Embodied Simulation Results

The embodied simulation was designed so that virtual heterogeneity could be instigated on a homogeneous swarm. This was to allow for the MATLAB simulation results to be verified on real robots. Several experiments were conducted to examine the efficiency of the RVF framework on virtually heterogeneous E-Puck robots. In addition to verification of the simulation results, the embodied simulations sought to examine the effect of varying the occupancy grid resolution.

This section will detail: results from experiments conducted on single robots of varying sensor range and speed; the results from the homogeneous experiments; the results from the heterogeneous swarm; and finally, the results from statistical testing conducted to ascertain the significance of the results.

5.5.2.1 Single Robot Experiments

The average times, and associated standard deviations, for the single robot experiments results are presented in the box plot in figure 5.8. The first conclusion that can be drawn from examining the values is that increasing the sensor range decreases the required exploration time. This is entirely expected, as a larger sensor range means that a robot can assess more of the area at any one time.

A result that was not anticipated is that, in general, both the 13x10 and 52x40 grid resolutions have a lower exploration time than the 26x20 grid. In the 13x10 case this is thought to be because each of the squares is worth a greater percentage of the overall coverage. Due to this, when new cells are discovered the coverage percentage rises more quickly, thus lowering the exploration time. For the 52x40 grid, the lower search time is likely to be due to the larger number of unexplored cells. If there are more frontier cells in range then the robot can discover unexplored cells more often, and therefore complete the exploration task more efficiently. The fact that the time for the 13x10 grid resolution is lower than the time for the 52x40 resolution suggests that the percentage value of cells has a greater effect than being constantly moving towards new cells, in the single robot case.

Figure 5.8: Box plot showing the results of the single robot experiments conducted in embodied simulation.

Overall the single robot results display interesting qualities. Though both the 13x10 grid and the 52x40 grid were faster, they have drawbacks. The 13x10 provides less accurate information about the environment. Also, although the 52x40 resolution leads to the robot having good information about the environment, due to the size of the grid each update step takes roughly twice as long as when the 26x20 grid is used. This often leads to the robot colliding with obstacles as it cannot react in a timely manner. This means that though the exploration time is slower for the 26x20 grid, it is possible that it is the best choice, providing a reasonable trade off between map accuracy and processing time.

5.5.2.2 Homogeneous Swarm Experiments

The normalised distribution of the results for the homogeneous swarm can be seen in figure 5.9. The first, and obvious, conclusion that may be drawn from both the local and global communication results is that using a homogeneous swarm to map the environment is more efficient than using a single robot. A second obvious result is that using global communication produces a faster exploration time than having the robots communicate locally. This is because the robots are constantly able to share their maps and thus have a full knowledge of the explored workspace.

In the case of local communication, the results seem to change from the single robot exper- iments; as the grid resolution becomes finer, the search time decreases. This is believed to be the result of having more cells to explore. As the robots’ exchange maps, areas are filled in more quickly. In the case of the 13x10 grid, this is likely to mean that after exchanging maps with other swarm members, the robot is not going to be in range of a frontier cell. This means that the robot must travel to the centre of mass of the unexplored region and thus move through

Figure 5.9: The normalised distribution of results for the homogeneous swarm, at the three varying grid resolutions and using the different communication modes with probability density on the y-axis. Note: The 26x20 line is overlaying the 13x10 in (b).

previously discovered regions to do so. The probability of this being true reduces as the grid resolution increases, due to the increase in the number of grid squares.

For global communication, it is found that the 13x10 and the 26x20 search times are similar, whereas the 52x40 time is shorter. This is again down to the prevalence of unexplored cells. As the exploration times were comparable between the 13x10 and 26x20 grids, it seems that introducing global communication reduces this discrepancy. The 52x40 grid provides considerably more cells to be explored, thus the robots are usually able to move towards unexplored cells.

Overall it is clear that the homogeneous swarm performs better than a single robot. It is also shown that a 52x40 grid generates a faster exploration time. It should be noted however that as the size of the grid resolution increases, so does the communication overhead required to exchange maps. For this reason, the robots required their batteries be changed more often during the 52x40 experiments. This could be a problem in a nuclear cave environment, where the robots may not be able to be retrieved easily.

5.5.2.3 Heterogeneous Swarm Experiments

As for the homogeneous swarm results the normalised distributions have been plotted for both the local and global communication cases and can be seen in figure 5.10. As with the homogeneous results, having the robots in constant communication decreased the average exploration time.

In the local communication paradigm, the 52x40 and the 13x10 grid resolution results are comparable, whereas the exploration time for the 26x20 grid was slower. This is akin to the single robot case. The 13x10 grid allows for a larger percentage increase in the coverage when a cell is discovered, whereas the 52x40 grid means that robots are more often exploring new cells. The

Figure 5.10: The normalised distribution of results for the heterogeneous swarm, at the three varying grid resolutions and using the different communication modes.

26x20 grid seems to fall in the middle of this trade off, and as such the exploration time in this case is slower.

When the heterogeneous swarm utilises global communication it seems that the 52x40 grid performs best. As with the homogeneous swarm this is likely due to the robots being able to spend more time exploring unexplored cells. The 13x10 grid performs better than the 26x20 grid, this is because each grid square is worth a higher percentage of the overall coverage. Interestingly, the trade-off between higher percentage cell value and density of unexplored cells seems to invert when compared to the single robot case. This is likely because when robots communicate, they are more likely to have explored the same cells in the 13x10 case, and thus in the 52x40 grid case the probability of finding new frontier cells is greater.

Overall, it has been shown that the heterogeneous swarm performs the exploration task more efficiently than the homogeneous swarm. This is in line with results found in previous work in the MATLAB simulation. In the next subsection, the statistical significance of these results will be explored.

5.5.2.4 Statistical Testing

Having found that both the swarm composition and the grid resolution influence the exploration time of the swarms, the next step was to determine the significance of these results. To do this, as in the MATLAB simulation case, T-tests were performed [75]. This involved the postulation of a null hypothesis which is rejected if the calculated T-value is below some threshold value. In this case a value of 0.05 was used, this gives a 98% confidence in the rejection of the null hypothesis.

These tests were performed when comparing the heterogeneous swarm results to the homo- geneous results, for the same value of grid resolution. They were also performed within each

Grid Resolution T-Value

13x10 4.2x10−16

26x20 9.2x10−19

52x40 4.8x10−5

Table 5.4: T-values for the comparison of the heterogeneous to the homogeneous swarm results for varying grid resolutions.

Grid Resolution Homogeneous T-Value Heterogeneous T-Value

13x10 vs 26x20 6.1x10−4 7.1x10−12

13x10 vs 52x40 1.3x10−12 0.07

26x20 vs 52x40 1.0x10−13 _3.1x10−9

Table 5.5: T-Values for the comparison of grid resolutions.

swarm composition, for the local communication paradigm. This was to determine whether the grid resolution has a significant impact on the exploration time.

Firstly, the homogeneous and heterogeneous swarms were compared. In each case the null hypothesis was ‘the swarm composition has no effect on the efficiency of the exploration time’. The T-values for these tests are collated in table 5.4. This table shows that for each grid resolution the null hypothesis may be rejected. That is to say that the performance of homogeneous and heterogeneous swarms was significantly different for each grid resolution. This proves that utilising a heterogeneous swarm decreases exploration time when using the RVF method when compared to a homogeneous swarm.

The second set of T-tests were conducted to observe whether the grid resolution has a bearing on the exploration time of the swarms. In each case the null hypothesis was ‘the grid resolution has no effect on the exploration time of the swarm’. The results of these tests are shown in table 5.5. The results show that in all except the heterogeneous 13x10 vs 52x40 case, the null hypothesis may be rejected. This shows that the grid resolution, in most cases, affects the exploration time of robots in a statistically significant way.

5.6

Chapter Summary

The aim of this chapter was to investigate the Reactive Virtual Forces framework as a potential control algorithm to guide a robotic swarm in the exploration and mapping of a nuclear cave environment. This was achieved through two experimental means: a MATLAB simulation designed to rapidly prototype and test the RVF framework; and an embodied simulation, designed to verify the MATLAB results and allow for homogeneous robots to be imbued with virtual heterogeneity.

In both cases, the RVF framework was compared with a homogeneous and heterogeneous swarm. It was found that the heterogeneous swarm can explore the environment more efficiently than its homogeneous counterpart, when using the RVF framework. This was found to be due to the inherent asymmetry of the heterogeneous swarm.

Additionally, the effect of occupancy grid resolution on swarm performance was studied. It was found that changing the resolution has a statistically significant result on the exploration time of the swarm. However, the resolution that led to the best performance was different depending on the swarm composition. Finally, the utility of the method for assigning areas as unreachable was explored. It was found that both homogeneous and heterogeneous swarms performed similarly. This experiment investigated whether it was possible for all robots to pass the goal simply by random encounter and showed that it is.

Overall, it has been shown that the reactive virtual forces framework, in combination with an occupancy grid, can be used to explore and map an unknown environment. So far in the RVF framework, it has been assumed that the pose of the robot is known. Within a nuclear cave environment this is not possible, thus a localisation method is required. Chapter six will outline the implementation of localisation within the RVF framework, and experiments designed to test it under this new paradigm.

The three key characteristics that a swarm must possess in order to explore and map a nuclear cave environment are: sensing, locomotion and control. Having reviewed the sensory and locomotive modalities available to a heterogeneous swarm within a nuclear cave, this chapter has put forward a solution to the control of such a swarm. Chapter six will further explore this control architecture and how it can be better applied to unknown environments.

C

H A P

6

L

OCALISATION

T

he aim of this thesis is to explore the three key components of a heterogeneous swarm capable of exploration and mapping of a nuclear cave environment: sensing, locomotion and control. Chapter three examined the sensing modalities that could be utilised in a nuclear cave. Subsequently, chapter four examined possible locomotion strategies that could be applicable to a nuclear cave environment. The reactive virtual forces framework was introduced in chapter five as a potential solution to controlling exploration and mapping within a nuclear cave environment. This control architecture has been shown to operate more efficiently on a heterogeneous swarm compared to a homogeneous swarm.

During the initial investigations into the effectiveness of the RVF framework it was assumed that the robots’ pose was known. Within a nuclear cave environment, this is not possible. Instead the robots will have to localise themselves without absolute positioning. Additionally, the per- formance of the RVF framework was not compared to other methods that exist. Thus, the aim of this chapter is twofold: to instigate localisation on robots using the RVF framework so that they may explore unknown environments without absolute positioning; and to assess the RVF framework on a performance scale.

As the MATLAB simulation had its accuracy verified by the embodied simulations, it was decided that the work in this chapter would be carried out within the simulation. For a full description of the MATLAB simulation environment, the reader should refer to chapter five.

This chapter is structured as follows: first, the Extended Kalman Filter used to localise the robots will be described; second, the comparative scale used to assess the performance of the RVF framework will be outlined; third, the experimental methodology used to investigate localisation will be explained; fourth, the results from these experiments will be presented; and finally, conclusions will be drawn about the effectiveness of the localised RVF framework.

6.1

Extended Kalman filter for Simultaneous Localisation and

Mapping

The extended Kalman filter (EKF) has been widely used in mobile robotics for simultaneous localisation and mapping (SLAM) [112] [110] [111] [51] [85] [201]. This method allows the estimation of a robot’s position and orientation based on odometry and distance sensor readings. In addition, EKF SLAM allows for a full definition of uncertainty for each landmark and the robot, through a covariance matrix. As discussed in chapter two; the full definition of uncertainty coupled with the prevalence of EKF SLAM in the literature, motivates the decision to use this method over more computationally efficient solutions such as FastSLAM [174] [173].

EKF SLAM works by finding landmarks in an environment and localising a robot relative to these. This process involves three steps:

1. The Predict Step - This involves a robot examining its odometry data and using this to estimate its position

2. The Update Step - This involves merging the odometry data and sensor data to update the position of the landmarks and robot in the state vector

3. Data Association - performed to decide if a robot believes it has discovered a new land- mark or is instead observing a previously discovered landmark.

The robot position and position of landmarks are stored in a state vector of size 1 x (3 + 2n), where n is the number of landmarks. This is coupled with a covariance matrix of size (3 + 2n) x (3 + 2n), which stores the uncertainty in the position of landmarks.

EKF SLAM provides a robot with localisation and a system for generating a landmark based map, however it does not have an inherent exploration method. As it stands, the RVF framework is an exploration algorithm without a method for localisation. It therefore seems logical to combine these two approaches to attain an algorithm capable of exploration, mapping and localisation in an unknown environment.

This section seeks to explain how EKF SLAM was implemented to work in conjunction with the RVF framework. This section will explore: the prediction step of the EKF, the update step of the EKF, methods for achieving data association in the EKF and the integration of the EKF into the RVF framework.

In document Characterisation of a nuclear cave environment utilising an autonomous swarm of heterogeneous robots (Page 142-150)