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PHODCOS

PHoDCOS — Pythagorean Hodograph-based Differentiable Coordinate System Logo

For the implementation details, please check the paper.

If you use this framework please cite our work:

@misc{arrizabalaga2024phodcospythagoreanhodographbaseddifferentiable,
      title={PHODCOS: Pythagorean Hodograph-based Differentiable Coordinate System}, 
      author={Jon Arrizabalaga and Fausto Vega and Zbyněk ŠÍR and Zachary Manchester and Markus Ryll},
      year={2024},
      eprint={2410.07750},
      archivePrefix={arXiv},
      primaryClass={cs.RO},
      url={https://arxiv.org/abs/2410.07750}, 
}

Quickstart

Create a python environment with python 3.9. For example, with conda:

conda create --name phodcos python=3.9
conda activate phodcos
pip install -r requirements.txt

Update the ~/.bashrc with

export PHODCOS_PATH=/path_to_PHODCOS
export PYTHONPATH=$PYTHONPATH:/$PHODCOS_PATH

Usage

Numerical analysis: Approximation error

To reproduce the numerical analysis demonstrating a 6th-order approximation, as shown in Fig. 2 of the paper, run the following command:

python examples/hermite_interpolation.py --interp_order 4 --n_start 1  --n_end 9 --visualize

The options are the following ones:

  • --interp_order: 2 or 4.
  • --n_start: Minimum number of segments when benchmarking.
  • --n_end: Maximum number of segments when benchmarking.
  • --n_eval: Multiplicity of discretization (per segment) when evaluating.
  • --visualize: Enable visualization.

Near-Rectilinear Halo Orbit (NRHO)

To assign PHODCOS to the Near-Rectilinear Halo Orbit (NRHO) chosen for the Lunar Gateway run the following command:

python examples/lunar_gateway.py

This will perform two parameterizations of the NRHO: one in the Earth-Centered Inertial (ECI) frame and the other in the Earth-Moon Barycentric Rotating (EMBR) frame. This is done both in normalized as well as SI units, resulting in a total of four parameterizations. These will be saved in the data folder for use in the lunar lander example or for visualization.

Lunar Lander: Trajectory optimization from the Moon to the NRHO

To replicate the trajectory optimization example of the paper, run the following command:

python examples/lunar_lander.py --case_study 0

where --case_study can be 0,1,2,3,4. This will save the results in the data folder, which can be used for visualization.

Note: This example assumes that you have run the NRHO example first.