Rendezvous of Asynchronous Mobile Robots with Lights

Okumura, Takashi; Wada, Koichi; Katayama, Yoshinori

doi:10.1007/978-3-319-98355-4_25

Cited by 7 publications

(18 citation statements)

References 22 publications

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“…Another possible proof of the validity of FAULTY 1 is found in [20], Lemma 2. It is proven that if robot A performs a LOOK right after B performed a COMPUTE while robots are of different colors, gathering is unavoidable.…”

Section: Proof Of Correctnessmentioning

confidence: 94%

“…Both solutions in ASYNC [12,23] and SSYNC [23] output a correct behavior independently of the initial value of the lights' colors. Recently, Okumura et al [20] presented an algorithm with two colors that gathers robots in ASYNC assuming rigid moves (that is, the move of every robot is never stopped by the scheduler before completion), or assuming non-rigid moves but robots are aware of δ (the minimum distance before which the scheduler cannot interrupt their Reference Synchrony Rigid Initial Color δ known # Colors [12] ASYNC NO NO NO 4 [23] SSYNC NO NO NO 2 (opt.) [23] ASYNC NO NO NO 3 [20] ASYNC yes yes NO 2 (opt.)…”

mentioning

confidence: 99%

“…[23] ASYNC NO NO NO 3 [20] ASYNC yes yes NO 2 (opt.) [20] ASYNC NO yes yes 2 (opt.) This paper ASYNC NO NO NO 2 (opt.)…”

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Optimally Gathering Two Robots

Heriban

Défago

Tixeuil

2018

Proceedings of the 19th International Conference on Distributed Computing and Networking

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We present an algorithm that ensures in finite time the gathering of two robots in the nonrigid ASYNC model. To circumvent established impossibility results, we assume robots are equipped with 2-colors lights and are able to measure distances between one another. Aside from its light, a robot has no memory of its past actions, and its protocol is deterministic. Since, in the same model, gathering is impossible when lights have a single color, our solution is optimal with respect to the number of used colors.

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Section: Proof Of Correctnessmentioning

confidence: 94%

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confidence: 99%

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Optimally Gathering Two Robots

Heriban

Défago

Tixeuil

2018

Proceedings of the 19th International Conference on Distributed Computing and Networking

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“…Furthermore, since robots in OBLOT are luminous robots with k = 1 color, this result implies that asynchronous luminous robots are at least as powerful as semi-synchronous traditional robots. Since their introduction, a large amount of work has been done on luminous robots ( [1], [2], [4], [8], [10], [17], [21], [23]- [26], [30]; see [11] for a recent review). In this paper we continue the investigation on the computational impact of lights, and examine the problem of forming a sequence of geometric patterns.…”

Section: A Frameworkmentioning

confidence: 99%

Forming Sequences of Patterns With Luminous Robots

et al. 2020

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The extensive studies on computing by a team of identical mobile robots operating in the plane in Look-Compute-Move cycles have been carried out mainly in the traditional OBLOT model, where the robots are silent (have no communication capabilities) and oblivious (in a cycle, they have no memory previous cycles). To partially overcome the limits of obliviousness and silence while maintaining some of their advantages, the stronger model of luminous robots, LUMI, has been introduced where the robots, otherwise oblivious and silent, carry a visible light that can take a number of different colors; a color can be seen by observing robots, and persists from a cycle to the next. In the study of the computational impact of lights, an immediate concern has been to understand and determine the additional computational strength of LUMI over OBLOT. Within this line of investigation, we examine the problem of forming a sequence of geometric patterns, PATTERNSEQUENCEFORMATION. A complete characterization of the sequences of patterns formable from a given starting configuration has been determined in the OBLOT model. In this paper, we study the formation of sequences of patterns in the LUMI model and provide a complete characterization. The characterization is constructive: our universal protocol forms all formable sequences, and it does so asynchronously and without rigidity. This characterization explicitly and clearly identifies the computational strength of LUMI over OBLOT with respect to the PATTERNSEQUENCEFORMATION problem. INDEX TERMS Autonomous mobile robots, distributed computing, oblivious, pattern formation, sequence of patterns, visible lights.

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“…The gathering problem is one of the benchmarking tasks in mobile robot networks, and has received a considerable amount of attention (e.g., [1,2,9,10,11,15,21,23,24,26,32,33,19]). The gathering task consists in all robots reaching a single point, not known beforehand, in finite time.…”

Section: Gatheringmentioning

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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Rendezvous of Asynchronous Mobile Robots with Lights

Cited by 7 publications

References 22 publications

Optimally Gathering Two Robots

Optimally Gathering Two Robots

Forming Sequences of Patterns With Luminous Robots

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

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