Using Symmetry Transformations in Equivariant Dynamical Systems for Their Safety Verification

Sibai, Hussein; Mokhlesi, Navid; Mitra, Sayan

doi:10.1007/978-3-030-31784-3_6

Cited by 14 publications

(15 citation statements)

References 22 publications

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“…Therefore, symSafetyVerif can speed up verification while preserving the soundness and precision of the reachability subroutines. In our earlier work [26], we introduced reachtube transformations using symmetry reduction for dynamical systems (single mode). Here, we extend the method across modes and we introduce the use of the virtual system, and we develop the corresponding verification algorithm.…”

Section: Symmetry-based Verification Algorithmmentioning

confidence: 99%

“…The first problem can be solved by: asking the method computeReachtube to compute tighter reachtubes as existing methods provide this option at the expense of more computation [13,8]. We can use symmetry in these tightening computations as well, as we did in [26]. We can also replace saved tubes in tubecache with newly computed tighter ones.…”

Section: Definitionmentioning

confidence: 99%

“…First, we show how symmetry transformations for parameterized dynamical systems can be used to compute reachable states (Theorem 2). Going well beyond the previous theory [26], this enables cached reach tubes to be reused for verification across different modes and across multiple agents.…”

Section: Introductionmentioning

confidence: 95%

“…In our recent work [26], we showed how this symmetry transforms can be used to produce new reach sets from other previously computed reach sets for non-parameterized dynamical systems. In this paper, we introduce the use of symmetry transforms of parameterized dynamical systems in their safety verification.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multi-agent Safety Verification Using Symmetry Transformations

Sibai

Mokhlesi

Fan

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

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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.

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Section: Symmetry-based Verification Algorithmmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-agent Safety Verification Using Symmetry Transformations

Sibai

Mokhlesi

Fan

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Sibai

Mitra

2021

Computer Aided Verification

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We present $$\mathsf {SceneChecker}$$ SceneChecker , a tool for verifying scenarios involving vehicles executing complex plans in large cluttered workspaces. $$\mathsf {SceneChecker}$$ SceneChecker converts the scenario verification problem to a standard hybrid system verification problem, and solves it effectively by exploiting structural properties in the plan and the vehicle dynamics. $$\mathsf {SceneChecker}$$ SceneChecker uses symmetry abstractions, a novel refinement algorithm, and importantly, is built to boost the performance of any existing reachability analysis tool as a plug-in subroutine. We evaluated $$\mathsf {SceneChecker}$$ SceneChecker on several scenarios involving ground and aerial vehicles with nonlinear dynamics and neural network controllers, employing different kinds of symmetries, using different reachability subroutines, and following plans with hundreds of waypoints in complex workspaces. Compared to two leading tools, DryVR and Flow*, $$\mathsf {SceneChecker}$$ SceneChecker shows 14$$\times $$ × average speedup in verification time, even while using those very tools as reachability subroutines.

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Verse: A Python Library for Reasoning About Multi-agent Hybrid System Scenarios

Zhu

Braught

et al. 2023

Computer Aided Verification

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We present the Verse library with the aim of making hybrid system verification more usable for multi-agent scenarios. In Verse, decision making agents move in a map and interact with each other through sensors. The decision logic for each agent is written in a subset of Python and the continuous dynamics is given by a black-box simulator. Multiple agents can be instantiated, and they can be ported to different maps for creating scenarios. Verse provides functions for simulating and verifying such scenarios using existing reachability analysis algorithms. We illustrate capabilities and use cases of the library with heterogeneous agents, incremental verification, different sensor models, and plug-n-play subroutines for post computations.

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Using Symmetry Transformations in Equivariant Dynamical Systems for Their Safety Verification

Cited by 14 publications

References 22 publications

Multi-agent Safety Verification Using Symmetry Transformations

Multi-agent Safety Verification Using Symmetry Transformations

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

Verse: A Python Library for Reasoning About Multi-agent Hybrid System Scenarios

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