practical.tex.bak

移动机器人同时定位与地图创建最前沿技术

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\newcommand{\coursetitle}{SLAM Summer School 2006}
\newcommand{\tutorialtitle}{Practical 3: SLAM using Monocular Vision}
\newcommand{\docauthor}{Javier Civera, University of Zaragoza\\
                        Andrew J. Davison, Imperial College London\\
                        J.M.M Montiel, University of Zaragoza.}
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\section{Objectives}
\begin{enumerate}
\item Understanding the characteristics of SLAM using a monocular
camera as a sensor.
\begin{enumerate}
\item Map management.
\item Feature initialization.
\item Near and far features.
\end{enumerate}
\item Understanding the inverse depth parametrization of the map
features in monocular SLAM.
\item Understanding the performance
limits of the constant velocity motion model for the camera as the
unique SLAM sensor without odometry.
\end{enumerate}


\section{Exercise 1. Feature selection and matching.}
One of the particular characteristics of the monocular SLAM
current computers cannot process all the information provided by
image sensors. So, heuristics to select which features are
included in the map are used. The desirable properties of the map
features are:
\begin{enumerate}
\item Saliency, features have to be identified by a texture patch.
\item About 14 map features have to be visible in the image, if not
new map features are initialized.
\item Spread over the whole image.
\end{enumerate}

The goal for this exercise is to do manually the feature
initialization in order to meet the previous criteria. Run
\texttt{mono\_slam.m}. With the user interface, you can add
features and perform step by step the EKF SLAM:
\begin{enumerate}
\item In the first image add about ten salient features spread over the image.
You can watch the movie \texttt{juslibol\_SLAM.mpg} with the
software mpeg\_play as an example on which features select (but you
can of course select other ones). This movie shows the results when
applying automatic feature selection.
\item As camera moves, some features will not be seen, and you will
have to add new ones in order to have around 14 map features
visible.
\end{enumerate}

\section{Exercise 2. Near features and far features.}
A camera is a bearing-only sensor. This means that the depth of a
feature cannot be estimated with a single image measurement. The
depth of the feature can be estimated only if the feature is
observed from different points of view (only if the camera
translates enough to produce a significant parallax). So, it can
be distant features whose depth cannot be correctly estimated for
a long time, or even never if the translation is never big enough
to produce parallax.

The goal of this exercise is to observe the different estimation
evolution for near and distant features and their influence in the
camera location estimate.

\begin{enumerate}
\item Open the video \texttt{parallax.mpg}.
      Observe the different motion \emph{in the image} of different depth features.
      Open the video \texttt{noparallax.mpg} and see now that the motion in the image
       of different depth features is the same.
\item Now analyse the video we are using for this practical (\texttt{juslibol.mpg}).
Distinguish in this video parts with \emph{low parallax motion}.
\item Run \texttt{mono\_slam.m}.
\begin{itemize}
\item  Observe what happens to the features in the 3D map
(initialization value and covariance and value and covariance
after some frames). Red dots are the estimated values and red
lines limit the $95\%$ acceptance region.
\item The code singles out features \#5 and \#15 and displays depth
estimation and its $95\%$ acceptance region: [lower limit,
estimation, upper limit]. When clicking, make sure that feature \#5
corresponds to a near one (for example, on the car) and feature \#15
corresponds to a far one (for example, the tree appearing on the
left).
\item   Notice the difference between the evolution of near and
distant features.
\item Observe the camera location uncertainty
evolution (Use the axes limit controls in the user interface).
\item Observe what happen to features and camera location uncertainties
during the low parallax motion part discussed in point 2. Notice
the difference between this part of the 3D map (constructed with
low parallax information) and the high parallax parts.
\end{itemize}
\end{enumerate}




\section{Exercise 3. Inverse depth parameterization.}

Initializing a feature in monocular SLAM is a challenging issue,
because the depth uncertainty is not well modelled by a Gaussian.
This problem is overcome using inverse depth instead of the
classical $XYZ$ representation.
\begin{figure}
\centering
\includegraphics[width=0.5\columnwidth]{FeatureObservationAndParameterization.eps}
\caption{Feature parameterization and measurement equation.}
\label{fig_feat_par}
\end{figure}

Matlab code of the practical is coded in inverse depth so state
vector is:
\begin{equation}
\x=\left(\x_v^\top, \y_1^\top, \y_2^\top, \ldots
\y_n^\top\right)^\top.
\end{equation}
it is composed of:
\begin{enumerate}
\item 13 components that correspond to the location and velocity of
the camera:
\begin{equation}
\x_v=\left(\begin{array}{c}\ere^{WC}\\\q^{WC}\\\uve^{W}\\\omegav^{W}\end{array}\right).
\end{equation}

\item The rest of the components are features. Each feature is represented by 6 parameters,
 that are the position of the camera the first time the feature was
 seen $x_i,  y_i,  z_i$, the ray coded with azimuth-elevation angles ($\theta,\phi$), in absolute reference,
 and the inverse depth, $\rho$, of the feature along the ray:
\begin{equation}
\y_i=\left(\begin{array}{cccccc}x_i & y_i & z_i & \theta_i &
\phi_i & \rho_i\end{array}\right)^\top
\end{equation}
So the transformation from the inverse depth coding to the
Eucleidean coding in the absolute frame is:
\begin{equation}
\left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}x_i\\y_i\\z_i\end{array}\right)+
                    \frac{1}{\rho_i}\m\left(\theta_i,
                    \phi_i\right).
\end{equation}
where:
\begin{equation}
\m=\left(\begin{array}{ccc}\cos\phi_i \sin\theta_i&
                     -\sin\phi_i&
                     \cos\phi_i \cos\theta_i\end{array}\right)^\top
                     \label{eq-m}
\end{equation}

\end{enumerate}
The goal of this exercise is to understand the inverse depth
parameterisation.
\begin{enumerate}
\item The code stores partial information about features \#5 and
\#15 in the file \texttt{history.mat}:

\begin{itemize}
\item \texttt{feature5History} is a 6 row matrix, Each column containing the feature \#5
location coded in inverse depth at step $k$.
\item \texttt{rhoHistory\_5} is a row vector containing the inverse depth estimation
history for feature 5.
\item \texttt{rhoHistory\_15} is a row vector containing the inverse depth estimation
history for feature 15.
\item \texttt{rhoStdHistory\_5} is a row vector containing the inverse depth
standard deviation history for feature 5.
\item \texttt{rhoStdHistory\_15} is a row vector containing the inverse depth standard deviation
history for feature 15.
\end{itemize}

\item Compute the $XYZ$ Euclidean location for feature \#5 after
processing all images.

\item Do a graph with the value of the inverse depth and the
  $95\%$ acceptance region history for both features \#5 and \#15.
  Use the matlab functions \texttt{open}, \texttt{figure}, \texttt{hold}, and \texttt{plot}.
  Comment the difference between the two graphs.

\item After processing the whole sequence, what is the estimation and the
acceptance region \emph{expressed in depth} for both features?

Think about a feature at infinity, what inverse depth would have?

Try to see in the previous graphs when the infinity is included in
both features estimation, that is, the feature can be at any depth
in the ray.
\end{enumerate}

\section{Exercise 4. Constant velocity motion model (optional)}
Monocular SLAM uses camera as the unique sensor, without any
odometry input. It is used a constant velocity model so the
systems needs as input both the camera frame rate and the maximum
expected angular and linear acceleration.

For a given camera acceleration, the frame rate defines the
acceptance region for the point matching, so for any acceleration,
the acceptance regions can be kept low if a frame rate high enough
is used.

The goal of this exercise is to analyse the effect of the linear
acceleration, the angular acceleration and the frame rate.

\begin{enumerate}
\item The initial tuning is $6\frac{m}{s^2}$ and $6\frac{\mbox{rad}}{s^2}$.
\item Increase the angular acceleration only (for instance, double
the value) and analyse the effect on the search region. Find this
parameter in the file \texttt{mono\_slam.m}, its name is
\texttt{sigma\_alphaNoise}.

\item Increase the linear acceleration only (for instance, double
the value), analyse the effect and compare with the previous
point. The name of this parameter is \texttt{sigma\_aNoise}.

\item Reduce the frame rate processing and see the effect:
\begin{enumerate}
\item 1 out of 2 images.
\item 1 out of 4 images.
\end{enumerate}
Clue: Find the variable step and the code associated with this
variable. You will also have to modify the variable
\texttt{deltat}, that codes the time between frames.

\end{enumerate}

\nocite{Hartley2004,Davison2003,Montiel2006RSS,Bar-Shalom-88}
\bibliographystyle{ieee}
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