Anissa Lamani

Asynchronous mobile robot gathering from symmetric configurations without global multiplicity detection

We consider a set of k autonomous robots that are endowed with visibility sensors (but that are otherwise unable to communicate) and motion actuators. Those robots must collaborate to reach a single vertex that is unknown beforehand, and to remain there hereafter. Previous works on gathering in ringshaped networks suggest that there exists a tradeoff between the size of the set of potential initial configurations, and the power of the sensing capabilities of the robots (i.e. the larger the initial configuration set, the most powerful the sensor needs to be). We prove that there is no such trade off. We propose a gathering protocol for an odd number of robots in a ring-shaped network that allows symmetric but not periodic configurations as initial configurations, yet uses only local weak multiplicity detection. Robots are assumed to be anonymous and oblivious, and the execution model is the non-atomic CORDA model with asynchronous fair scheduling. Our protocol allows the largest set of initial configurations (with respect to impossibility results) yet uses the weakest multiplicity detector to date. The time complexity of our protocol is O(n2), where n denotes the size of the ring. Compared to previous work that also uses local weak multiplicity detection, we do not have the constraint that k < n/2 (here, we simply have 2 < k < n-3).

Optimal grid exploration by asynchronous oblivious robots

We consider deterministic terminating exploration of a grid by a team of asynchronous oblivious robots. We first consider the semi-synchronous atomic model ATOM. In this model, we exhibit the minimal number of robots to solve the problem w.r.t. the size of the grid. We then consider the asynchronous non-atomic model CORDA. ATOM being strictly stronger than CORDA, the previous bounds also hold in CORDA, and we propose deterministic algorithms in CORDA that matches these bounds. The above results show that except in two particular cases, 3 robots are necessary and sufficient to deterministically explore a grid of at least three nodes. The optimal number of robots for the two remaining cases is: 4 for the (2,2)-Grid and 5 for the (3,3)-Grid, respectively.

Gathering an even number of robots in an odd ring without global multiplicity detection

We propose a gathering protocol for an even number of robots in a ring-shaped network that allows symmetric but not periodic configurations as initial configurations, yet uses only local weak multiplicity detection. Robots are assumed to be anonymous and oblivious, and the execution model is the non-atomic CORDA model with asynchronous fair scheduling. In our scheme, the number of robots k must be greater than 8, the number of nodes n on a network must be odd and greater than k+3. The running time of our protocol is O(n2) asynchronous rounds.

Ring Exploration by Oblivious Agents with Local Vision

The problem of exploring a discrete environment by identical oblivious asynchronous agents (or robots) devoid of direct means of communication has been well investigated so far. The (terminating) exploration requires that starting from a configuration where no two agents occupy the same node, every node needs to be visited by at least one agent, with the additional constraint that all agents eventually stop moving. Agents have sensors that allow them to see their environment and move accordingly. The previous works on this problem assume agents having an unlimited visibility, that is, they can sense the agents on every node of the ring, whatever the ring size. In this paper, we address deterministic exploration in an anonymous, unoriented ring using oblivious, and myopic agents. By myopic, we mean that their visibility is limited in terms of sensing distance. We consider the strongest possible myopia that is, an agent can only sense agents located at its own and at its immediate neighboring nodes. Our contribution is threefold. We first prove that within such settings, no deterministic exploration is possible in the semi-synchronous model. The result is also valid for the (fully) asynchronous model and holds for any k 6. Finally, we provide optimal (in terms of number of agents) deterministic algorithms in the fully synchronous model for both cases 3 6.

Robot networks with homonyms: the case of patterns formation

In this paper, we consider the problem of formation of a series of geometric patterns by a network of oblivious mobile robots that communicate only through vision. So far, the problem has been studied in models where robots are either assumed to have distinct identifiers or to be completely anonymous. To generalize these results and to better understand how anonymity affects the computational power of robots, we study the problem in a new model in which n robots may share up to 1 ≤ h ≤ n different identifiers. We present necessary and sufficient conditions, relating symmetricity and homonymy, that makes the problem solvable. We also show that in the case where h = n, making the identifiers of robots invisible does not limit their computational power. This contradicts a recent result of Das et al. To present our algorithms, we use a function that computes the Weber point for many regular and symmetric configurations. This function is interesting in its own right, since the problem of finding Weber points has been solved up to now for only few other patterns.

Optimal Torus Exploration by Oblivious Robots

We consider autonomous robots that are endowed with motion actuators and visibility sensors. The robots we consider are weak, i.e., they are anonymous, uniform, unable to explicitly communicate, and oblivious (they do not remember any of their past actions). In this paper, we propose an optimal (w.r.t. the number of robots) solution for the terminating exploration of a torus-shaped network by a team of

Constructing self-stabilizing oscillators in population protocols

k

Enabling Ring Exploration with Myopic Oblivious Robots

such robots. In more details, we first show that it is impossible to explore a simple torus of arbitrary size with (strictly) less than four robots, even if the algorithm is probabilistic. If the algorithm is required to be deterministic, four robots are also insufficient. This negative result implies that the only way to obtain an optimal algorithm (w.r.t. the number of robots participating to the algorithm) is to make use of probabilities. Then, we propose a probabilistic algorithm that uses four robots to explore all simple tori of size

Constructing Self-stabilizing Oscillators in Population Protocols

\ell \times L

Asynchronous Ring Gathering by Oblivious Robots with Limited Vision

, where