78 lines
2.2 KiB
Markdown
78 lines
2.2 KiB
Markdown
# mpc_python
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I keep here my Jupyter notebooks on R&D on Model Predictive Control applyied to path-following problems in driverless vehicles. Includes also a Pybullet simulation to showcase the results.
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This mainly uses **[CVXPY](https://www.cvxpy.org/)** as a framework.
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## Notebooks Contents
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1. State space model derivation -> analytical and numerical derivaion
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2. MPC -> implementation and testing various improvements
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3. Obstacle Avoidance -> Using constrains to avaoid collisions
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<!--nobody cares about this
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## About
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The MPC is a model predictive path following controller which does follow a predefined reference by solving an optimization problem. The resulting optimization problem is shown in the following equation:
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The terns of the cost function are the sum of the **reference tracking error**, **heading effort** and **actuaction rate of change**.
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Where R,P,Q are the cost matrices used to tune the response.
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The vehicle model is described by the bicycle kinematics model using the state space matrices A and B:
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The state variables **(x)** 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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* **v** velocuty of the robot
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* **theta** heading of the robot
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The inputs **(u)** of the model are:
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* **a** linear acceleration of the robot
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* **delta** steering angle of the robot
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-->
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## Results
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Racing car model is from: *https://github.com/erwincoumans/pybullet_robots*.
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Results:
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To run the pybullet demo:
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```bash
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python3 mpc_demo/mpc_demo_pybullet.py
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```
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To run the simulation-less demo:
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```bash
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python3 mpc_demo/mpc_demo_pybullet.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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## References & Special Thanks:
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* [Prof. Borrelli - mpc papers and material](https://borrelli.me.berkeley.edu/pdfpub/IV_KinematicMPC_jason.pdf)
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* [AtsushiSakai - pythonrobotics](https://github.com/AtsushiSakai/PythonRobotics/)
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* [erwincoumans - pybullet](https://pybullet.org/wordpress/)
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* [alexliniger - mpcc](https://github.com/alexliniger/MPCC) and his [paper](https://onlinelibrary.wiley.com/doi/abs/10.1002/oca.2123)
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* [arex18 - rocket-lander](https://github.com/arex18/rocket-lander)
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