AutoGenU for Jupyter

Introduction

This project provides the continuation/GMRES method (C/GMRES method) based solvers for nonlinear model predictive control (NMPC) and an automatic code generator for NMPC, called AutoGenU.

The following C/GMRES based solvers are provided:

• MultipleShootingCGMRESSolver : The multiple shooting based C/GMRES method with condensing of the state and the Lagragne multipliers with respect to the state equation.
• SingleShootingCGMRESSolver : The original C/GMRES method (single shooting).

Requirement

• C++17 (MinGW or MSYS and PATH to either are required for Windows users)
• CMake
• Python 3.8 or later, Jupyter Lab or Jupyter Notebook, SymPy, and collection (to generate ocp.hpp, main.cpp, and CMakeLists.txt by AutoGenU.ipynb)
• Python 3.8 or later, NumPy, Matplotlib, and seaborn (to plot simulation data on AutoGenU.ipynb)
• ffmpeg (to generate animations in pendubot.ipynb, cartpole.ipynb, hexacopter.ipynb, and mobilerobot.ipynb)

The python modules can be installed via

pip install -r requirements.txt

Usage

Submodules

Please confirm that you clone this repository as

git clone https://github.com/mayataka/autogenu-jupyter --recursive

Otherwise, please do the following command:

git submodule update --init --recursive

AutoGenU

AutoGenU.ipynb generates following source files under your setting state equation, constraints, cost function, and parameters:

• ocp.hpp
• main.cpp
• CMakeLists.txt

You can also build source files for numerical simulation, execute numerical simulation, and plot or save simulation result on AutoGenU.ipynb.

C/GMRES based solvers of NMPC

The C/GMRES based solvers in src/solver directory can be used independently of AutoGenU.ipynb. You are then required the following files:

• ocp.hpp: write the optimal control problem (OCP) in your model

In addition to these files, you have to write CMakeLists.txt to build source files.

Demos

Demos are presented in cartpole.ipynb, pendubot.ipynb, hexacopter.ipynb, and mobilerobot.ipynb. You can obtain the following simulation results jusy by runnig these .ipynb files. The details of the each OCP formulations are described in each .ipynb files.

License

MIT

Citing autogenu-jupyter

We'd appriciate if you use cite the following conference paper:

@inproceedings{katayama2020autogenu,
  title={Automatic code generation tool for nonlinear model predictive control with {J}upyter},
  author={Sotaro Katayama and Toshiyuki Ohtsuka},
  booktitle={{The 21st IFAC World Congress 2020}},
  pages={7033-7040},
  year={2020}}

References

1. T. Ohtsuka A continuation/GMRES method for fast computation of nonlinear receding horizon control, Automatica, Vol. 40, No. 4, pp. 563-574 (2004)
2. C. T. Kelly, Iterative methods for linear and nonlinear equations, Frontiers in Apllied Mathematics, SIAM (1995)
3. Y. Shimizu, T. Ohtsuka, M. Diehl, A real‐time algorithm for nonlinear receding horizon control using multiple shooting and continuation/Krylov method, International Journal of Robust and Nonlinear Control, Vol. 19, No. 8, pp. 919-936 (2008)