Variables del Modelo Hedónico Casas en Condominio

The MATLAB simulation was designed to prototype and examine the RVF framework rapidly. Multiple experiments were conducted to investigate the efficiency of the RVF framework, the results from these trials will be presented in this section. In addition, statistical tests conducted to determine the significance of the results will be detailed.

This section will present: results from the verification of the strong nuclear force; results from the investigations into the performance of the RVF framework on homogeneous and het- erogeneous swarms; results from the tests that were run to examine the effect of individual parameters; results from attempts to determine unreachable zones; statistical analysis to deter-

Figure 5.7: A delineation of the experiments conducted in embodied simulation, along with the location of methodology and results within the thesis.

mine the significance of the results; and finally, results from an additional test to examine the behaviour of the heterogeneous vs homogeneous swarm.

5.5.1.1 Verifying Strong Nuclear Force

This experiment was used to verify the utility of the strong nuclear force in the RVF framework. The assessment was completed by comparing the time taken for a single robot to reach 80% coverage both with and without the strong nuclear force.

The average time taken without using the strong nuclear force was 708 seconds, with a standard deviation of 146 seconds. When the strong nuclear force was introduced to the framework this average time dropped significantly to 330 seconds, with a standard deviation of 52 seconds. In addition to the time take to reach 80% coverage, the average number of collisions in each scenario was recorded. In the case where only the gravitational force was used the average number of collisions was found to be 3.7 per run, however when introducing the strong nuclear force this decreased to an average of 0.8 per run.

This was the result that was expected. When the robot uses only the gravitational force to explore the unknown environment, it will spend much of its time revisiting previously explored areas. The introduction of the strong nuclear force means that the robot is more often exploring new regions. This is because it will continue to push the frontier of exploration until there are no longer frontier cells within its sensor range, at which point the gravitational force takes it to a new area. This result reinforces the utility of the strong nuclear force in the RVF framework.

Swarm Composition Time (seconds) Standard Deviation Homogeneous 231 36 Heterogeneous Sensing 222 43 Heterogeneous Speed 223 34 Heterogeneous Charge 221 34 Heterogeneous Diameter 232 50 Heterogeneous Mass 242 38

Table 5.2: Shows the results of making individual parameters of the swarm heterogeneous.

5.5.1.2 Examining Performance in Differing Swarm Compositions

These experiments compared the effectiveness of the RVF framework on a heterogeneous and homogeneous swarm. To compare the swarm’s efficiency, the average time taken for three of the four robots in the swarm to reach 80% coverage was calculated over thirty trials. This end condition allowed for the experiments to conclude in a reasonable amount of time for comparison, whilst also giving a coverage of the map that is similar to what is expected in the real environment, taking into account unreachable zones.

The average time for the homogeneous swarm was found to be 231 seconds with a standard deviation of 36 seconds, whereas the time for the heterogeneous swarm was found to be 181 seconds with a standard deviation of 41 seconds. This was not the expected result. As both swarms utilise the same average values for all parameters that were varied, it was assumed a similar exploration time would be recorded. Instead, the heterogeneous swarm appears significantly more efficient at exploring the environment.

This was an interesting result and warranted further investigation to understand why the heterogeneous swarm performed better. This investigation was twofold: first the statistical significance of these results needed to be verified; second, it was decided that a further experiment with swarms initialised in the same starting positions was useful to observe the behaviours of the swarm. These additional investigations will be described later in the ‘Statistical Testing’ and ‘Further Investigation into Homogeneity vs Heterogeneity’ sections respectively.

5.5.1.3 Individual Parameter Investigation

The individual parameter investigations were conducted to examine the effect of each parameter defining heterogeneity on the exploration time. These parameters were speed, sensor range, charge, mass and diameter. The results are summarised in table 5.2.

The results show that introducing heterogeneity to single parameters only very slightly affects the result. In the case of sensor range, charge and speed the average exploration time compared to the homogeneous swarm was decreased by a small amount. For mass, the exploration time was increased marginally. Finally, for diameter the exploration time remained roughly the same. These

results are interesting and suggest that no one parameter greatly effects the exploration time, instead it is the combination of the heterogeneous characteristics. The statistical significance of these results will be discussed in the ‘Statistical Testing’ section.

5.5.1.4 Determining Unreachable Zones

This simulation was designed to investigate the feasibility of using goal passing to determine unreachable areas within a nuclear cave. A goal point was defined as the edge of an unreachable zone, which was then passed between robots when they encountered one another until all robots had visited the goal. Once all robots have attempted to enter the zone and failed, it is determined to be unreachable by the swarm. The time taken to for all robots to attempt to enter the zone was recorded both for the heterogeneous and homogeneous swarms.

The average time taken to pass the goal between all the robots in the homogeneous case was 561s with standard deviation of 202 seconds, whereas in the heterogeneous case this reduced to 518s with a standard deviation of 129 seconds.

As these results fall within each others standard deviation it suggests that the homogeneous and heterogeneous swarms took a similar time to pass the goal between all robots. This result was not expected because it was assumed that the heterogeneous swarm would underperform, due to the robot with a reduced sensor range. It was assumed that this robot would cause a bottleneck, as robots are only able to pass the goal when another robot in within sensor range. It is possible that the robot with enhanced sensor range made up for this bottleneck.

The results show that it is possible for the robots to pass a goal between themselves. This goal could represent an area that a robot could not traverse, or an area that requires further investigation due to its importance. The active use of this function is to mark areas that could not be explored due to all the robots not being able to reach it. This experiment captured the essence of this, showing that it is a feasible concept.

5.5.1.5 Statistical Testing

To discern whether the improved efficiency of the heterogeneous swarm over the homogeneous swarm was statistically significant, T-test were conducted to compare the results. A T-test postulates a null hypothesis, which is rejected if the calculated T-value is below a certain threshold. The T-value used for thirty trials is 0.05, this gives a certainty of 98% in the rejection of the null hypothesis. Two null hypotheses were investigated during these T-tests, the first was to examine the significance of the results compared to a homogeneous swarm; the second was to investigate the significance when compared to a heterogeneous swarm. These hypotheses were:

1. Null hypothesis 1 - ‘the mean time for exploration for the heterogeneous swarms should be the same as that of the homogeneous swarm’

Swarm Composition T-value under Hypothesis 1 T-value under Hypothesis 2 Homogeneous N/A 4.9x10−6 Heterogeneous 4.9x10−6 N/A Heterogeneous Sensing 0.40 3.1x10−4 Heterogeneous Speed 0.35 8.0x10−5 Heterogeneous Charge 0.26 1.4x10−4 Heterogeneous Diameter 0.96 7.1x10−5 Heterogeneous Mass 0.27 1.6x10−7

Table 5.3: The results of the T-testing individual parameters defining heterogeneity.

2. Null hypothesis 2 - ‘the mean time of exploration for the entirely heterogeneous swarm should be the same as that of the swarm when individual parameters defining heterogeneity are changed, keeping all other parameters homogeneous’

The results from the T-tests are shown in table 5.3.

An interesting result comes from hypothesis 1; only in the entirely heterogeneous case can we reject the null hypothesis. This shows that in the case where all parameters are heterogeneous, a significant difference is made to the exploration time. However, in the case of individual heterogeneity no significant difference is recorded.

The second hypothesis compares the results to the entirely heterogeneous case. From the T-values we see that making all parameters heterogeneous has a considerably more significant effect on the results than changing any one parameter.

5.5.1.6 Further Investigation into Homogeneity vs Heterogeneity

Having observed that the heterogeneous swarm was significantly more efficient at exploring the environment when compared to its homogeneous counterpart, it was decided that further investigation was necessary. A test was devised to observe the behaviour of both swarms while mapping the same environment. This involved initialising both swarms in the same starting locations and having them explore the same environment until 80% coverage was achieved by at least three robots. It was decided each robot would be given an initial starting location of one of the four corners. During these experiments, the exploration behaviour of the swarms was observed and noted quantitatively.

After completing numerous runs of this experiment, it became clear that the asymmetry of the heterogeneous swarm seemed to be benefiting the exploration effort. This was down to the movement of the robots before and after sharing maps.

In the homogeneous case, each robot would explore its initial corner and then moved towards the centre of the map. As all robots are the same in the homogeneous case, they would all reach the centre of the map at approximately the same time. This led to robots all sharing their maps at the same time and subsequently exploring similar regions.

In the heterogeneous case, robots followed a similar behavioural pattern; they would explore their initial corner and then move towards the centre of the map. However, as the robots are heterogeneous, they would reach the centre at different times. This meant that maps are not shared at the same time in the centre and thus robots do not seek to explore the same regions after a map has been shared. Interestingly, the two robots that were given the same parameters in the heterogeneous swarm tended to pair off and explore similar regions. This is an example of physical form effecting behaviour in a way that is beneficial to the desired outcome.

Overall, these experiments highlighted an unexpected benefit of the heterogeneous swarm: asymmetry between agents. This meant that the robots tended to explore different regions of the map and were less likely to follow similar paths to those taken by their teammates.