Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
JPScore
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
92
Issues
92
List
Boards
Labels
Service Desk
Milestones
Merge Requests
3
Merge Requests
3
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Packages & Registries
Packages & Registries
Container Registry
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
JuPedSim
JPScore
Commits
cfa18800
Commit
cfa18800
authored
Jul 06, 2015
by
Arne Graf
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
thesis folder added
parent
736c6262
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
168 additions
and
0 deletions
+168
-0
doc/argraf/thesis_ar_gr02a.tex
doc/argraf/thesis_ar_gr02a.tex
+168
-0
No files found.
doc/argraf/thesis_ar_gr02a.tex
0 → 100644
View file @
cfa18800
%% LyX 2.0.6 created this file. For more info, see http://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
\RequirePackage
{
fix-cm
}
\documentclass
[english]
{
article
}
\usepackage
[T1]
{
fontenc
}
\usepackage
[utf8]
{
luainputenc
}
\setlength
{
\parskip
}{
\medskipamount
}
\setlength
{
\parindent
}{
0pt
}
\usepackage
{
amsmath
}
\usepackage
{
amssymb
}
\usepackage
{
fixltx2e
}
\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\numberwithin
{
equation
}{
section
}
\numberwithin
{
figure
}{
section
}
\numberwithin
{
table
}{
section
}
\makeatother
\usepackage
{
babel
}
\begin{document}
\title
{
Automated Routing in Pedestrian Dynamics
}
\author
{
Arne Graf
}
\date
{
2015-09-01
}
\maketitle
\section
{
Introduction
}
\section
{
ODE based Model (dep.? -> opt.?)
}
\section
{
Modelling
}
\subsection
{
Eikonal Equation
}
The ``Eikonal Equation'' in a domain
$
\Omega
$
, subset of
$
\mathbb
{
R
}^{
n
}$
,
\begin{align*}
\vert\nabla
u(x)
\vert\quad
=
&
\quad
F(x),x
\in\Omega
,
\\
\mathrm
{
s.t.
\qquad
u|
_{
\partial\Omega
}
\quad
=
}
&
\quad
0
\\
\end{align*}
yields ``first-arrival-times'' in a spacial domain provided a target
region within the domain.
\subsection
{
Safe Navigation using the Floorfield
}
\subsection
{
Distances-Field
}
\subsubsection
{
Cost of a ``full'' preprocessing step
}
\subsubsection
{
Distances-Field and repulsive Wall-Forces
}
\subsection
{
Variant Model
}
In the latter, a new approach in modeling is described, aiming for
the avoidance of faulty interaction of pedestrians and walls while
maintaining the positive characteristics of row-formation, stop-and-go
waves and such, like seen in experimental data. In many of the existing
models using mathematical formulations in continouus domain, agents
breach wall-surfaces and get stuck inside of walls or obstacles.
There are two mechanics used to avoid ``clipping'':
\begin{enumerate}
\item
The routing of pedestirans makes use of the eikonal-equation, computed
with an inhomogenious speed-function,
$
s
(
x
)
$
, which favours keeping
a distance to obstacles, walls and corners.
\item
The distance to the closest wall of each pedestrian affects the moving
speed if and only if the agent's moving vector includes a component
geared towards the wall.
\end{enumerate}
In order to keep the model simple, repulsive wall forces as seen in
Social Force Models are omitted. An analogy to repulsive pedestrian
forces though is used to keep agents from colliding with each other.
The model differs from SFMs, as other agents effect the desired moving
direction in full, the magnitude on the other hand is effected by
other agents only to a certain degree (as described in ).
\begin{alignat*}
{
1
}
\Delta\vec
{
x
}
\quad
=
\quad
&
\Delta
t
\cdot\vec
{
v
}_{
res
}
\\
\vec
{
v
}_{
res
}
\quad
=
\quad
&
\left
(1-
\frac
{
1
}{
2
}
\left
[(\vec{v}_{n}\cdot(-\nabla distances)_{n})+\vert(\vec{v}_{n}\cdot(-\nabla distances)_{n})\vert\right]
\right
)
\cdot\vec
{
v
}_{
n
}
\\
\vec
{
v
}_{
n
}
\quad
=
\quad
&
g(g(
\vec
{
v
}_{
ff
}
)+g(
\sum\vec
{
v
}_{
repP,i
}
))
\\
\vec
{
v
}_{
ff
}
\quad
=
\quad
&
v
_{
ff
}
(
\vec
{
x
}
)
\\
\end{alignat*}
\begin{align*}
\Delta\vec
{
v
}
\quad
=
&
\quad\Delta
t
\cdot\vec
{
v
}_{
res
}
\\
\vec
{
v
}_{
res
}
\quad
=
&
\quad\bigg
(1-
\frac
{
1
}{
2
}
\bigg
[\langle\vec{v}_{n},(-\nabla distances)_{n}\rangle+\big\vert\langle\vec{v}_{n},(-\nabla distances)_{n}\rangle\big\vert\bigg]
\bigg
)
\cdot\vec
{
v
}_{
n
}
\\
\vec
{
v
}_{
n
}
\quad
=
&
\quad
g
\big
(
\quad
g(
\vec
{
v
}_{
ff
}
)+g(
\underset
{
\small
i
}{
\sum
}
\vec
{
v
}_{
repP,i
}
)
\quad\big
)
\\
\vec
{
v
}_{
ff
}
\quad
=
&
\quad
v
_{
ff
}
(
\vec
{
x
}
)
\end{align*}
\subsection
{
Idea of Separation of a Moving-Vector into Direction and Magnitute
}
\subsubsection
{
no clipping
}
\subsubsection
{
Recycling the Distances Field (neg. Gradient must be saved)
}
$
\vec
{
v
}_{
res
}
\quad
=
\quad\bigg
(
1
-
\frac
{
1
}{
2
}
\bigg
[
\langle\vec
{
v
}_{
n
}
,
(-
\nabla
distances
)
_{
n
}
\rangle
+
\big\vert\langle\vec
{
v
}_{
n
}
,
(-
\nabla
distances
)
_{
n
}
\rangle\big\vert\bigg
]
\bigg
)
\cdot\vec
{
v
}_{
n
}$
\section
{
Testing
}
\section
{
Shortcomings
}
\subsection
{
Floorfield
}
\subsubsection
{
Multiple Goals
}
The floorfield is a usefull tool in routing of pedestirans through
any geometry.
\subsubsection
{
Multiple Floors
}
\paragraph
{
Neighboring Relations
}
\subsection
{
Avoid Clipping
}
\section
{
Outlook
}
\subsection
{
Usage in JuPedSim
}
\subsection
{
Floorfields in Triangulated Domains
}
\subsection
{
Parallelization
}
\section
{
Appendices
}
\subsection
{
Classes and their Relations
}
\subsection
{
Code Snippets
}
\section
{
Bibliography
}
\end{document}
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment