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:

• ContinuationGMRES : The original C/GMRES method (single shooting).
• MultipleShootingCGMRES : The multiple shooting based C/GMRES method with condensing of the state and the Lagragne multipliers with respect to the state equation.
• MSCGMRESWithInputSaturation : The multiple shooting based C/GMRES method with condensing of the state, the Lagragne multipliers with respect to the state equation, and variables with respect to the constraints on the saturation function on the control input.

Requirement

• C++11 (MinGW or MSYS and PATH to either are required for Windows users)
• CMake
• Python 3.6 or later, Jupyter Lab or Jupyter Notebook, SymPy (to generate nmpc_model.hpp, nmpc_model.cpp, main.cpp, and CMakeLists.txt by AutoGenU.ipynb)
• Python 3.6 or later, NumPy, Matplotlib, seaborn (to plot simulation data on AutoGenU.ipynb)
• ffmpeg (to generate animations in pendubot.ipynb, cartpole.ipynb, hexacopter.ipynb, and mobilerobot.ipynb)

Usage

AutoGenU

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

• nmpc_model.hpp
• nmpc_model.cpp
• 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:

• nmpc_model.hpp: write parameters in your model
• nmpc_model.cpp: write equations of your model
• main.cpp: write parameters of solvers

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

Demos

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

Pendubot

Inverting a pendubot using MSCGMRESWithInputSaturation solver.

Cartpole

Inverting a cartpole using ContinuationGMRES solver.

Hexacopter

Trajectory tracking of a hexacopter using MultipleShootingCGMRES solver.

Mobile robot

Obstacle avoidance of a mobile robot using MultipleShootingCGMRES solver with the semi-smooth Fischer-Burmeister method for inequality constraints.

License

MIT

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)