*6.3. Baseline Statement*

In this section, a baseline of performance on the main indicators is established from runnings of both *Yamauchi* and *minPos* approaches under ideal communication conditions. Since the exploration problem is expected to be more difficult under non-ideal communication conditions than otherwise [20], the obtained results may be considered as a baseline of the first four indicators—defined before in

Section 6.2—with respect to the corresponding performance achieved in runnings conducted under non-ideal communication conditions.

#### 6.3.1. Collected Data

In order to conduct the assessment and comparison stated above, at least ten realistic software-in-the-loop simulations were executed on the *Maze* scenario presented in Figure 10. All collected data is presented in Table 4 and are organised obeying the following scheme. The columns refer to (from left to right): **f**igure of **m**erits (FM); approaches, where *Y* and *MP* stand for *Yamauchi* and *MinPos*, respectively; and the fleet size |*R*|. In each fleet size, the average *AVE* and standard deviation *StD* values are registered.

**Table 4.** Yamauchi and MinPos results under ideal communication conditions on Maze environment.


#### 6.3.2. Baseline Assessment

We start the analysis highlighting that both approaches can adequately explore all the environments presented above in Section 6.1.1. Coherently, both approaches achieve high levels of *CR*. This can be seen clearer in Figure 12.

**Figure 12.** Coverage ratio (CR) under ideal communication conditions. Both approaches achieve a coverage bigger than 99% of the terrain regardless of the fleet size.

Furthermore, the *minPos* approach outperforms *Yamauchi* concerning TT as was expected. However, the most notorious differences of performance are observed on fleets which size is less than or equal to five robots, as can be seen in Figure 13.

**Figure 13.** Total exploration time (TT) under ideal communication conditions. Both approaches show a decreasing trend of TT as the fleet size increase. Nevertheless, the fact that the performance improvements are decreasing suppose the existence of a limit on the benefit from robots adding.

In crowded environments, going from one location to another is often more difficult than in the presence of fewer robots. Therefore, due to collision avoidance manoeuvres, both approaches show an increasing *PL* when the fleet size increases. This behaviour may be observed in the corresponding chart in Figure 14. On the one hand, *Yamauchi* presents a trend with an almost invariant slope along the different fleet size values. On the other hand, under *MinPos*, the trend of *PL* presents a positive but minor slope from one to five-robot-sized fleet after what it becomes very steep.

**Figure 14.** Path length (PL) under ideal communication conditions. The trend of PL is upward in both cases.

Hence, the analysis is divided into two cases. Firstly, when fleet size is less than or equal to five robots, *MinPos* is more efficient than *Yamauchi* since both approaches achieve very similar coverage ratios (see Figure 12) despite in the latter robots need to traverse longer distances than in the former, on average. That is expected since the *Yamauchi* approach does not take care about the dispersion of the fleet as the *MinPos* does and consequently, in the former robots are forced to deal with crowding more frequently than in the latter. This is a remarkable difference given that the energy needed to support an exploration mission will be closely related to the distance traversed by robots.

Contrarily, as the fleet size increase beyond five robots, the shape of the scenario and the peculiar wall distribution all together seem to make the crowding unavoidable for the *MinPos* approach, causing a severe worsening on its *PL* performance.

Finally, it is interesting to observe the over-sensing-cell phenomenon, because, by observing the amount of rework done by the fleet during exploration tasks, it also gives a good measure of the system efficiency.

In this case, we start the analysis pointing that in an ideal world—with perfect communications, perfect sensing and instantaneous actions—there would be no place for over-sensing. Nevertheless, in the real world, communications and sensing systems are not perfect and, more important, all actions take time. Even the ones which do not involve motion such as sensing, computing and communicating actions need some window time to be executed. Therefore, many things can happen simultaneously, e.g., sensing actions conducted on the same objects. In such a case, two or more robots might report the discovery of the same cells.

In conclusion, even under ideal communication conditions, it is possible to register some level of over-sensing, and this level is unavoidable because of the parallel nature of the system. However, it is equally interesting to analyse the over-sensing results: (i) When the fleets are obeying different policies; (ii) To have a baseline against which the results obtained under non-ideal communication conditions may be compared.

Backing to the experiments, during the simulation runnings we verify that the most significant over-sensing record is mainly generated at starting steps when all robots are very close to each other (recall that all robots start from the same corner of the scenario, see Table 3) and, in consequence, its sensing scopes overlap each other, significantly. In Figure 15 the robot placement setup at the starting time is shown.

**Figure 15.** Robot placement setup at starting time. Robots are represented by black dots. The sensing scope of the robot placed right in the corner is represented by a grey area where it is possible to see the laser aces and the obstruction caused by some teammates. Robots are placed from the corner along the *x* and *y* axes. As the fleet size increase, new robots are placed next following the row of robots on each axis, alternately.

Conversely, after this initial period, the robots overlap each other less frequently, and hence the *OSR* remains almost unchangeable over time, in both approaches. Despite this, minor differences may be highlighted. Due to a better fleet distribution on the terrain—which decreases the probability of simultaneous sensing events—the fleet makes slightly less rework under *MinPos* approach than under *Yamauchi* approach (see Figure 16).

### 6.3.3. Conclusions

Concerning the maze scenario, the conclusions of the section are: (i) Regarding fleets integrated with at most five robots, the *MinPos* approach is clearly advantageous (outperforming the *Yamauchi* approach in all assessed figures of merit); (ii) The benefits of employing the *MinPos* approach are severely affected when fleet increase beyond five robots, decreasing quickly or even disappearing when it is about eight robots.

**Figure 16.** Over-sensing ratio (OSR) under ideal communication conditions. This shows how as fleet size increases the trend of OSR is upward as well. This is expected since the more robots sensing the environment the higher the probability of simultaneously sensing the same cells.

### *6.4. AAMO Assessment*

This section aims to study the impact of using different *HO-Threshold* values on the performance of the proposed *AAMO* approach when the fleet is asked to explore an environment under non-ideal communication conditions. Moreover, these results are compared with the one achieved by other approaches like *Yamauchi* and *MinPos*—when they are subject to non-ideal communication conditions too—and also with an *event-based-connectivity* strategy that does make all efforts in favour of connectivity (regardless the total exploration time).

This last comparison is namely important because the performance of this kind of strategy may serve as an upper bound on the connectivity level over time and the total exploration time as well. To do so, typically two strategies (based on different connection requirements, see Section 1.1.1) can be considered: the ones which force the robots to be connected only on task-arrival time (kind of event-based connectivity) or the ones which force the robots to keep always connected—even during the path traversal periods (continuous connectivity). In the former, the robots are forced to select only between tasks which location would not cause isolation on arrival—regarding the current task assignment of the fleet. Nevertheless, it does not take into account the connectivity level along the path between the current robot location and the location of the task under consideration. Conversely, the latter imposes stronger restrictions on the fleet mobility in order to guarantee connectivity at all times. Consequently, depending on the application field the latter strategy would be recommended but is more complex to implement than the former. On the contrary, the former allows a simpler implementation but could lead to a lower level of connectivity along the exploration. Concerning this document, a connectivity-at-task-arrival-time based strategy is used for comparison purposes.

Besides, it is also important to highlight that, despite *Yamauchi* and *MinPos* assume ideal communication conditions, neither approach needs to be modified or adapted in order to properly run under non-ideal communication condition. Nevertheless, in the *MinPos* case, some severe degradation is expected because of the following working hypothesis are not guaranteed anymore: All robots share the same map and know the position of the other fleet members, at all times. This could lead to incoordinations that, in turn, would harm the dispersion strategy on which the approach is strongly based. Conversely, in the *Yamauchi* case, the level of expected degradation is fewer due to the coordination level between robots is fewer as well. Robots only try to avoid going to the same task simultaneously.
