ABSTRACT: Anonymous mobile robots are often classified into synchronous,
semi-synchronous and asynchronous robots when discussing the pattern formation
problem. For semi-synchronous robots, all patterns formable with memory are
also formable without memory, with the single exception of forming a point
(i.e., the gathering) by two robots. However, the gathering problem for two
semi-synchronous robots without memory is trivially solvable when their local
coordinate systems are consistent, and the impossibility proof essentially uses
the inconsistencies in their coordinate systems. Motivated by this, this paper
investigates the magnitude of consistency between the local coordinate systems
necessary and sufficient to solve the gathering problem for two oblivious
robots under semi-synchronous and asynchronous models. To discuss the magnitude
of consistency, we assume that each robot is equipped with an unreliable
compass, the bearings of which may deviate from an absolute reference
direction, and that the local coordinate system of each robot is determined by
its compass. We consider two families of unreliable compasses, namely,static
compasses with constant bearings, and dynamic compasses the bearings of which
can change arbitrarily.
For each of the combinations of robot and compass models, we establish the
condition on deviation \phi that allows an algorithm to solve the gathering
problem, where the deviation is measured by the largest angle formed between
the x-axis of a compass and the reference direction of the global coordinate
system: \phi < \pi/2 for semi-synchronous and asynchronous robots with static
compasses, \phi < \pi/4 for semi-synchronous robots with dynamic compasses, and
\phi < \pi/6 for asynchronous robots with dynamic compasses. Except for
asynchronous robots with dynamic compasses, these sufficient conditions are
ABSTRACT: In this paper we propose and prove correct a new self-stabilizing velocity
agreement (flocking) algorithm for oblivious and asynchronous robot networks.
Our algorithm allows a flock of uniform robots to follow a flock head emergent
during the computation whatever its direction in plane. Robots are
asynchronous, oblivious and do not share a common coordinate system. Our
solution includes three modules architectured as follows: creation of a common
coordinate system that also allows the emergence of a flock-head, setting up
the flock pattern and moving the flock. The novelty of our approach steams in
identifying the necessary conditions on the flock pattern placement and the
velocity of the flock-head (rotation, translation or speed) that allow the
flock to both follow the exact same head and to preserve the flock pattern.
Additionally, our system is self-healing and self-stabilizing. In the event of
the head leave (the leading robot disappears or is damaged and cannot be
recognized by the other robots) the flock agrees on another head and follows
the trajectory of the new head. Also, robots are oblivious (they do not recall
the result of their previous computations) and we make no assumption on their
initial position. The step complexity of our solution is O(n).
ABSTRACT: This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems.
TAAS. 01/2009; 4.
Proceedings of the 1st International Conference on Robot Communication and Coordination, ROBOCOMM 2007, Athens, Greece, October 15-17, 2007; 01/2007
Principles of Distributed Systems, 10th International Conference, OPODIS 2006, Bordeaux, France, December 12-15, 2006, Proceedings; 01/2006
Stabilization, Safety, and Security of Distributed Systems, 8th International Symposium, SSS 2006, Dallas, TX, USA, November 17-19, 2006, Proceedings; 01/2006
ABSTRACT: Consider a system composed of mobile robots that move on the plane, each of which independently executing its own instance of an algorithm. Given a desired geometric pattern, the flocking problem consists in ensuring that the robots form this pattern and maintain it while moving together on the plane. In this paper, we explore flocking in the presence of faulty robots, where the desired pattern is a regular polygon. We propose a distributed fault tolerant flocking algorithm assuming a semi-synchronous model with a k-bounded scheduler, in the sense that no robot is activated no more than k times between any two consecutive activations of any other robot.The algorithm is composed of three parts: failure detector, ranking assignment, and flocking algorithm. The role of the rank assignment is to provide a persistent and unique ranking for the robots. The failure detector identifies the set of currently correct robots in the system. Finally, the flocking algorithm handles the movement and reconfiguration of the flock, while maintaining the desired shape. The difficulty of the problem comes from the combination of the three parts, together with the necessity to prevent collisions and allow the rotation of the flock. We formally prove the correctness of our proposed solution.
Journal of Systems and Software.
ABSTRACT: This paper presents a distributed algorithm whereby a group of mobile robots self-organize and position themselves into forming a circle in a loosely synchronized environment. In spite of its apparent simplicity, the difficulty of the problem comes from the weak assumptions made on the system. In particular, robots are anonymous, oblivious (i.e., stateless), unable to communicate directly, and disoriented in the sense that they share no knowledge of a common coordinate system. Furthermore, robots’ activations are not synchronized. More specifically, the proposed algorithm ensures that robots deterministically form a non-uniform circle in a finite number of steps and converges to a situation in which all robots are located evenly on the boundary of the circle.
Theoretical Computer Science.
ABSTRACT: Résumé: Nous adressons le problème de contrôle d'un groupe de robots mobiles pour former un cercle uniforme. Plus précisément, nous étudions la convergence d'un algorithme distribué pour la formation d'un cercle par simulation ordinateur. L'algorithme fonctionne sous les hypothèses que les robots sont : (1) amnésiques dans le sens qu'ils sont incapables de se rappeler les actions et les observations passées, (2) ils ne partagent aucun sens de direction et (3) ils ne peuvent pas communiquer directement entre eux. L'algorithme résout le problème dans deux étapes. Chaque problème est résolu par un algorithme différent. Le premier algorithme prend une configuration dans laquelle les robots sont étalés arbitrairement dans le plan et les arrange de manière déterministe pour former un cercle non dégénéré. Le deuxième algorithme prend une configuration dans laquelle les robots sont déjà localisés dans la circonférence du cercle éventuellement converge vers une situation dans laquelle tous les robots sont distribués uniformément dans la circonférence du cercle. L'algorithme est auto-stable puisque commençant de n'importe quel état toujours il converge vers la formation d'un cercle. Abstract: We address the problem of controlling a team of robots to form a uniform circle. More specifically, we study the convergence of a distributed circle formation algorithm using computer simulation. The algorithm operates under the hypothesis that robots (1) are oblivious in the sense that they are unable to recall past actions and observations, (2) share no common sense of direction, and (3) have no direct communication. The algorithm solves the problem of circle formation in two steps, each of which is solved by a different algorithm. The first algorithm takes a configuration wherein the robots are spread arbitrarily on the plane, deterministically arranges them to form a non degenerate circle. The second algorithm, takes a configuration where the robots are already located on the boundary, eventually converges toward a situation wherein all robots are uniformly distributed on the circumference of the circle. The algorithm is self-stabilizing 1 since starting from any arbitrary state always converges towards the formation of a circle.
and Technology Agency.
ABSTRACT: In this paper, we look at the time complexity of two agreement problems in networks of oblivious mobile robots, namely, at the gathering and scattering problems. Given a set of robots with arbitrary initial locations and no initial agreement on a global coordinate system, gathering requires that all robots reach the exact same but not predetermined location. In contrast, scattering requires that no two robots share the same location. These two abstractions are fundamental coordination problems in cooperative mobile robotics. Oblivious solutions are appealing for self-stabilization since they are self-stabilizing at no extra cost. As neither gathering nor scattering can be solved deterministically under arbitrary schedulers, probabilistic solutions have been proposed recently.The contribution of this paper is twofold. First, we propose a detailed time complexity analysis of a modified probabilistic gathering algorithm. Using Markov chains tools and additional assumptions on the environment, we prove that the convergence time of gathering can be reduced from O(n2) (the best known bound) to O(1) or , depending on the model of multiplicity detection. Second, using the same technique, we prove that scattering can also be achieved in fault-free systems with the same bounds.
Information Processing Letters.