orientation part of the data (if considered), the residual vector $\bm{f}(\bm{x}) = \bm{f}^\tp{ee}(\bm{x}) - \bm{\mu}$ is replaced by a geodesic residual computed with the logarithmic map $\bm{f}(\bm{x}) = \mathrm{Log}_{\bm{\mu}}\!\big(\bm{f}^\tp{ee}(\bm{x})\big)$, see \cite{Calinon20RAM} for details.
 
-The approach can also be extended to target objects/landmarks with positions $\bm{\mu}$ and rotation matrices $\bm{A}$, as depicted in Fig.~\ref{fig:transformations}. %, whose columns are basis vectors forming a coordinate system
+The approach can also be extended to target objects/landmarks with positions $\bm{\mu}$ and rotation matrices $\bm{U}$, as depicted in Fig.~\ref{fig:transformations}. %, whose columns are basis vectors forming a coordinate system
 We can then define an error between the robot endeffector and an object/landmark expressed in the object/landmark coordinate system as 
 \begin{equation}
 \begin{aligned}
-	\bm{f}(\bm{x}) &= \bm{A}^\trsp \big(\bm{f}^\tp{ee}(\bm{x}) - \bm{\mu}\big), \\
-	\bm{J}(\bm{x}) &= \bm{A}^\trsp \bm{J}^\tp{ee}(\bm{x}). 
+	\bm{f}(\bm{x}) &= \bm{U}^\trsp \big(\bm{f}^\tp{ee}(\bm{x}) - \bm{\mu}\big), \\
+	\bm{J}(\bm{x}) &= \bm{U}^\trsp \bm{J}^\tp{ee}(\bm{x}). 
 \end{aligned}
 \label{eq:fJU}
 \end{equation}
@@ -2483,7 +2483,7 @@ Based on the above definitions, $\bm{f}(\bm{x})$ and $\bm{J}(\bm{x})$ are in thi
 
 \begin{SCfigure}
 \centering
-\includegraphics[width=.6\textwidth]{images/iLQR_objectBoundaries01.jpg}
+\includegraphics[width=.6\textwidth]{images/iLQR_objectBoundaries01.png}
 \caption{\footnotesize
 Example of a viapoints task in which a planar robot with 3 joints needs to sequentially reach 2 objects, with object boundaries defining the allowed reaching points on the objects surfaces. \emph{Left:} Reaching task with two viapoints at $t=25$ and $t=50$. \emph{Right:} Corresponding values of the cost function for the endeffector space at $t=25$ and $t=50$.
 }
@@ -3226,6 +3226,9 @@ Search and exploration problems can be formulated in various ways. Ergodic contr
 }
 \end{figure}
 
+
+%ergodicControl-fromCrudetoPrecise01.jpg
+
 %\begin{figure}
 %\centering{