# Exploiting symmetry for discrete-time reachability computations

arXiv: https://arxiv.org/abs/1801.00516 · HTML: https://mlsanity.com/paper/1801.00516/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Exploiting Symmetry in Dynamics for Model-Based Reinforcement Learning with Asymmetric Rewards](https://mlsanity.com/paper/2403.19024/) (2024)
- [Symmetries-enhanced Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2501.01136/) (2025)

## Abstract (arXiv)

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.