Changes between Version 4 and Version 5 of doc/tec/mas/social_forces

Timestamp:

Nov 19, 2018 9:41:26 AM (6 years ago)

Author:

sward

Comment:

--

doc/tec/mas/social_forces

@@ -6 +6 @@
 
 Agent movement and close-range interaction is implemented using a modified Social Force Model. The implementation uses concepts from the original Social Force Model ([#helbing1995 Helbing, 1995]) and an extension of it for close-rage collision prediction and avoidance ([#karamouzas2014 Karamouzas et. al, 2014]).\\
-The Social Forces approach is based on the idea that pedestrian movement is results from forces exerted on the pedestrian by its surroundings and goals. These forces can be either '''repulsive''' or '''attractive'''. Repulsive forces are associated with obstacles such as buildings, trees or other pedestrians. The current goal of each pedestrian exerts an attractive force on it. The resulting force on a **pedestrian α** is the sum of all attractive and repulsive forces,
+The Social Forces approach is based on the idea that pedestrian movement is the result of all forces exerted on the pedestrian by its surroundings and goals. These forces can be either '''repulsive''' or '''attractive'''. Repulsive forces are associated with obstacles such as buildings, trees or other pedestrians. The current goal of each pedestrian exerts an attractive force on it. The resulting force on a **pedestrian α** is the sum of all attractive and repulsive forces,
 {{{
 #!Latex
@@ -13 +13 @@
 \end{equation*}
 }}}
+This force determines the acceleration of the pedestrian. 
+Thus, the pedestrian's walking speed is given by
+{{{
+#!Latex
+\begin{equation*}
+\frac{d\vec{v}_{\alpha}}{dt} = \vec{F}_{\alpha}.
+\end{equation*}
+}}}
+In the MAS, a simple Euler-forward method is used for time-integration.\\\\
 The forces considered here are repulsion by obstacles and other pedestrians as well as the acceleration term driving the pedestrian toward its target. \\\\
 The repulsion by an '''obstacle //B//''' is defined as
@@ -51 +60 @@
 }}}
 Here, τ is the time until, given the current trajectory, a collision between the two pedestrians would occur, τ,,0,, = 3 s and k is a constant to sets the units with a value of 1.5 m^2^ kg.\\\\
+
 The **acceleration force** 
 {{{
@@ -59 +69 @@
 }}}
 describes the tendency of a pedestrian to accelerate toward its target. Here, τ,,α,, is a relaxation time ([wiki:/doc/app/agtpar#tau_accel_agent tau_accel_agent]) that describes how quickly the pedestrian approaches v,,0,, its desired walking speed with the direction to its current target, e.\\\\
-The pedestrian's walking speed is given by
-{{{
-#!Latex
-\begin{equation*}
-\frac{d\vec{v}_{\alpha}}{dt} = \vec{F}_{\alpha},
-\end{equation*}
-}}}
-with a simple Euler-forward method used for time-integration.\\