/PINNs-based-MPC

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.

Primary LanguagePythonMIT LicenseMIT

arXiv DOI MIT License LinkedIn

Physics-Informed Neural Networks-based Model Predictive Control for Multi-link Manipulators

Prospective contribution to the MATHMOD 2022 Vienna conference.

Table of Contents
  1. About The Project
  2. Getting Started
  3. Usage
  4. License
  5. Contact

About The Project

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.

Citing

If you use this project for academic work, please consider citing our publication:

J. Nicodemus, J. Kneifl, J. Fehr, and B. Unger
Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators
ArXiv e-print 2109.10793, 2021.

Built With

Getting Started

To get a local copy up and running follow these simple steps.

Prerequisites

A python environment is required, we recommend using a virtual environment.

Installation

  1. Clone the repo 
    git clone git@github.com:Jonas-Nicodemus/PINNs-based-MPC.git
  2. Go into the directory 
    cd PINNs-based-MPC
  3. Install dependencies 
    pip install -r requirements.txt

Usage

There are two executable scripts located in src.

  • train_pinn.py can be executed to learn weights and overwrite the already existing ones, which can be found under resources/weights.
  • main.py, then evaluates the PINN first in self-loop prediction mode and subsequently in closed-loop mode connected to the real system (emulated by RK45) for the given reference trajectory.

License

Distributed under the MIT License. See LICENSE for more information.

Contact

Jonas Nicodemus - jonas.nicodemus@simtech.uni-stuttgart.de

Benjamin Unger - benjamin.unger@simtech.uni-stuttgart.de

Jonas Kneifl - jonas.kneifl@itm.uni-stuttgart.de

Jörg Fehr - joerg.fehr@itm.uni-stuttgart.de

Project Link: https://github.com/Jonas-Nicodemus/PINNs-based-MPC