InterJournal Complex Systems, 388
Status: Submitted
Manuscript Number: [388]
Submission Date: 509
Revised On: 30920
Long range correlations in a network of mobile robots
Author(s): Sorinel Adrian Oprisan

Subject(s): CX.14, CX.01, CX.14

Category: Brief Article

Abstract:

We propose a new stochastic model for the functional self-organization. Our model does not require any hierarchical decision-maker or direct communication between the individuals in order to organize the environment. The environment is a two-dimensional rectangular lattice with a number of initially random distributed physical objects, which have to be sorted by some individuals - random walk like robots. The goal of the dynamics is to organize, or sort, the given physical objects in order to form some well-defined lattice structures (patterns, or virtual objects). The principal goal of the study is to understand how can be achieved a collective task assignment without any centralized organizer. How a collective representation emerges at the level of the colony without any symbolic representation at the individual level? Our new model is based on the following assumptions: The environment is a rectangular two-dimensional lattice. The lattice sites are occupied by physical objects denoted with the letters a, b, c, ... A free site is said to be occupied by a null type object. At any moment, a robot carries an object. The transported object may be of the null type (free robot). The robots move randomly through the lattice, only one robot being allowed at one site (random walk). When a robot moves to a given site, it must decide if there are conditions to put down the carrying object and to pick up the existing one. In the present work, we have presented the main theoretical and numerical results concerning the stochastic dynamics of a new functional self-organization algorithm. The proposed distributed sorting algorithm is less efficient than a hierarchical organized system, but its great advantage is that it does not require any map of the environment, global representation or supervisor. In this model, the memory of the individuals (robots) is efficiently organized and there is no information loss. Turning our focus to physical realization of this model, we argued that, contrarily to generally accepted viewpoint, a random walk like motion allows global information acquisition despite of the local orientated behavior. The result is important to experiments on the stochastic functional self-organization processes made on high dimensional environment. We have shown that there are at least two general mechanisms involved in the functional self-organization processes. The first mechanism, previously studied, refer to the information fluxes and global emergent behavior by means of nonlinear coupling between the individuals (robots). Secondly, it is obvious from the present study, that even without any coupling the environment can be organized according to some given goal (see Oprisan, 1996). This is possible because, after a transient time of the order of lattice size (conventional Monte-Carlo time step), every individual (robot, entity) has global information. This effect was observed and reported in our previous numerical simulations.

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