% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system robotrain (robotrain_desc.tex)
% Generated by MTT on Sun Sep 12 20:03:30 BST 2004.

The acausal bond graph of system \textbf{robotrain} is
displayed in Figure \Ref{fig:robotrain_abg.ps}.
The model is based on an off-hooked design of a passive multiple
trailer system for indoor service robots
\footnote{{Jaehyoung Lee, Woojin Chung, Munsang Kim, Chongwon Lee and Jeabok-Song,
    A passive multiple trailer system for indoor service robots,
    \emph{Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems},
    Maui, Hawaii, USA, 2001}}
The equations of motion for each trailer are given by:
\begin{align}
  v_i &= v_{i-1}\cos \phi_i+D_{i-1}\dot\theta_{i-1}\sin \phi_i\\
  \dot\theta_i &= \frac{1}{L_i}\left(v_{i-1}\sin \phi_i+D_{i-1}\dot\theta_{i-1}\cos \phi_i\right)\\
  \phi_i &= \theta_{i-1}-\theta_i
\end{align}
where $v$ and $\dot\theta$ are the translational and rotational velocity of each trailer (in the body axis system), $L$ and $D$ are the lengths of the front and rear moment arms, and the subscripts $_i$ and $_{i-1}$ refer to any trailer and the one in front of it.

The label file is listed in Section \Ref{sec:robotrain_lbl} and the
subsystems are listed in Section \Ref{sec:robotrain_sub}.

\subsection{Trajectory}
The trajectory of each of the trailer hooks in response to a constant forward and rotational velocity is shown in figure \Ref{fig:trajectory.ps}. 
\fig{trajectory}{trajectory.ps}{0.9}{Trajectory of trailer links}
The plot was generated with the following script:
\footnotesize
\verbatiminput{make_trajectory.sh}
\normalsize

