Formal Methods for Mobile Robots

Potop-Butucaru, Maria; Sznajder, Nathalie; Tixeuil, Sébastien; Urbain, Xavier

doi:10.1007/978-3-030-11072-7_12

Cited by 6 publications

(2 citation statements)

References 56 publications

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“…While we describe a way to extend our model to non-rigid non-self-stabilizing algorithms, the actual implementation is not complete yet. Also, although the proof arguments sustaining our abstract model are relatively simple, for the sake of having a completely mechanically verified result, we would like to have rewrite them formally using a proof assistant such as CoQ [29]. An execution of robot r is defined as a possibly infinite sequence of activation cycles of r. A global execution is a sequence of events on both robots, such that the event of each robot r is a robot execution of r, and the interleaving of events follows the rules of the activation model:…”

Section: Discussionmentioning

confidence: 99%

Using Model Checking to Formally Verify Rendezvous Algorithms for Robots with Lights in Euclidean Space

Défago¹,

Heriban²,

Tixeuil³

et al. 2019

Preprint

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The paper details the first successful attempt at using model-checking techniques to verify the correctness of distributed algorithms for robots evolving in a continuous environment. The study focuses on the problem of rendezvous of two robots with lights.There exist many different rendezvous algorithms that aim at finding the minimal number of colors needed to solve rendezvous in various synchrony models (e.g., FSYNC, SSYNC, ASYNC). While these rendezvous algorithms are typically very simple, their analysis and proof of correctness tend to be extremely complex, tedious, and error-prone as impossibility results are based on subtle interactions between robots activation schedules.The paper presents a generic verification model written for the SPIN model-checker. In particular, we explain the subtle design decisions that allow to keep the search space finite and tractable, as well as prove several important theorems that support them. As a sanity check, we use the model to verify several known rendezvous algorithms in six different models of synchrony. In each case, we find that the results obtained from the model-checker are consistent with the results known in the literature. The model-checker outputs a counter-example execution in every case that is known to fail.In the course of developing and proving the validity of the model, we identified several fundamental theorems, including the ability for a well chosen algorithm and ASYNC scheduler to produce an emerging property of memory in a system of oblivious mobile robots, and why it is not a problem for luminous rendezvous algorithms. * Research partly supported by JST SICORP and JSPS KAKENHI Grant No. 17K00019. 1 Chirality denotes the ability to distinguish left from right.

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Section: Discussionmentioning

confidence: 99%

Using Model Checking to Formally Verify Rendezvous Algorithms for Robots with Lights in Euclidean Space

Défago¹,

Heriban²,

Tixeuil³

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Along with the application studies in the robotics and electronics fields [1][2][3][4][5], computer science research has attempted to design theoretical models [6][7][8][9][10] which best formalize and simulate generic distributed systems, and to study efficient algorithms for some primitive tasks. Such an analytical investigation aims at providing a rigorous and universal methodology to study the collaborative strategies for mobile multi-agent systems [10][11][12][13], model peculiar realworld scenarios [14][15][16], prove and analyze the correctness of algorithmic solutions [17,18], and investigate their computational complexity [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Uniform Circle Formation for Fully, Semi-, and Asynchronous Opaque Robots with Lights

2023

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In the field of robotics, a lot of theoretical models have been settled to formalize multi-agent systems and design distributed algorithms for autonomous robots. Among the most investigated problems for such systems, the study of the Uniform Circle Formation (UCF problem earned a lot of attention for the properties of such a convenient disposition. Such a problem asks robots to move on the plane to form a regular polygon, running a deterministic and distributed algorithm by executing a sequence of look–compute–move cycles. This work aims to solve the UCF problem for a very restrictive model of robots: they are punctiform, anonymous, and indistinguishable. They are completely disoriented, i.e., they share neither the coordinate system nor chirality. Additionally, they are opaque, so collinearities can hide important data for a proper computation. To tackle these system limitations, robots are equipped with a persistent light used to communicate and store a constant amount of information. For such a robot model, this paper presents a solution for UCF for each of the three scheduling modes usually studied in the literature: fully synchronous, semi-synchronous, and asynchronous. Regarding the time complexity, the proposed algorithms use a constant number of cycles (epochs) for fully synchronous (semi-synchronous) robots, and linearly, many epochs in the worst case for asynchronous robots.

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A process calculus BigrTiMo of mobile systemsand its formal semantics

Xie

Zhu

2021

Form. Asp. Comput.

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In this paper, we present a process calculus called BigrTiMo that combines the rTiMo calculus and the Bigraph model. BigrTiMo calculus is capable of specifying a rich variety of properties for structure-aware mobile systems. Compared with rTiMo, our BigrTiMo calculus can specify not only time, mobility and local communication, but also remote communication. We then investigate the operational semantics of the BigrTiMo calculus and develop an executable formal specification of our BigrTiMo calculus in a declarative language called Maude. In addition, we verify safety properties and liveness properties of the mobile systems described by BigrTiMo using state exploration and LTL model checking in Maude. Based on Hoare and He's Unifying Theories of Programming (UTP), we study the semantic foundation of this highly expressive modelling language and propose a denotational semantic model and a set of algebraic laws for it. The semantic model in this paper covers time, location, communication and global shared variable at the same time. We also demonstrate the proofs of some algebraic laws based on our denotational semantics. Moreover, we explore how the algebraic semantics relates with the operational semantics and denotational semantics, which is conducted by the study of deriving the operational semantics and denotational semantics from algebraic semantics. We prove the equivalence between the derived transition system (e.g., the operational semantics) and the derivation strategy, which indicates that the operational semantics is sound and complete.

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Formal Methods for Mobile Robots

Cited by 6 publications

References 56 publications

Using Model Checking to Formally Verify Rendezvous Algorithms for Robots with Lights in Euclidean Space

Using Model Checking to Formally Verify Rendezvous Algorithms for Robots with Lights in Euclidean Space

Uniform Circle Formation for Fully, Semi-, and Asynchronous Opaque Robots with Lights

A process calculus BigrTiMo of mobile systemsand its formal semantics

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