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presentation.lyx
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#LyX 2.0 created this file. For more info see http://www.lyx.org/
\lyxformat 413
\begin_document
\begin_header
\textclass beamer
\begin_preamble
\usetheme{default}
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% or ...
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% or whatever (possibly just delete it)
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\use_default_options false
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\language english
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\end_header
\begin_body
\begin_layout Standard
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status open
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This file is a solution template for:
\end_layout
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Talk at a conference/colloquium.
\end_layout
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Talk length is about 20min.
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Style is ornate.
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\end_inset
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\begin_layout Standard
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status collapsed
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Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
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In principle, this file can be redistributed and/or modified under the terms
of the GNU Public License, version 2.
However, this file is supposed to be a template to be modified for your
own needs.
For this reason, if you use this file as a template and not specifically
distribute it as part of a another package/program, the author grants the
extra permission to freely copy and modify this file as you see fit and
even to delete this copyright notice.
\end_layout
\end_inset
\end_layout
\begin_layout Title
Modelling Crowd Behaviour in the Polymensa using the Social Force Model
\end_layout
\begin_layout Author
M.
\begin_inset space ~
\end_inset
Vifian, M.
\begin_inset space ~
\end_inset
Roggo, M.
\begin_inset space ~
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Aebli
\end_layout
\begin_layout Date
GESS Presentations, December 2011
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If you have a file called "institution-logo-filename.xxx", where xxx is a
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The following causes the table of contents to be shown at the beginning
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Delete this, if you do not want it.
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Outline
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LatexCommand tableofcontents
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\begin_layout Standard
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status open
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Structuring a talk is a difficult task and the following structure may not
be suitable.
Here are some rules that apply for this solution:
\end_layout
\begin_layout Itemize
Exactly two or three sections (other than the summary).
\end_layout
\begin_layout Itemize
At *most* three subsections per section.
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Talk about 30s to 2min per frame.
So there should be between about 15 and 30 frames, all told.
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\begin_layout Itemize
A conference audience is likely to know very little of what you are going
to talk about.
So *simplify*!
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In a 20min talk, getting the main ideas across is hard enough.
Leave out details, even if it means being less precise than you think necessary.
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If you omit details that are vital to the proof/implementation, just say
so once.
Everybody will be happy with that.
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\begin_layout Section
Introduction and Motivation
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status open
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michael section
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\begin_layout Subsection
Introduction, Motivation and Fundamental Questions
\begin_inset Argument
status open
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Basic Problem
\end_layout
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\end_layout
\begin_layout BeginFrame
General Introduction and Motivation
\end_layout
\begin_layout Itemize
Mensa seems suboptimal.
\end_layout
\begin_deeper
\begin_layout Pause
\end_layout
\end_deeper
\begin_layout Itemize
General motivation: mensa dynamics predictable?
\end_layout
\begin_deeper
\begin_layout Pause
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\end_deeper
\begin_layout Itemize
Matlab simulation
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\begin_deeper
\begin_layout Pause
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\end_deeper
\begin_layout Itemize
Goal: Simulation with close resemblance to actual observed crowd behaviour.
\end_layout
\begin_layout Subsection
Fundamental Questions
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\begin_layout BeginFrame
Fundamental Questions.
\end_layout
\begin_layout Itemize
How do pedestrian groups with different destinations interact with one another?
\end_layout
\begin_deeper
\begin_layout Pause
\end_layout
\end_deeper
\begin_layout Itemize
How do pedestrian groups interact when all pedestrians return to a cash
register once they have obtained their meals?
\end_layout
\begin_deeper
\begin_layout Pause
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\end_deeper
\begin_layout Itemize
How accurately are pedestrian-dynamic models able to depict the empirically
collected data?
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\begin_deeper
\begin_layout Pause
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\end_deeper
\begin_layout BeginFrame
Variables of Interests
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\begin_layout Itemize
Time it takes for agents to enter and exit mensa.
\end_layout
\begin_deeper
\begin_layout Pause
\end_layout
\end_deeper
\begin_layout Itemize
The number of times agent paths are blocked by other agents.
\end_layout
\begin_deeper
\begin_layout Pause
\end_layout
\end_deeper
\begin_layout Itemize
Queue locations.
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\begin_layout Section
Description of Model
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status open
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michael section
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\end_layout
\begin_layout Subsection
Sources
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\begin_layout BeginFrame
Social Force Model Sources
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\begin_layout Itemize
\series bold
Social Force Model for Pedestrian dynamics (1995)
\series default
– Dirk Helbing et al.
First publication of Social Force Model.
\end_layout
\begin_deeper
\begin_layout Pause
\end_layout
\end_deeper
\begin_layout Itemize
\series bold
Self-organized Pedestrian Crowd Dynamics (2005)
\series default
– Helbing et al.
Extensions to Social Force Model.
\end_layout
\begin_layout Subsection
Description
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\begin_layout BeginFrame
General
\end_layout
\begin_layout Itemize
All pedestrian interactions reduced to forces.
\end_layout
\begin_layout Pause
\end_layout
\begin_layout Itemize
Forces
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\begin_deeper
\begin_layout Enumerate
Destination
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\begin_layout Enumerate
Other Agents
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\begin_layout Enumerate
Boarders
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\begin_layout Enumerate
Objects of Attraction
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\end_deeper
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Destination Force
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<1->
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{
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Unit Vector towards destination:
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status open
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}
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\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
\begin_inset Formula $\vec{e}_{\alpha}(t):=\frac{\vec{r}_{\alpha}^{k}-\vec{r}_{\alpha}(t)}{||\vec{r}_{\alpha}^{k}-\vec{r}_{\alpha}(t)||}$
\end_inset
\begin_inset Note Note
status open
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r_alpha^k = closest point on destination polygon
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<2->
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{
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Force towards destination:
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status collapsed
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}
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\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
\begin_inset Formula $\vec{F}_{\alpha}^{0}(\vec{v}_{\alpha},\vec{v}_{\alpha}^{0},\vec{e}_{\alpha}(t)):=\frac{1}{\tau_{\alpha}}(v_{\alpha}^{0}\vec{e}_{\alpha}-\vec{v}_{\alpha})$
\end_inset
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status open
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v_alpha^0= agent desired speed (init), v_alpha= actual velocity, tau= relaxation
constant
\end_layout
\end_inset
\end_layout
\end_deeper
\begin_layout BeginFrame
Other Agents Force
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename forceagent.pdf
width 100text%
\end_inset
\end_layout
\begin_layout BeginFrame
Other Agents Force (alternative)
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status open
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<1->
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\end_inset
\begin_inset ERT
status collapsed
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{
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\end_inset
according to more recent Social Force model:
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status collapsed
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}
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\end_inset
\end_layout
\begin_deeper
\begin_layout Standard
\begin_inset Formula
\begin{align*}
\vec{F}_{\alpha\beta}(t)= & A_{\alpha}^{1}\exp\left[(r_{\alpha\beta}-d_{\alpha\beta})/B_{\alpha}^{1}\right]\vec{n}_{\alpha\beta}\\
& \cdot\left(\lambda_{\alpha}+(1-\lambda_{\alpha})\frac{1+\cos(\varphi_{\alpha\beta})}{2}\right)\\
& +A_{\alpha}^{2}\exp\left[(r_{\alpha\beta}-d_{\alpha\beta})/B_{\alpha}^{2}\right]\vec{n}_{\alpha\beta}
\end{align*}
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status open
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This approach does not introduce an elliptical potential.
The first term is not of great importance and can be neglected which also
reduces the required calculation times.
The second term is the exponentially decaying force field equation.
The constants of which must be appropriately chosen.
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Boundary Forces
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<1->
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{
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Boundary Forces:
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status collapsed
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}
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\begin_deeper
\begin_layout Itemize
\begin_inset Formula $\text{boundry Repulsion Force }\vec{F}_{\alpha B}=-\nabla_{\vec{r_{\alpha B}}}U_{^{0}\alpha B}e^{-||\vec{r}_{\alpha B}||/R}$
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status open
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Very similar to other agent forces.
The boarder point of boarder B closest to the agent causes this force.
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\end_inset
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Total Forces
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\begin_layout Itemize
\series bold
Note:
\series default
attractive object forces calculated in similar fashion.
\begin_inset Note Note
status open
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For the interested see the report or the paper.
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<1->
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{
\end_layout
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Superposition of all Forces:
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status collapsed
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}
\end_layout
\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
\begin_inset Formula $\vec{F}_{\alpha}(t)=\vec{F_{\alpha}^{0}}(\vec{v}_{\alpha}\vec{v}_{\alpha}^{0}\vec{e}_{\alpha})+\sum_{\beta}\vec{F}_{\alpha\beta}(\vec{e}_{\alpha},\vec{r}_{\alpha}-\vec{r}_{\beta})+\sum_{B}\vec{F}_{\alpha B}(\vec{e}_{\alpha},\vec{r}_{\alpha}-\vec{r}_{B}^{\alpha})+\sum_{i}\vec{F}_{\alpha i}(\vec{e}_{\alpha},\vec{r}_{\alpha}-\vec{r}_{i},t)$
\end_inset
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\end_deeper
\begin_layout BeginFrame
Using the force
\end_layout
\begin_layout Standard
\align right
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filename useforce.jpg
lyxscale 30
height 40theight%
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status open
\begin_layout Plain Layout
<1->
\end_layout
\end_inset
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
{
\end_layout
\end_inset
Putting it all together
\begin_inset ERT
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\begin_layout Plain Layout
}
\end_layout
\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
\begin_inset Formula $\frac{d\vec{w_{\alpha}}}{dt}:=\vec{F}_{\alpha}(t)+fluctuations$
\end_inset
\begin_inset Note Note
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\begin_layout Plain Layout
Differential equation from which agent velocities are calculated.
Fluctuations add a random factor to reduce agents getting stuck.
\end_layout
\end_inset
\end_layout
\begin_layout Itemize
\begin_inset Formula $\text{Actual velocity }\vec{v}_{\alpha}=\vec{w}_{\alpha}\cdot\begin{cases}
1 & ,\text{ if }||\vec{w}_{\alpha}||<v_{0}^{\alpha}\\