PANTR: A proximal algorithm with regularized Newton updates for nonconvex constrained optimization

This repository contains a set of benchmarks, including the ones used in the L-CSS/CDC submission of the PANTR method.

PANTR source code

The source code of PANTR is available on the develop branch of the alpaqa repository, at https://github.com/kul-optec/alpaqa/tree/develop.

Instructions (Linux only)

```sh

Install alpaqa and dependencies, initialize virtual environment

./scripts/get-dependencies.sh

Generate and compile the benchmark problems and the benchmark driver

./scripts/build-benchmarks.sh

Activate the virtual environment

. ./.venv/bin/activate

Run the benchmarks and export the figures

cd new-benchmarks-paper; doit -n$(($(nproc) / 2)) ```

Results

Hanging chain

hanging_chain.py

Model dynamics from [1].

Average solver run times for different MPC horizons

Average solver run times for horizon 60

Simplified quadcopter

quadcopter.py

Model dynamics:

$$ \begin{equation} \begin{aligned} \dot x &= v \ \dot v &= \begin{pmatrix} \cos\psi \cos\theta & \cos\psi \sin\theta \sin\phi-\sin\psi \cos\phi & \cos\psi \sin\theta \cos\phi + \sin\psi \sin\phi \ \sin\psi \cos\theta & \sin\psi \sin\theta \sin\phi + \cos\psi \cos\phi & \sin\psi \sin\theta \cos\phi - \cos\psi \sin\phi \ -\sin\theta & \cos\theta \sin\phi & \cos\theta \cos\phi \ \end{pmatrix} \begin{pmatrix} 0 \ 0 \ a_t \end{pmatrix} - \begin{pmatrix} 0 \ 0 \ g \end{pmatrix} \ \begin{pmatrix} \dot \phi \ \dot \theta \ \dot \psi \end{pmatrix} &= \omega. \end{aligned} \end{equation} $$

Average solver run times for different MPC horizons

Average solver run times for horizon 60

Quadcopter

realistic_quadcopter.py

Model dynamics from [2]:

$$ \begin{equation} \begin{aligned} \dot x &= v \ \dot v &= \begin{pmatrix} \cos \psi \cos \theta - \sin \phi \sin \psi \sin \theta & -\cos \phi \sin \psi & \cos \psi \sin \theta + \cos \theta \sin \phi \sin \psi \ \cos \theta \sin \psi + \cos \psi \sin \phi \sin \theta & \cos \phi \cos \psi & \sin \psi \sin \theta - \cos \psi \cos \theta \sin \phi \ -\cos \phi \sin \theta & \sin \phi & \cos \phi \cos \theta \ \end{pmatrix} \begin{pmatrix} 0 \ 0 \ a_t \end{pmatrix} - \begin{pmatrix} 0 \ 0 \ g \end{pmatrix} \ \begin{pmatrix} \dot \phi \ \dot \theta \ \dot \psi \end{pmatrix} &= \begin{pmatrix} \cos \theta & 0 & -\cos \phi \sin \theta \ 0 & 1 & \sin \phi \ \sin \theta & 0 & \cos \phi \cos \theta \ \end{pmatrix} \omega. \end{aligned} \end{equation} $$

Average solver run times for different MPC horizons

Average solver run times for horizon 60

• [1]  Wirsching, Leonard & Bock, Hans & Diehl, Moritz. (2006). Fast NMPC of a chain of masses connected by springs. Proceedings of the IEEE International Conference on Control Applications. 591 - 596. https://doi.org/10.1109/CACSD-CCA-ISIC.2006.4776712
• [2]  Powers, C., Mellinger, D., Kumar, V. (2015). Quadrotor Kinematics and Dynamics. In: Valavanis, K., Vachtsevanos, G. (eds) Handbook of Unmanned Aerial Vehicles. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9707-1_71