Kaa: A Python Implementation of Reachable Set Computation Using Bernstein Polynomials

13 pages•Published: September 25, 2020

Edward Kim and Parasara Sridhar Duggirala

Abstract

Reachable set computation is one of the many widely-used techniques for the verification of safety properties of dynamical systems. One of the simplest algorithms for computing reachable sets for discrete nonlinear systems uses parallelotope bundles and Bernstein polynomials. In this paper, we describe Kaa, a terse Python implementation of reachable set computation which leverages the widely used symbolic package sympy. Additionally, we simplify the user interface and provide easy-to-use plotting utilities. We believe that our tool has pedagogical value given the simplicity of the implementation and its user- friendliness.

Keyphrases: bernstein polynomials, nonlinear dynamical systems, reachable set computation

In: Goran Frehse and Matthias Althoff (editors). ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20), vol 74, pages 184-196.

Links:	https://easychair.org/publications/paper/Flp2
	https://doi.org/10.29007/rs5n

BibTeX entry

@inproceedings{ARCH20:Kaa_Python_Implementation_Reachable,
  author    = {Edward Kim and Parasara Sridhar Duggirala},
  title     = {Kaa: A Python Implementation of Reachable Set Computation Using Bernstein Polynomials},
  booktitle = {ARCH20. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20)},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {74},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/Flp2},
  doi       = {10.29007/rs5n},
  pages     = {184-196},
  year      = {2020}}

Download PDF Open PDF in browser