diff --git a/doc/rcfs.pdf b/doc/rcfs.pdf index aeea9767195766c273a6069ed610f78e0597faa5..6e66cf92d5dee741242c8d7821e8a46e21050f1f 100644 Binary files a/doc/rcfs.pdf and b/doc/rcfs.pdf differ diff --git a/doc/rcfs.tex b/doc/rcfs.tex index 90ff864ac96e440ceae80cf0c76776c5246fad16..881bfcaef381d99ac4f8f791d58e6af035a2535e 100644 --- a/doc/rcfs.tex +++ b/doc/rcfs.tex @@ -97,6 +97,7 @@ innerleftmargin=0.3em,innerrightmargin=0.3em,innertopmargin=0.3em,innerbottommar %} \title{\huge Learning and Optimization in Robotics\\[4mm]\emph{Lecture notes}} +%Math Cookbook for robot manipulation %A practical guide to learning and control problems in robotics\\solved with second-order optimization \author{Sylvain Calinon, Idiap Research Institute} \date{} @@ -1013,7 +1014,7 @@ or as the regularized version (ridge regression) For example, if we want to fit a reference path, which can also be sparse or composed of a set of viapoints, while minimizing velocities (or similarly, any other derivatives, such as computing a minimum jerk trajectories), we can solve \begin{align} - \bm{\hat{w}} &= \arg\min_{\bm{w}} \|\bm{\Psi}\bm{w} - \bm{x}\|^2 + \lambda \|\bm{\nabla}\!\bm{\Psi}\bm{w}\|^2 \\ + \bm{\hat{w}} &= \arg\min_{\bm{w}} \frac{1}{2}\|\bm{\Psi}\bm{w} - \bm{x}\|^2 + \frac{\lambda}{2} \|\bm{\nabla}\!\bm{\Psi}\bm{w}\|^2 \\ &= {(\bm{\Psi}^\trsp\bm{\Psi} + \lambda\bm{\nabla}\!\bm{\Psi}^\trsp\bm{\nabla}\!\bm{\Psi})}^{-1} \bm{\Psi}^\trsp \bm{x}. \label{eq:ridge2} \end{align}