Formation of General Position by Asynchronous Mobile Robots Under One-Axis Agreement

Abstract

The traditional distributed model of autonomous, homogeneous, mobile point robots usually assumes that the robots do not create any visual obstruction for the other robots, i.e., the robots are see through. In this paper, we consider a slightly more realistic model, by incorporating the notion of obstructed visibility (i.e., robots are not see through) for other robots. Under the new model of visibility, a robot may not have the full view of its surroundings. Many of the existing algorithms demand that each robot should have the complete knowledge of the positions of other robots. Since, vision is the only mean of their communication, it is required that the robots are in general position (i.e., no three robots are collinear). We consider asynchronous robots. They also do not have common chirality (or any agreement on a global coordinate system). In this paper, we present a distributed algorithm for obtaining a general position for the robots in finite time from any arbitrary configuration. The algorithm also assures collision free motion for each robot. This algorithm may also be used as a preprocessing module for many other subsequent tasks performed by the robots.

Mutual Visibility by Robots with Persistent Memory

“…The algorithm runs in O(log(n)) rounds for n ≥ 4 robots. The only solution to the mutual visibility problem for asynchronous oblivious robots has been proposed in [14] under the assumption that the robots have an agreement in one coordinate axis and they have knowledge of total number of robots in the system. Thus, all the existing solutions for the mutual visible problem either assume persistent memory for both communication and internal memory purposes or one axis agreement or the knowledge of n, total number of robots in the system.…”

Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

“…m 20 If ∃ a rotational-free path for r (1) then r (1) moves toward c(R); concurrently, r (2) moves toward a point that makes predicate u 1 true, without swapping its role with r (1) nor crossing C j ↓ (R), for any j. m 21 If ∃ a rotational-free path for r (1) then r (1) moves toward c(R); Else let C i ↓ (R) be the circle where r (1) resides, then r (1) moves toward a point t that halves its distance from C i+1 ↓ (R). If r (2) ∈ [t 60 ,t 55 ), then it moves toward t x if such a point exists else toward t 55 .…”

“…Informally, this means that R is symmetric (cf b 0 ), there exist at least two robots on the axis of reflection and at least two of them are not critical for C(R) (cf b 2 ), there is no robot in c(R) (cf ¬c), or r (2) has not yet reached its target (cf ¬u 1 ). Figures 15.…”

“…Moreover, in R there is no robot in c(R) (cf ¬c). An example of such t 55 r (2) = t 60 r r (2) r r (1) configurations is provided in Figure 15.(f). In such a case it is easy to see that r (1) admits a rotational-free path.…”

“…[28,30,31]) or asynchronous (cf. [2,14,22,21,24]): pendently, and the duration of each phase is finite but unpredictable. As a result, robots do not have a common notion of time.…”