mpc_python

Python implementation of mpc controller for path tracking.

About

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

The vehicle dynamics are described by the differential drive model:

• \dot{x} = v\cos{\theta}
• \dot{y} = v\sin{\theta}
• \dot{\theta} = w

The state variables of the model are:

• x coordinate of the robot
• y coordinate of the robot
• \theta heading of the robot

The inputs of the model are:

• v linear velocity of the robot
• w angular velocity of the robot

Demo

To run the demo:

python3 mpc_demo/main.py

Requirements

pip3 install --user --requirement requirements.txt