updated README.md

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mcarfagno 2020-04-07 17:05:36 +01:00
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@ -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: 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} $ ![](img/quicklatex1.gif)
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 $
The vehicle dynamics are described by the differential drive model: The vehicle dynamics are described by the differential drive model:
* $\dot{x} = v\cos{\theta}$ ![](img/quicklatex2.gif)
* $\dot{y} = v\sin{\theta}$
* $\dot{\theta} = w$
The state variables of the model are: The state variables of the model are:

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@ -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: 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} $ ![](img/quicklatex1.gif)
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 $
The vehicle dynamics are described by the differential drive model: The vehicle dynamics are described by the differential drive model:
* $\dot{x} = v\cos{\theta}$ ![](img/quicklatex2.gif)
* $\dot{y} = v\sin{\theta}$
* $\dot{\theta} = w$
The state variables of the model are: The state variables of the model are:

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