Multi-agent Safety Verification Using Symmetry Transformations

Abstract

We show that symmetry transformations and caching can enable scalable, and possibly unbounded, verification of multi-agent systems. Symmetry transformations map solutions and to other solutions. We show that this property can be used to transform cached reachsets to compute new reachsets, for hybrid and multi-agent models. We develop a notion of virtual system which define symmetry transformations for a broad class of agent models that visit waypoint sequences. Using this notion of virtual system, we present a prototype tool CacheReach that builds a cache of reachtubes for this system, in a way that is agnostic of the representation of the reachsets and the reachability analysis subroutine used.Our experimental evaluation of CacheReach shows up to 66% savings in safety verification computation time on multi-agent systems with 3-dimensional linear and 4-dimensional nonlinear fixed-wing aircraft models following sequences of waypoints. These savings and our theoretical results illustrate the potential benefits of using symmetry-based caching in the safety verification of multi-agent systems.

Symmetry Abstractions for Hybrid Systems and their Applications

“…In contrast, this paper, we focus on hybrid systems instead of continuous dynamical systems. In [42], we extended the result of [41] to the parameterized dynamical systems and multi-agent settings. That allowed us to tackle hybrid automata as well.…”

“…We constructed a representative mode p * of all the modes, using symmetry, and then used p * as a proxy to share reachsets across different modes using a cache. However, in [42], we did not develop the general abstraction-based view of symmetry (Definition 5 and Theorem 3). As a result, we did not have a fixed point analysis (Theorem 6 and Corollary 7), and we were not able to verify unbounded-time safety properties.…”

“…Our abstraction is an extension of the concept of virtual system for parameterized dynamical systems that we defined in [42], to hybrid systems. Throughout the paper, we use subscript v to denote the variables and functions of the abstract (or virtual) automaton and no subscript for those of the concrete one.…”

$$\mathsf {SceneChecker}$$: Boosting Scenario Verification Using Symmetry Abstractions

“…In a more closely related research, we presented a modified version of DryVR that utilizes symmetry to cache reachsets aiming to accelerate simulation-based safety verification of continuous dynamical systems [28]. We developed the related tool CacheReach that implements a hybrid system verification algorithm that uses symmetry to accelerate reachability analysis [29]. CacheReach caches and shares computed reachsets between different modes of non-interacting agents using symmetry.…”

“…In addition to the abstraction of [14], SceneChecker 1) maps the unsafe set to an abstract unsafe set and verifies the abstract automaton instead of the concrete one and 2) decreases the over-approximation error of the abstraction through refinement. SceneChecker does not cache reachsets and thus saves cache-access and reachset-transformation times and does not incur overapproximation errors due to caching that CacheReach suffers from [29]. At the implementation level, SceneChecker accepts plans that are general directed graphs and polytopic unsafe sets while CacheReach accepts only single-path plans and hyperrectangle unsafe sets.…”