diff --git a/doc/rcfs.pdf b/doc/rcfs.pdf index 6e66cf92d5dee741242c8d7821e8a46e21050f1f..8dc1b0611350433e08269f3528baaa55a1ff7b63 100644 Binary files a/doc/rcfs.pdf and b/doc/rcfs.pdf differ diff --git a/doc/rcfs.tex b/doc/rcfs.tex index 881bfcaef381d99ac4f8f791d58e6af035a2535e..70b287459f2ee71f003a1adc54aa279d8d7c8d56 100644 --- a/doc/rcfs.tex +++ b/doc/rcfs.tex @@ -96,8 +96,8 @@ innerleftmargin=0.3em,innerrightmargin=0.3em,innertopmargin=0.3em,innerbottommar % urlcolor=black %} -\title{\huge Learning and Optimization in Robotics\\[4mm]\emph{Lecture notes}} -%Math Cookbook for robot manipulation +\title{\huge A Math Cookbook for Robot Manipulation} +%Learning and Optimization in Robotics\\[4mm]\emph{Lecture notes} %A practical guide to learning and control problems in robotics\\solved with second-order optimization \author{Sylvain Calinon, Idiap Research Institute} \date{} @@ -114,7 +114,7 @@ innerleftmargin=0.3em,innerrightmargin=0.3em,innertopmargin=0.3em,innerbottommar %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} -This technical report presents several learning and optimal control techniques in robotics in the form of simple toy problems that can be easily coded. It comes as part of \textbf{Robotics Codes From Scratch (RCFS)}, a website containing interactive sandbox examples and exercises, together with a set of standalone source code examples gathered in a git repository, which can be accessed at: +This cookbook presents several learning and optimal control recipes for robotics (essentially for robot manipulators), complemented by simple toy problems that can be easily coded. It accompanies \textbf{Robotics Codes From Scratch (RCFS)}, a website containing interactive sandbox examples and exercises, together with a set of standalone source code examples gathered in a git repository, which can be accessed at: \begin{center} \url{https://rcfs.ch} %\url{https://gitlab.idiap.ch/rli/robotics-codes-from-scratch} @@ -1004,7 +1004,7 @@ which ensures that $w_4=w_5$ and $w_6=-w_3+2w_5$. These constraints guarantee th Based on observed data $\bm{x}$, the superposition weights $\bm{\hat{w}}$ can be estimated as a simple least squares estimate \begin{equation} - \bm{\hat{w}} = \bm{\Psi}^\psin \bm{x} = {(\bm{\Psi}^\trsp\bm{\Psi}}^{-1} \bm{\Psi}^\trsp \bm{x}, + \bm{\hat{w}} = \bm{\Psi}^\psin \bm{x} = {(\bm{\Psi}^\trsp\bm{\Psi})}^{-1} \bm{\Psi}^\trsp \bm{x}, \end{equation} or as the regularized version (ridge regression) \begin{equation}