updated README.md

.ipynb_checkpoints/README-checkpoint.md

@@ -6,21 +6,11 @@ Python implementation of mpc controller for path tracking.
 
 The MPC is a model predictive path following controller which does follow a predefined reference path Xref and Yref by solving an optimization problem. The resulting optimization problem is shown in the following equation:
 
-MIN $ J(x(t),U) = \sum^{t+T-1}_{j=t} (x_{j,ref} - x_{j})^T_{j}Q(x_{j,ref} - x_{j}) + u^T_{j}Ru_{j} $
-
-s.t.
-
-$ x(0) = x0 $
-
-$ x_{j+1} = Ax_{j}+Bu_{j})$    for $t< j <t+T-1 $
-
-$ U_{MIN} < u_{j} < U_{MAX} $   for $t< j <t+T-1 $
+![](img/quicklatex1.gif)
 
 The vehicle dynamics are described by the differential drive model:
 
-* $\dot{x} = v\cos{\theta}$ 
-* $\dot{y} = v\sin{\theta}$
-* $\dot{\theta} = w$
+![](img/quicklatex2.gif)
 
 The state variables of the model are:
 

README.md

@@ -6,21 +6,11 @@ Python implementation of mpc controller for path tracking.
 
 The MPC is a model predictive path following controller which does follow a predefined reference path Xref and Yref by solving an optimization problem. The resulting optimization problem is shown in the following equation:
 
-min $ J(x(t),U) = \sum^{t+T-1}_{j=t} (x_{j,ref} - x_{j})^T_{j}Q(x_{j,ref} - x_{j}) + u^T_{j}Ru_{j} $
-
-s.t.
-
-$ x(0) = x0 $
-
-$ x_{j+1} = Ax_{j}+Bu_{j})$    for $t< j <t+T-1 $
-
-$ U_{MIN} < u_{j} < U_{MAX} $   for $t< j <t+T-1 $
+![](img/quicklatex1.gif)
 
 The vehicle dynamics are described by the differential drive model:
 
-* $\dot{x} = v\cos{\theta}$ 
-* $\dot{y} = v\sin{\theta}$
-* $\dot{\theta} = w$
+![](img/quicklatex2.gif)
 
 The state variables of the model are: