51 lines
1.1 KiB
Markdown
51 lines
1.1 KiB
Markdown
# mpc_python
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Python implementation of mpc controller for path tracking.
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## About
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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:
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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} $
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s.t.
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$ x(0) = x0 $
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$ x_{j+1} = Ax_{j}+Bu_{j})$ for $t< j <t+T-1 $
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$ U_{MIN} < u_{j} < U_{MAX} $ for $t< j <t+T-1 $
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The vehicle dynamics are described by the differential drive model:
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* $\dot{x} = v\cos{\theta}$
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* $\dot{y} = v\sin{\theta}$
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* $\dot{\theta} = w$
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The state variables of the model are:
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* $x$ coordinate of the robot
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* $y$ coordinate of the robot
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* $\theta$ heading of the robot
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The inputs of the model are:
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* $v$ linear velocity of the robot
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* $w$ angular velocity of the robot
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## Demo
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To run the demo:
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```bash
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python3 mpc_demo/main.py
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```
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## Requirements
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```bash
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pip3 install --user --requirement requirements.txt
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```
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