Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling

Description

Code for the randUP (randomized uncertainty propagation) and robUP (robustified uncertainty propagation) algorithms, containing experiments for our paper at CoRL 2020 (https://arxiv.org/abs/2008.10180).

<p align="center"> <img src="exps/freeflyer/figs/random_set_prop.png" width="90%"/> <br /><em>Three steps of randUP: (1) sample all uncertain parameters, (2) propagate them through the dynamics, and (3) take the convex hull of the states. Using random sets theory, we prove that this approximation converges to the convex hull of the true reachable sets.</em> </p> <br /> <p align="center"> <img src="exps/freeflyer/figs/adv_change_3.png" width="40%"/> <br /><em>Adversarial sampling (robUP) improves accuracy by actively searching for parameters maximizing the size of the reachable sets.</em> </p>

Setup

Python 3.5.2 is required. It is advised to run the following commands within a virtual environment.

  python -m venv ./venv
  source venv/bin/activate

For trajectory optimization of an uncertain spacecraft, clone ccscp

  git submodule init
  git submodule update

Then, install the package as

  pip install -r requirements.txt

Experiments can be reproduced using the notebooks in the exps/ folder

  jupyter notebook

BibTeX

@inproceedings{LewPavone2020,
  title        = {Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Sampling},
  author       = {Lew, Thomas and Pavone, Marco},
  booktitle    = {Conference on Robot Learning},
  year         = {2020},
  url          = {https://arxiv.org/abs/2008.10180}
}