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On the Synthesis of Mobile Robots Algorithms: the Case of Ring Gathering
"... Abstract. Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that selforganize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs. This paper is the fi ..."
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Abstract. Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that selforganize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs. This paper is the first to propose a formal framework to automatically design distributed algorithms that are dedicated to autonomous mobile robots evolving in a discrete space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. Our contribution is threefold. First, we propose an encoding of the gathering problem as a reachability game. Then, we automatically generate an optimal distributed algorithm for three robots evolving on a fixed size uniform ring. Finally, we prove by induction that the generated algorithm is also correct for any ring size except when an impossibility result holds (that is, when the number of robots divides the ring size). 1
Optimal Torus Exploration by Oblivious Mobile 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 ..."
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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 torusshaped network by a team of k 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 ` × L, where 7 ≤ ` ≤ L. Hence, in such tori, four robots are necessary and sufficient to solve the (probabilistic) terminating exploration. As a torus can be seen as a 2dimensional ring, our result shows, perhaps surprisingly, that increasing the number of possible symmetries in the network (due to increasing dimensions) does not come at an extra cost w.r.t. the number of robots that are necessary to solve the problem.