From aa824d63a413b48d9afa918e901142d95827e685 Mon Sep 17 00:00:00 2001
From: Sylvain CALINON <sylvain.calinon@idiap.ch>
Date: Wed, 7 Aug 2024 09:06:40 +0200
Subject: [PATCH] min jerk added in doc

---
 doc/rcfs.pdf | Bin 13170838 -> 13170942 bytes
 doc/rcfs.tex |   3 ++-
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/doc/rcfs.pdf b/doc/rcfs.pdf
index aeea9767195766c273a6069ed610f78e0597faa5..6e66cf92d5dee741242c8d7821e8a46e21050f1f 100644
GIT binary patch
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diff --git a/doc/rcfs.tex b/doc/rcfs.tex
index 90ff864..881bfca 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}
-- 
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