The Power of Lights: Synchronizing Asynchronous Robots Using Visible Bits

Abstract

Abstract-In this paper we study the power of using lights, i.e. visible external memory, for distributed computation by autonomous robots moving in LookCompute-Move (LCM) cycles. With respect to the LCM cycles, the most common models studied in the literature are the fully-synchronous (FSYNC), the semisynchronous (SSYNC), and the asynchronous (ASYNC). In this paper we introduce in the ASYNC model, the weakest of the three, the availability of visible external memory: each robot is equipped with a light bulb that is visible to all other robots, and that can display a constant numbers of different colors; the colors are persistent, that is they are not automatically reset at the end of each cycle.We first study the relationship between ASYNC with visible bits and SSYNC. We prove hat asynchronous robots, when equipped with a constant number of colors, are strictly more powerful than traditional semisynchronous robots. We also show that, when enhanced with visible lights, the difference between asynchrony and semi-synchrony disappears; this result must be contrasted with the strict dominance ASYNC <SSYNC between the models without lights.We then study the relationship between ASYNC with visible bits and FSYNC. We prove that asynchronous robots with a constant number of visible bits, if they can remember a single snapshot, are strictly more powerful than fully-synchronous robots. This is to be contrasted with the fact that, without lights, ASYNC robots are not even as powerful as SSYNC, even if they remember an unlimited number of previous snapshots. These results demonstrate the power of using visible external memory for distributed computation with autonomous robots. In particular, asynchrony can be overcome with the power of lights.

Synchronized Dancing of Oblivious Chameleons

“…For each class we determine the minimum number of colours needed to perform a feasible dance, and present a simple algorithm that allows such a number to suffice (in order of magnitude). In view of the recent result of [3] showing that asynchronous oblivious chameleons with a small constant number of colours can simulate any behaviour of any semi-synchronous oblivious iguanid lizards, it follows that all our results hold also in the fully asynchronous model. Due to space limitations, proofs are sketched or omitted.…”

“…However, as recently shown in [3], any result for SSYNC iguanid lizards can be achieved by ASYNC chameleons with a constant number of colours. This means that the results of the previous section still hold in ASYNC with just an increase in the multiplicative constant of the number of colours.…”

Zombie Swarms: An Investigation on the Behaviour of Your Undead Relatives

“…Until that day, our models also introducea novel framework for signaling between autonomous robots, extending to sound the light-based signalling introduced in [12]. It is worthwhile to remark that sound-based communication and the notion of activation level, with its impact on speed and long-lasting effects due to decay, substantially change the scenario.…”

“…A first attempt of modeling direct communication appears in [12], where the entities can communicate by turning on and off external bulb lights, i.e. lights visible to all entities.…”

“…In this paper, we introduce for the first time, to the best of our knowledge, audio signals as a direct communication mean. The first important difference between lights in [12] and audio modeled here is that the intensity of the audio signal emitted by an entity decreases following the inverse-square law. The second main difference with the common features of ASYNC is that the entity the perceives the audio signal will move with a speed that is proportional to the perceived intensity (inversely proportional to its distance from the source): in all previous works in literature, the speed of the entities never changes during the execution of the protocols.…”