*2.6. Global Objectives*

The exploration aims for the full coverage of a bounded indoor environment, a priori totally unknown, with a team of terrestrial robots, in minimal time and avoiding isolation situations as much as possible. In this context, isolation refers to the fact of being unconnected from any other fleet member. In this work, the multi-robot system is designed to address these objectives from the following definitions.

#### 2.6.1. Full Coverage

Given the *Eknown* and *Eunknown* previously defined in Section 2.1, it is possible to claim that the completion condition is reached when *E* = *Eknown* or equivalently *Eunknown* = ∅. Although this condition is straightforward, it is useless in practice. Alternatively, the completion condition is conceived considering the sensing activity of the robots over time. Let *seni*(*t*) = *sen*(*Xi*(*t*)) be the information gathered by the robot *i* at time *t* in the configuration *Xi*(*t*). From this, *Eknown* at completion time T is defined as follows:

$$E\_{kuvwu} = \bigcup\_{i=1}^{M} \bigcup\_{t=0}^{\mathcal{T}} \operatorname{sem}\_i(t) \tag{3}$$

Finally, the completion condition may be written as in (4) implying that there are no reachable configurations where any robot can gather new information.

$$\exists \nexists X\_i \mid \textit{sen}\_i \bigcap \to\_{unknonuvu} \neq \mathcal{Q} \tag{4}$$
