%
%  2004/Lecture notes/Lecture28/Lecture28.tex
%
\documentclass[pdf,mmoll,slideColor%,colorBG
]{prosper}
\RequirePackage{color}

\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,natbib}
%\usepackage[T1,noTS1]{mathtime}
\SetMathAlphabet{\mathbf}{normal}{\encodingdefault}{ptm}{b}{n}
\usepackage{subfigure}
\usepackage{rotating}
\usepackage{graphicx}
%\usepackage[dvips]{color}
\usepackage{epsfig}
\graphicspath{{../figs/}}

\newcommand{\ee}{\end{equation}} 
\newcommand{\be}{\begin{equation}} 
\newcommand{\ec}{\end{center}} 
\newcommand{\bc}{\begin{center}} 
\newcommand{\eea}{\end{eqnarray}} 
\newcommand{\bea}{\begin{eqnarray}} 
%\newcommand{\sumprime}{\mathop{{\sum}'}} 
\newcommand{\bd}{\begin{description}} 
\newcommand{\ed}{\end{description}} 
\newcommand{\bi}{\begin{itemize}} 
\newcommand{\ei}{\end{itemize}} 
\newcommand{\pa}{\partial} 
\newcommand{\hor}{\left(\frac{h}{R_0}\right)} 

\newcommand{\code}[0]{\ttfamily}
\newcommand{\co}[0]{\hbox{c}}
\newcommand{\si}[0]{\hbox{s}}
\newcommand{\pprime}[0]{\prime\prime}
\newcommand{\ppprime}[0]{\prime\prime\prime}
\newcommand{\conv}{\operatorname{conv}}
\newcommand{\pos}{\operatorname{pos}}
\newcommand{\lin}{\operatorname{lin}}
\newcommand{\vertop}{\operatorname{vert}}
\newcommand{\spanop}{\operatorname{span}}
\newcommand{\supp}{\operatorname{supp}}
\newcommand{\intoper}{\operatorname{int}}
\newcommand{\half}{\operatorname{half}}
\newcommand{\rad}{\operatorname{rad}}
\newcommand{\diam}{\operatorname{diam}}
\newcommand{\push}{\operatorname{push}}
\newcommand{\sqz}{\operatorname{sqz}}
\newcommand{\sgn}{\operatorname{sgn}}
%\renewcommand{\Re}{\Bbb{R}}
\renewcommand{\Re}{\mathbf{R}}
\newcommand{\vv}[1]{\mathbf{#1}}
\newcommand{\uu}[1]{\hat {\vv #1}}
\newcommand{\defterm}[1]{\textbf{#1}}
\newcommand{\rot}{\operatorname{rot}}

\newcommand{\btimes}{\times}
\newcommand{\bomega}{\omega}

 
\newcommand{\bis}{\begin{itemstep}} 
\newcommand{\eis}{\end{itemstep}} 

\makeatletter
\define@key{PDF}{Movie}{\pdf@addtoks{#1}{Movie}}
\define@key{PDF}{Activation}{\pdf@addtoks{#1}{Activation}}
\newcommand{\moviewithpreview}[3]{% args: width, preview, movie
   \pdfmark[{\includegraphics[width=#1]{#2}}]{%
   pdfmark=/ANN,Subtype=/Movie,Movie=<< /F (#3) >>,%
   Activation=<< /ShowControls true /Mode /Repeat >>}}
\newcommand{\movie}[3]{% args:width, height, movie
   \pdfmark[{\hbox to #1 {\vbox to #2 { }}}]{%
   pdfmark=/ANN,Subtype=/Movie,Movie=<< /F (#3) /Poster true >>,%
   Activation=<< /ShowControls true /Mode /Repeat >>}}
\makeatother

\title{28.  Quasidynamic parts orienting}
\subtitle{ Mechanics of Manipulation}
\author{Matt Mason}
\institution{Carnegie Mellon}
\email{matt.mason@cs.cmu.edu \\
http://www.cs.cmu.edu/\symbol{"7E}mason}
\slideCaption{Lecture 28. \hfill Mechanics of Manipulation }

\begin{document}

\maketitle

%=======================================================================
%
% SLIDE 2
%

\begin{slide}[R]{Lecture 28.  Quasidynamic parts orienting}
\vspace{-0.5in}
\includegraphics[height=3.0in]{TOC28}
\end{slide}

%=======================================================================
%
% SLIDE 3
%
%

\begin{slide}[R]{Outline.}

\begin{itemize}
\item What is ``quasidynamic''?
\item Demonstrate tray tilting.
\item Analysis of wrench in corner; of wrench at bottom.
\item Analysis of wrench in uncertain pose.
\end{itemize}

\end{slide}

%========
%
% Slide 4
%

\begin{slide}[R]{Quasidynamic}
\begin{minipage}[t]{6cm}
\begin{itemize}
\item[]Remember the peg in hole problem?  
\begin{itemize}
\item[] Static analysis: identify jamming and wedging conditions, and
  avoid them.
\item[] Quasistatic analysis: not applicable.  Non-jamming applied
  force is balanced only by dynamic load.
\item[] Dynamic analysis:  too hard.  Doubles the state variables.
\end{itemize}
\item[] Quasidynamic
\begin{itemize}
\item[] Assume velocity is negligible.
\item[] Solve for acceleration, assume object moves in direction of
acceleration. 
\end{itemize}
\end{itemize}
\end{minipage}
\hfill
\begin{minipage}[t]{4cm}
\begin{figure}[h!]
\includegraphics[width=4cm]{jwpeg}
%\includegraphics[height=3cm]{*file*}
\end{figure}\end{minipage}
\end{slide}

%=======
%
% Slide 5
%

\begin{slide}[R]{Tray tilting}
\movie{1.0\linewidth}{.67\linewidth}%
{PartsOrienting86.mov}
\end{slide}

%========
%
% Slide 6
%

\begin{slide}[R]{Assumptions}
\begin{enumerate}
\item Rigid body Newtonian mechanics with Coulomb friction.
\item Known shapes, mass distribution, coefficient of friction.
\item Friction with floor of tray is negligible.
\item Quasidynamic $\ldots$
\begin{itemize}
\item Centripetal acceleration is negligible.
\item Impact:  object just stops.
\end{itemize}
\end{enumerate}
\end{slide}

%=======================================================================
%
% SLIDE 7
%
%
\begin{slide}[R]{Goal for example plan}
\begin{minipage}[t]{6cm}
\begin{trivlist}
\item[]Initially wrench is oriented, and anywhere along the bottom wall.
\item[]Goal is for wrench to be in same orientation, in lower left corner.
\item[]Find a single action, a single applied force, that accomplishes the goal.
\end{trivlist}
\end{minipage}
\hfill
\begin{minipage}[t]{4cm}
\begin{figure}[h!]
\includegraphics[width=4cm]{wrtask}
%\includegraphics[height=3cm]{*file*}
\end{figure}\end{minipage}
\end{slide}

%=======================================================================
%
% SLIDE 7.5
%
%
\begin{slide}[R]{Plan of attack}
\begin{trivlist}
\item
Remember ambiguities.  We cannot just look at the desired contact mode to find a good tilt angle.  We have to exclude all the undesired contact modes.
\begin{itemize}
\item[]For every possible initial configuration $\ldots$
\item[]\qquad For every undesired contact mode
\item[]\qquad \qquad Exclude the tilt angles 
\end{itemize}

\item
If any tilt angles are not excluded by some contact mode for some initial configuration, then you have an action that produces the desired contact mode for every possible initial configuration.
\end{trivlist}
\end{slide}

%=======================================================================
%
% SLIDE 8
%
%
\begin{slide}[R]{Recall contact modes for wrench in corner}
\begin{figure}[h!]
\includegraphics[height=6cm]{wrmode}
\end{figure}
\end{slide}

%=======================================================================
%
% SLIDE 9
%
%
\begin{slide}[R]{Recall analysis of mode ``rsrs''}
\begin{minipage}[t]{6cm}
\begin{itemize}
\item[]We used force dual:
\item[]Represent dynamic load by acceleration center
\item[]Transform negated contact forces by force dual
\item[]Find positive linear span of force dual and negated contact forces
\item[]Result is candidate applied forces
\item[]Intersect with line at infinity to get tilt directions
\end{itemize}
\end{minipage}
\hfill
\begin{minipage}[t]{4cm}
\begin{figure}[h!]
\includegraphics[width=4cm]{wrrsrs}
%\includegraphics[height=3cm]{*file*}
\end{figure}\end{minipage}
\end{slide}

%=======================================================================
%
% SLIDE 10
%
%
\begin{slide}[R]{Analysis of mode ``ssrr''}
\begin{trivlist}
\item[]We'll use moment labeling
\item[]Transform acceleration center to dynamic load line of force
\item[]Find positive linear span of dynamic load and negated contact forces
\item[]Result is candidate applied forces
\item[]Intersect with wrenches through {\sc COM} to get tray tilt directions.
\end{trivlist}
\begin{figure}[h!]
\includegraphics[height=3cm]{wrssrr}
\end{figure}
\end{slide}

%=======================================================================
%
% SLIDE 11
%
%
\begin{slide}[R]{All possible actions from lower left corner}
\begin{minipage}[t]{6cm}
\begin{trivlist}
\item[]Analyze the other modes.
\item[]Record all modes corresponding to wrenches through {\sc COM}
\item[]In this case, no ambiguities
\end{trivlist}
\end{minipage}
\hfill
\begin{minipage}[t]{4cm}
\begin{figure}[h!]
\includegraphics[width=4cm]{wrmap4}
%\includegraphics[height=3cm]{*file*}
\end{figure}\end{minipage}
\end{slide}

%=======================================================================
%
% SLIDE 12
%
%
\begin{slide}[R]{Analysis of wrench on bottom wall}
Do the same thing for the wrench against the bottom wall, and intersect\\
\begin{figure}[h!]
\includegraphics[height=6cm]{wrmaps}
%\includegraphics[height=3cm]{*file*}
\end{figure}
\end{slide}

%=======================================================================
%
% SLIDE 13
%
%
\begin{slide}[R]{Parts orienting}
\begin{trivlist}
\item[]Assume initial location of object is everywhere:  any orientation, any place in the tray.
\item[]Goal is for it to be somewhere.  Some particular somewhere.
\item[]For every pose and every contact mode, identify the corresponding tilt angles.
\item[]Define a graph.  
\begin{itemize}
\item[]Each node is a set of configurations.  
\item[]Each edge is a range of tilt angles, the tilt angles that map the wrench from the source node configurations to the sink node configurations.
\item[]The root is the set of all configurations.
\end{itemize}
\item[]Do a breadth-first search of the tree.  When you reach a node with just one configuration, you're done.
\end{trivlist}

How big is the tree?  In theory, it could be big.  In practice, it's not.
\end{slide}

%=======================================================================
%
% SLIDE last
%

\begin{slide}[R]{Next:  Impact.}
\vspace{-0.5in}
\includegraphics[height=3.0in]{TOC29}
\end{slide}
\end{document}



\end{document}