Asynchronous Mobile Robot Gathering from Symmetric Configurations without Global Multiplicity Detection

Abstract

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 ring-shaped 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(n 2 ), 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).

Asynchronous Exclusive Perpetual Grid Exploration without Sense of Direction

“…, nm − 1} is different and represents one of the cells occupied by the robots. The three configurations on Figure 1, for example, are respectively denoted by the sorted sequences (5,10,11), (2,3,5), and (6,8,9).…”

“…The discrete model permits to simplify many robot protocols by reasoning on finite structures (i.e., graphs) rather than on infinite ones. However, as noted in most related papers [5][6][7][9][10][11][12], this simplicity comes with the cost of extra symmetry possibilities, especially when the authorized paths are also symmetric.…”

“…Assuming visibility capabilities, anonymous and oblivious robots, the three main problems that have been studied in the discrete robot model are gathering [9][10][11] (all robots are requested to reach a single node, not known beforehand), exploration with stop [4][5][6][7]12] (all nodes must be visited by at least one robot, and eventually all robots must stop moving forever), and exclusive perpetual exploration [1,2] (all nodes must be visited by all robots infinitely often, and no node or edge should be occupied by more than one robot at any time).…”

“…In the same paper, they provide an algorithm to perpetually and exclusively explore any partial grid provided that the number of robots enables a solution. However, the considered scheduling model is synchronous and contrary to the vast majority of existing solutions in the literature [4][5][6][7][9][10][11][12], robots have a strong sense of direction as they agree on the four basic directions: North, South, East, and West. This strong settings permits to break all cases of initial symmetry since a global total order can be inferred on the vertices of the graph.…”

Gathering and Exclusive Searching on Rings under Minimal Assumptions

“…With local multiplicity detection capability, an algorithm starting from rigid configurations where the number of robots k is strictly smaller than n 2 has been designed in [21]. In [22], the case where k is odd and strictly smaller than n − 3 has been solved. In [23], the authors provide an algorithm for the case where n is odd, k is even, and 10 ≤ k ≤ n−5.…”