Positional Encoding by Robots with Non-rigid Movements

Abstract

Consider a set of autonomous computational entities, called robots, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant δ > 0, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than δ amount. This model is known in literature as non-rigid movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having O(1) bits of persistent memory and ability to make circular moves.

Uniform Circle Formation for Swarms of Opaque Robots with Lights

“…swarm cardinality, robot ranks, configuration properties, etc.) through the swarm configuration, in a sort of stigmergic behavior [2,3,16,23]. In [3], Bramas et al develop the level-slicing technique for solving the fault-tolerant Gathering problem using the mutual distance of another robot.…”

Pattern Formation by Robots with Inaccurate Movements

“…However, notice that 1) the movement is still error-free if the destination is close enough, i.e., within δ, and 2) there is no error whatsoever in the direction of the movement even if the destination is far away. In [1], it was shown that these two properties allow robots to implement positional encoding even in the Non-Rigid model. This motivates us to consider a new movement model.…”