We propose a new self-stabilizing flocking algorithm for oblivious robot networks, and prove its correctness. With this algorithm, a flock head emerges from a uniform flock of robots, and the algorithm allows those robots to follow the head, whatever its direction on the plane. Robots are oblivious in that they do not recall the result of their previous computations and do not share a common coordinate system. The novelty of our approach consists in identifying the sufficient conditions to set on the flock pattern placement and the velocity of the flock-head (rotation, translation or speed), such that the flock head and the flock pattern are both preserved while the flock moves (following the head). Additionally, our system is both self-healing and self-stabilizing. In case the head leaves (e.g., disappears or is damaged) the flock agrees on a new head and follows its trajectory. Also, robots keep no record of their previous computations and we make no assumption on their initial position. The step complexity of our solution is O(n).

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).

In this paper we present the self-stabilizing implementation of a class of token based algorithms. In the current work we only consider interactions between weak nodes. They are uniform, they do not have unique identifiers, are static and their interactions are restricted to a subset of nodes called neighbours. While interacting, a pair of neighbouring nodes may create mobile agents (that materialize in the current work the token abstraction) that perform traversals of the network and accelerate the system stabilization. In this work we only explore the power of oblivious stateless agents. Our work shows that the agent paradigm is an elegant distributed tool for achieving self-stabilization in Tiny Interaction Protocols (TIP). Nevertheless, in order to reach the full power of classical self-stabilizing algorithms more complex classes of agents have to be considered (e.g. agents with memory, identifiers or communication skills). Interestingly, our work proposes for the first time a model that unifies the recent studies in mobile robots(agents) that evolve in a discrete space and the already established population protocols paradigm.

In this paper we address the stabilizing token circulation and leader election problems in population protocols model augmented with oracles. Population protocols is a recent model of computation that captures the interactions of biological systems. In this model emergent global behavior is observed while anonymous finite-state agents(nodes) perform local peer interactions. Uniform self-stabilizing leader election or token circulation are impossible in such systems without additional assumptions. Therefore, the classical model has been augmented with the eventual leader detector, $\Omega?$, that eventually detects the presence or the absence of a leader. In this work we propose some impossibility results related to self-stabilizing implementation of leader election and token circulation in this model. Then we propose deterministic and probabilistic self-stabilizing solutions for token circulation and leader election for various topologies (chains, trees and arbitrary networks). Additionally, we prove the necessity of the eventual leader or token detector even in environments helped by randomization. All the proposed algorithms are memory optimal -- they need only one memory bit per agent.

Flocking is the ability of a group of robots to follow a leader or head whenever it moves in a plane (two dimensional Cartesian space). In this paper we propose and prove correct an architecture for a selforganizing and stabilizing flocking system. Contrary to the existing work on this topic our flocking architecture does not rely on the existence of a specific leader a priori known to every robot in the network. In our approach robots are uniform, start in an arbitrary configuration and the head of the group is elected via algorithmic tools. Our contribution is threefold. First, we propose novel probabilistic solutions for leader election in asynchronous settings under bounded schedulers. Additionally, we prove the impossibility of deterministic leader election when robots have no common coordinates and start in an arbitrary configuration. Secondly, we propose a collision free deterministic algorithm for circle formation designed for asynchronous networks. Thirdly, we propose a deterministic flocking algorithm totally independent of the existence of an a priori known leader. The proposed algorithm also works in asynchronous networks.

In this paper we address the stabilizing leader election problem in the popu- lation protocols model augmented with oracles. Population protocols is a recent model of computation that captures the interactions of biological systems. In this model emergent global behavior is observed while anonymous nite-state agents(nodes) perform local peer interactions. Uniform self-stabilizing leader election is impossible in such systems without additional assumptions. Therefore, the classical model has been augmented with the even- tual leader detector, ?, that eventually detects the presence or absence of a leader. In the augmented model several solutions for leader election in rings and complete networks have been proposed. In this work we extend the study to trees and arbitrary topologies. We propose deterministic and probabilistic solutions. All the proposed algorithms are memory optimal | they need only one memory bit per agent. Additionally, we prove the necessity of the eventual leader detector even in environments helped by randomization.