Changes between Version 9 and Version 10 of doc/tec/mas

Timestamp:

Aug 30, 2018 7:41:05 AM (6 years ago)

Author:

sward

Comment:

--

doc/tec/mas

@@ -56 +56 @@
 
 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 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,
+{{{
+#!Latex
+\begin{equation*}
+\vec{F_{\alpha}} = \sum_i{\vec{F_i}}.
+\end{equation*}
+}}}
+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
+{{{
+#!Latex
+\begin{equation*}
+\vec{F}_{\alpha B} = - \nabla_{\vec{r}_{\alpha B}} U(|\vec{r}_{\alpha B}|),
+\end{equation*}
+}}}
+with the repulsive potential
+{{{
+#!Latex
+\begin{equation*}
+U = (|\vec{r}_{\alpha B}|) = U_0 \cdot e^{-|\vec{r}_{\alpha B}|/R_{B}}.
+\end{equation*}
+}}}
+In the MAS, //U_0// is [wiki:/doc/app/agtpar#repuls_wall repuls_wall] and //R_B// is [wiki:/doc/app/agtpar#sigma_rep_wall sigma_rep_wall].\\\\
+The repulsion by another **pedestrian //β//** is defined as
+{{{
+#!Latex
+\begin{equation*}
+\vec{F}_{\alpha \beta} = - \nabla_{\vec{r}_{\alpha \beta}} V(|\vec{r}_{\alpha \beta}|),
+\end{equation*}
+}}}
+with the repulsive potential
+{{{
+#!Latex
+\begin{equation*}
+V = (|\vec{r}_{\alpha \beta}|) = V_0 \cdot e^{-|\vec{r}_{\alpha \beta}|/R_{\beta}}.
+\end{equation*}
+}}}
+In the MAS, //U_0// is [wiki:/doc/app/agtpar#repuls_wall repuls_wall] and //R// is [wiki:/doc/app/agtpar#sigma_rep_wall sigma_rep_wall].\\
+
+
 
 \\