dubins is a library for control of a highly-constrained Dubins vehicle as implemented in Pydrake, a Python model-based design and verification tool for robots. This is my final project for the MIT course 6.832: Underactuated Robotics. To complete this project, I combined the notion of a control-Lyapunov Function and trajectory optimization to control the long-term behavior of a highly constrained system in the presence of trajectory disturbances.
My implementation, while not perfect, marks a drastic improvement over the optimal controller when trajectory disturbances are present. For more information and analysis, please read my term paper.
The repository contains:
- Lyapunov Control - functions for applying a Control Lyapunov Function (CLF) to our system.
- Trajectory Optimization - functions for creating a PyDrake
MathematicalProgramthat navigates the Dubins vehicle to a desired start and end state. - mCLF - a custom algorithm for robust trajectory optimization, combining the concepts of a CLF with trajectory optimization to control the systme in the presence of disturbances.
- Miscellaneous visualization tools, which were useful in writing my final report.
Explore the demo.ipynb Jupyter notebook for examples (and visualizations) of how this code can work!
This code is not entirely finished. It was completed for a term project; many variables are hard-coded into my code, and the function library is not entirely clear. If you want to modify this library, please do so! I welcome any and all contributions.
First, clone this repository.
git clone https://github.com/deliastephens/dubins.git
dubins builds on the PyDrake libraries, which can be installed via these instructions. On my machine, I have to run the following in the dubins directory after downloading the binaries, unpacking, and setting up my PYTHONPATH. PyDrake is not compatible with Anaconda, so make sure to deactivate your conda environments before installation!
./install_prereqs.sh
pip3.9 install --requirement /opt/drake/share/drake/setup/requirements.txt --requirement requirements.txt
export PYTHONPATH=`pwd`:${PYTHONPATH}
If required, a manual pip install of numpy and matplotlib may be required.
To activate a Python virtualenvironment,
source venv/bin/activate
Finally, this project is best viewed through the wonderful lens of a Jupyter notebook. To start a Jupyter notebook, simply run
jupyter notebook
If you change any of the files, you must restart the kernel.
[1] T. Maillot, U. Boscain, J.-P. Gauthier, and U. Serres, “Lyapunov and minimum-time path planning for drones,” Jul. 2013. [Online]. Available:https://hal.archives-ouvertes.fr/hal-00847812
[2] B. Paden, M. Cap, S.Z. Yong, D. Yershov, and E. Frazzoli, “A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles, ”arXiv:1604.07446 [cs], Apr. 2016, arXiv: 1604.07446. [Online]. Available: http://arxiv.org/abs/1604.07446
[3] Russ Tedrake. Underactuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832). Downloaded on 19 May 2021 from http://underactuated.mit.edu/