arXiv subjects

Sébastien Tixeuil

Publications and source records attributed to Sébastien Tixeuil.

At least 37 records · Page 2Linked to original sources

arXiv2022

Fault-Tolerant Offline Multi-Agent Path Planning

We study a novel graph path planning problem for multiple agents that may crash at runtime, and block part of the workspace. In our setting, agents can detect neighboring crashed agents, and change followed paths at runtime. The objective is then to prepare a set of paths and switching rules for each agent, ensuring that all correct agents reach their destinations without collisions or deadlocks, despite unforeseen crashes of other agents. Such planning is attractive to build reliable multi-robot systems. We present problem formalization, theoretical analysis such as computational complexities, and how to solve this offline planning problem.

cs.RO↗

arXiv2021

Unreliable Sensors for Reliable Efficient Robots

The vast majority of existing Distributed Computing literature about mobile robotic swarms considers computability issues: characterizing the set of system hypotheses that enables problem solvability. By contrast, the focus of this work is to investigate complexity issues: obtaining quantitative results about a given problem that admits solutions. Our quantitative measurements rely on a newly developed simulation framework to benchmark pen and paper designs. First, we consider the maximum traveled distance when gathering robots at a given location, not known beforehand (both in the two robots and in the n robots settings) in the classical OBLOT model, for the FSYNC, SSYNC, and ASYNC schedulers. This particular metric appears relevant as it correlates closely to what would be real world fuel consumption. Then, we introduce the possibility of errors in the vision of robots, and assess the behavior of known rendezvous (aka two robots gathering) and leader election protocols when sensors are unreliable. We also introduce two new algorithms, one for fuel efficient convergence, and one for leader election, that operate reliably despite unreliable sensors.

cs.CG↗

arXiv2021

Computer Aided Formal Design of Swarm Robotics Algorithms

Previous works on formally studying mobile robotic swarms consider necessary and sufficient system hypotheses enabling to solve theoretical benchmark problems (geometric pattern formation, gathering, scattering, etc.). We argue that formal methods can also help in the early stage of mobile robotic swarms protocol design, to obtain protocols that are correct-by-design, even for problems arising from real-world use cases, not previously studied theoretically. Our position is supported by a concrete case study. Starting from a real-world case scenario, we jointly design the formal problem specification, a family of protocols that are able to solve the problem, and their corresponding proof of correctness, all expressed with the same formal framework. The concrete framework we use for our development is the PACTOLE library based on the COQ proof assistant.

cs.CG↗

arXiv2020

Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs

In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of \emph{arbitrary} communication graphs. As a result, we clarify the solvability of the uniform bipartition problem with arbitrary communication graphs when agents in the population have designated initial states, under various assumptions such as the existence of a base station, symmetry of the protocol, and fairness of the execution. When the problem is solvable, we present protocols for uniform bipartition. When global fairness is assumed, the space complexity of our solutions is tight.

cs.DC↗

arXiv2020

Stand Up Indulgent Rendezvous

We consider two mobile oblivious robots that evolve in a continuous Euclidean space. We require the two robots to solve the rendezvous problem (meeting in finite time at the same location, not known beforehand) despite the possibility that one of those robots crashes unpredictably. The rendezvous is stand up indulgent in the sense that when a crash occurs, the correct robot must still meet the crashed robot on its last position. We characterize the system assumptions that enable problem solvability, and present a series of algorithms that solve the problem for the possible cases.

cs.DC↗

arXiv2020

Quixo Is Solved

Quixo is a two-player game played on a 5$\times$5 grid where the players try to align five identical symbols. Specifics of the game require the usage of novel techniques. Using a combination of value iteration and backward induction, we propose the first complete analysis of the game. We describe memory-efficient data structures and algorithmic optimizations that make the game solvable within reasonable time and space constraints. Our main conclusion is that Quixo is a Draw game. The paper also contains the analysis of smaller boards and presents some interesting states extracted from our computations.

cs.GT↗

arXiv2020

Ressource Efficient Stabilization for Local Tasks despite Unknown Capacity Links

Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing, fake messages may be placed in communication links by an adversary. When the number of such fake messages is unknown, self-stabilization may require huge resources: (a) generic solutions (a.k.a. data link protocols) require unbounded resources, which makes them unrealistic to deploy and (b) specific solutions (e.g., census or tree construction) require $O(n\log n)$ or $O(Δ\log n)$ bits of memory per node, where $n$ denotes the network size and $Δ$ its maximum degree, which may prevent scalability. We investigate the possibility of resource efficient self-stabilizing protocols in this context. Specifically, we present a self-stabilizing protocol for $(Δ+1)$-coloring in any n-node graph, under the asynchronous message-passing model. It is deterministic, it converges in $O(kΔn^2\log n)$ message exchanges, where $k$ is the bound of the link capacity in terms of number of messages, and it uses messages on $O(\log\log n+\logΔ)$ bits with a memory of $O(Δ\logΔ+\log\log n)$ bits at each node. The resource consumption of our protocol is thus almost oblivious to the number of nodes, enabling scalability. Moreover, a striking property of our protocol is that the nodes do not need to know the number, or any bound on the number of messages initially present in each communication link of the initial (potentially corrupted) network configuration. This permits our protocol to handle any future network with unknown message capacity communication links. A key building block of our coloring scheme is a spanning directed acyclic graph construction, that is of independent interest, and can serve as a useful tool for solving other tasks in this challenging setting.

cs.DC↗

arXiv2019

Gathering on Rings for Myopic Asynchronous Robots with Lights

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: $M_{init}$, which denotes the number of nodes between two border nodes, and $O_{init}$, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility.

cs.DC↗

arXiv2019

Multi-hop Byzantine Reliable Broadcast with Honest Dealer Made Practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g. digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment.

cs.DC↗

arXiv2019

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

The paper details the first successful attempt at using model-checking techniques to verify the correctness of distributed algorithms for robots evolving in a \emph{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.

cs.DC↗

arXiv2019

Asynchronous Scattering

In this paper, we consider the problem of scattering a swarm of mobile oblivious robots in a continuous space. We consider the fully asynchronous setting where robots may base their computation on past observations, or may be observed by other robots while moving. It turns out that asynchronous scattering is solvable in the most general case when both vision (the ability to see others robots positions) and weak local multiplicity detection are available. In the case of a bidimensional Euclidean space, ASYNC scattering is also solvable with blind robots if moves are rigid. Our approach is constructive and modular, as we present a proof technique for probabilistic robot protocols that is of independent interest and can be reused for other purposes. On the negative side, we show that when robots are both blind and have no multiplicity detection, the problem is unsolvable, and when only one of those is available, the problem remains unsolvable on the line.

cs.MA↗

arXiv2018

Reliable Broadcast in Dynamic Networks with Locally Bounded Byzantine Failures

Ensuring reliable communication despite possibly malicious participants is a primary objective in any distributed system or network. In this paper, we investigate the possibility of reliable broadcast in a dynamic network whose topology may evolve while the broadcast is in progress. In particular, we adapt the Certified Propagation Algorithm (CPA) to make it work on dynamic networks and we present conditions (on the underlying dynamic graph) to enable safety and liveness properties of the reliable broadcast. We furthermore explore the complexity of assessing these conditions for various classes of dynamic networks.

cs.DC↗

arXiv2018

Optimal Self-Stabilizing Mobile Byzantine-Tolerant Regular Register with bounded timestamp

This paper proposes the first implementation of a self-stabilizing regular register emulated by $n$ servers that is tolerant to both mobile Byzantine agents, and \emph{transient failures} in a round-free synchronous model. Differently from existing Mobile Byzantine tolerant register implementations, this paper considers a more powerful adversary where (i) the message delay (i.e., $δ$) and the period of mobile Byzantine agents movement (i.e., $Δ$) are completely decoupled and (ii) servers are not aware of their state i.e., they do not know if they have been corrupted or not by a mobile Byzantine agent.The proposed protocol tolerates \emph{(i)} any number of transient failures, and \emph{(ii)} up to $f$ Mobile Byzantine agents. In addition, our implementation uses bounded timestamps from the $\mathcal{Z}\_{13}$ domain and it is optimal with respect to the number of servers needed to tolerate $f$ mobile Byzantine agents in the given model.

cs.DC↗

arXiv2018

Ring Exploration with Myopic Luminous Robots

We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Different from the usual Look-Compute-Move (LCM) model, we consider two characteristics: myopia and luminosity. Myopia means each robot has a limited visibility. We consider the weakest assumption for myopia: each robot can only observe its neighboring nodes. Luminosity means each robot maintains a non-volatile visible light. We consider the weakest assumption for luminosity: each robot can use only two colors for its light. The main interest of this paper is to clarify the impact of luminosity on exploration with myopic robots. As a main contribution, we prove that 1) in the fully synchronous model, two and three robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively, and 2) in the semi-synchronous and asynchronous models, three and four robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively. These results clarify the power of lights for myopic robots since, without lights, five robots are necessary and sufficient to achieve terminating exploration in the fully synchronous model, and no terminating exploration algorithm exists in the semi-synchronous and asynchronous models. We also show that, in the fully synchronous model (resp., the semi-synchronous and asynchronous models), the proposed perpetual exploration algorithm is universal, that is, the algorithm solves perpetual exploration from any solvable initial configuration with two (resp., three) robots and two colors. On the other hand, we show that, in the fully synchronous model (resp., the semi-synchronous and asynchronous models), no universal algorithm exists for terminating exploration, that is, no algorithm may solve terminating exploration from any solvable initial configuration with three (resp., four) robots and two colors.

cs.DC↗

arXiv2017

Probabilistic Asynchronous Arbitrary Pattern Formation

We propose a new probabilistic pattern formation algorithm for oblivious mobile robots that operates inthe ASYNC model. Unlike previous work, our algorithm makes no assumptions about the local coordinatesystems of robots (the robots do not share a common "North" nor a common "Right"), yet it preserves theability from any initial configuration that contains at least 5 robots to form any general pattern (and not justpatterns that satisfy symmetricity predicates). Our proposal also gets rid of the previous assumption (in thesame model) that robots do not pause while moving (so, our robots really are fully asynchronous), and theamount of randomness is kept low -- a single random bit per robot per Look-Compute-Move cycle is used.Our protocol consists in the combination of two phases, a probabilistic leader election phase, and a deterministicpattern formation one. As the deterministic phase does not use chirality, it may be of independentinterest in the deterministic context. A noteworthy feature of our algorithm is the ability to form patternswith multiplicity points (except the gathering case due to impossibility results), a new feature in the contextof pattern formation that we believe is an important asset of our approach.

cs.DC↗

arXiv2017

Optimally Gathering Two Robots

We present an algorithm that ensures in finite time the gathering of two robots in the non-rigid 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.

cs.DC↗

arXiv2017

Optimal Storage under Unsynchrononized Mobile Byzantine Faults

In this paper we prove lower and matching upper bounds for the number of servers required to implement a regular shared register that tolerates unsynchronized Mobile Byzantine failures. We consider the strongest model of Mobile Byzantine failures to date: agents are moved arbitrarily by an omniscient adversary from a server to another in order to deviate their computation in an unforeseen manner. When a server is infected by an Byzantine agent, it behaves arbitrarily until the adversary decides to move the agent to another server. Previous approaches considered asynchronous servers with synchronous mobile Byzantine agents (yielding impossibility results), and synchronous servers with synchronous mobile Byzantine agents (yielding optimal solutions for regular register implementation, even in the case where servers and agents periods are decoupled). We consider the remaining open case of synchronous servers with unsynchronized agents, that can move at their own pace, and change their pace during the execution of the protocol. Most of our findings relate to lower bounds, and characterizing the model parameters that make the problem solvable. It turns out that unsynchronized mobile Byzantine agent movements requires completely new proof arguments, that can be of independent interest when studying other problems in this model. Additionally, we propose a generic server-based algorithm that emulates a regular register in this model, that is tight with respect to the number of mobile Byzantine agents that can be tolerated. Our emulation spans two awareness models: servers with and without self-diagnose mechanisms. In the first case servers are aware that the mobile Byzantine agent has left and hence they can stop running the protocol until they recover a correct state while in the second case, servers are not aware of their faulty state and continue to run the protocol using an incorrect local state.

cs.DC↗

arXiv2017

Parameterized Verification of Algorithms for Oblivious Robots on a Ring

We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of formal methods to automatically prove those. Our work is the first to study the verification problem of such algorithms in the parameter-ized case. We show that safety and reachability problems are undecidable for robots evolving asynchronously. On the positive side, we show that safety properties are decidable in the synchronous case, as well as in the asynchronous case for a particular class of algorithms. Several properties on the protocol can be decided as well. Decision procedures rely on an encoding in Presburger arithmetics formulae that can be verified by an SMT-solver. Feasibility of our approach is demonstrated by the encoding of several case studies.

cs.DC↗