From e5f5f1b12e37653579f9cd66c76c89ca6f090e79 Mon Sep 17 00:00:00 2001
From: mcarfagno <m.carfagno@outlook.com>
Date: Tue, 7 Apr 2020 17:05:36 +0100
Subject: [PATCH] updated README.md

---
 .ipynb_checkpoints/README-checkpoint.md |  14 ++------------
 README.md                               |  14 ++------------
 img/quicklatex1.png                     | Bin 0 -> 4163 bytes
 img/quicklatex2.png                     | Bin 0 -> 1235 bytes
 4 files changed, 4 insertions(+), 24 deletions(-)
 create mode 100644 img/quicklatex1.png
 create mode 100644 img/quicklatex2.png

diff --git a/.ipynb_checkpoints/README-checkpoint.md b/.ipynb_checkpoints/README-checkpoint.md
index 0296083..e35fa2b 100644
--- a/.ipynb_checkpoints/README-checkpoint.md
+++ b/.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:
 
diff --git a/README.md b/README.md
index aff415d..e35fa2b 100644
--- a/README.md
+++ b/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:
 
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