*2.1. Environment Model*

The environment *<sup>E</sup>* is defined as a bounded planar workspace *<sup>E</sup>* <sup>⊆</sup> <sup>R</sup><sup>2</sup> previously unknown. Besides, *E* is represented by an occupancy grid structure [4] where each cell *c* can belong to three different probabilistic states *S* = { *f* , *o*, *u*}, standing for free, occupied and unknown, respectively. Typically, P(*state*(*c*) = *<sup>f</sup>*) = <sup>1</sup> − P(*state*(*c*) = *<sup>o</sup>*) is assumed. When |P(*state*(*c*) = *<sup>f</sup>*) − 0.5| < the cell *c* is labelled as *unknown*; otherwise it is labelled as *free* or *occupied*, accordingly. These states represent all possible theoretical situations in which a point of the environment can be classified over time. The mapping algorithm frequently updates the probability value of each cell on each robot. Despite this, only the current classification of each cell at a given decision time step is considered. Consequently, the representation of *E* belongs to the domain of matrices *Sm*×*n*. Furthermore, the region already explored *Eknown* and the remaining that is yet unexplored *Eunknown* at time *t* may be defined from this representation as follows: *Eunknown*(*t*) = {*<sup>c</sup>* ∈ *<sup>E</sup>* | |P(*state*(*c*, *<sup>t</sup>*) = *<sup>f</sup>*) − 0.5| < } and *Eknown*(*t*) = {*c* ∈ *E* \ *Eunknown*(*t*)}.
