Exploiting symmetry for discrete-time reachability computations
Abstract
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to maintain the state variables within a target tube despite disturbances. Our method exploits symmetry to compute the reachable sets in a lower-dimensional space, enabling a significant computational speedup. To achieve this, we present a general method for symmetry reduction based on the Cartan frame, which simplifies the dynamic programming iteration without algebraic manipulation of the state update equations. We illustrate the results by computing a backward reachable set for a six-dimensional reach-avoid game of two Dubins vehicles.
Cite
@article{arxiv.1801.00516,
title = {Exploiting symmetry for discrete-time reachability computations},
author = {John Maidens and Murat Arcak},
journal= {arXiv preprint arXiv:1801.00516},
year = {2018}
}