LMPC Examples

This repo collects few LMPC examples. In particular we implemented:

• The linear LMPC to solve the constrainted linear quadratic regulator (folder LinearMPC)
• The nonlinear LMPC to solve nonlinear constrainted minimum time problems and simple racing problems (folder Nonlinear LMPC).
• The decentralized nonlinaer LMPC for cooperative control of dinamically decoupled systems coupled by feasibility constraints (folder CoopLMPC)

For more details please check the README file in each folder

Native/VirtualEnv Installation

The code is written in Python 2.7 and the following packages are required

apt install coinor-libipopt-dev
pip install cvxpy
apt install -y libblas-dev
pip install ipopt
pip intall casadi

Docker Installation

We also provide Dockerfiles and scripts to build a Docker image and instantiate containers to run the code in this repository. To do so, first we need to install Docker CE. Instructions for installing via the apt repository for Ubuntu are included below. Instructions for MacOS can be found here.

Ubuntu

# Update apt package index
sudo apt update

# Install packages to allow apt to use a repository over HTTPS
sudo apt install -y apt-transport-https \
  ca-certificates \
  curl \
  software-properties-common

# Add Docker's official GPG key
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo apt-key add -

# Add Docker repository
sudo add-apt-repository \
  "deb [arch=amd64] https://download.docker.com/linux/ubuntu \
  $(lsb_release -cs) \
  stable"

# Update apt package index
sudo apt update

# Install Docker CE
sudo apt install docker-ce

# Add user to docker group
export user=$(whoami)
sudo usermod -aG docker $user

Docker related files are included in the docker directory. The bash script start_LMPC_docker.sh builds the image, which extends the continuumio/anaconda image by adding the cvxpy and ipopt Python libraries.

Running with Docker

In order to (re)build the image and start the container, run the following command from the base directory of the repository:

bash docker/start_LMPC_docker.sh -r

The -r flag triggers a rebuild of the image. There is no harm in always including this flag to ensure that changes to the Dockerfile are implemented. If the -r flag is not specified, a container will be instantiated using the most recent build of the image.

Once the container is running, open up a new terminal and use the following command to start a bash session in the container (you can get the name of the container using docker container ls):

docker exec -it ${container_name} bash

We can then run our code within this environment.

Important Notes

• Upon container instantiation the base directory of the repository is mounted to /home/LMPC within the container
• python-tk is installed and TkAgg needs to be selected as the matplotlib backend as opposed to the default Qt5Agg (which doesn't seem to work). This can be done by including the following code once before the first time matplotlib.pyplot is imported:

import matplotlib
matplotlib.use('TkAgg')

• A Jupyter notebook server can be started within the container using the command:

/opt/conda/bin/jupyter notebook --notebook-dir=/home/LMPC --ip=0.0.0.0 --port=8888 --allow-root

Once it is up and running, enter the following URL into a web browser:

localhost:8888/?token=[server_token]

where server_token can be found in the terminal print-out after starting the notebook server