*2.2. Robot Model*

Given a robot team *R* = {*R*1, *R*2,..., *RM*} consisting of *M* homogeneous circular rigid mobile robots with wireless communication capabilities, a traditional representation defines each robot: *Ri* = (*xi*, *yi*, *θi*,*ri*,*si*, *ci*), where *i* ∈ [1..*M*] and *Xi*(*t*) = {*xi*(*t*), *yi*(*t*), *θi*(*t*)} represents the configuration vector of the robot *i* at time *t* (position of its centre and heading with respect to the inertial frame), *ri* represents the radius of the robot body, and *si*, *ci* represent the sensory capabilities as maximum radius of sensing and maximum range of communication, respectively.

#### *2.3. Communication Model*

This model aims to support the connectivity awareness ability of robots needed to deal with disconnection situations during the exploration. Given the position of their teammates and obstacles, robots can estimate the connectivity degree of a specific location considering some of the communication constraints that are widely present in real scenarios, mainly indoor (e.g., office-like and buildings).

The signal strength function (Γ*<sup>i</sup>* represents a slight adaptation of the signal strength function presented in [38]) <sup>Γ</sup>*<sup>i</sup>* : <sup>N</sup> <sup>×</sup> *<sup>S</sup>m*×*<sup>n</sup>* <sup>×</sup> <sup>R</sup> <sup>→</sup> <sup>R</sup> is defined as follows:

$$\begin{aligned} \Gamma\_i(j, E\_{known}(t), t) &= \Gamma\_i^0 - d\_{Att}(i, j, t) - w\_{Att}(i, j, E\_{known}(t), t) \\ \Gamma\_i^0 &= 10 \cdot D\_{af} \cdot \log\_{10}(c\_i/r\_i) \\ d\_{Att}(i, j, t) &= 10 \cdot D\_{af} \cdot \log\_{10}(d\_i(j, t)/r\_i) \\ d\_i(j, t) &= \left\| X\_i(t), X\_j(t) \right\|\_2 \\ w\_{Att}(i, j, E\_{known}(t), t) &= \begin{cases} w\_i(j, E\_{known}(t), t) \cdot \mathcal{W}\_{af} & \text{if } w\_i(j, E\_{known}(t), t) < \mathcal{C} \\ \mathcal{C} \cdot \mathcal{W}\_{af} & \text{otherwise} \end{cases} \end{aligned} \tag{1}$$

where, *dAtt* and *wAtt* stand for *distance attenuation* and *wall attenuation* terms, respectively. In addition, *di*(*j*, *t*) represents the Euclidean distance between two robot locations at time *t*: typically the transmitter (*Xi*(*t*)) and receiver (*Xj*(*t*)), *wi*(*j*, *Eknown*(*t*), *t*) represents the number of walls (robots cannot distinguish between different kind of rigid obstacles, but the term *wall* is used for simplicity and in order to be consistent with the underlying proposal) present in the known region between transmitter and receiver locations at time *t*, *Da f* represents a distance attenuation factor, and *Wa f* represents a wall attenuation factor. Finally, *C* represents the maximum number of walls up to which the *Wa f* factor causes a significant effect in function Γ*i*. When *wi*(*j*, *Eknown*(*t*), *t*) ≥ *C*, the distance attenuation effect dominates. Finally, note that in [38] the independent term Γ<sup>0</sup> *<sup>i</sup>* is suggested to be either derived empirically or obtained directly from the wireless network device specification. Nevertheless, in this work the model is adapted in order to become independent from specific deployments (communication devices), deriving the Γ<sup>0</sup> *<sup>i</sup>* value so that the signal strength Γ*i*(*j*, *Eknown*(*t*), *t*) = 0 when *di*(*j*, *t*) = *ci*.

In Figure 2 the shape of the function Γ*i*, as well as the attenuation effects caused by both distances and walls, are plotted.

**Figure 2.** Behaviour of the signal strength model. (**a**) The signal strength function Γ*<sup>i</sup>* (dBm) is plotted for a [0..5] range of walls and [0..30] (m) range of distances; (**b**) Attenuation caused by distance; (**c**) Attenuation caused by wall interference.

Unfortunately, due to uncertain and incomplete knowledge, the Γ*<sup>i</sup>* function only can either confirm the absence of connectivity or deliver an optimistic estimation of connectivity level instead. Although this model represents a valuable improvement in relation to others (e.g., the classic disk or line of sight models [20]), for the sake of simplicity other impairments also common in communication (e.g., bandwidth, information losses, fading, and multi-path propagation phenomenon [39,40]) are not considered in this work.
