Variables del Modelo Hedónico Casas independientes

The embodied simulation was designed so that investigations into the effect of heterogeneity could be conducted using a homogeneous team of robots. This involved imbuing robots with virtual heterogeneity in sensing and through restricting maximum speed, whilst also varying the virtual parameters of charge and mass.

The robots used to conduct the experiments were the E-pucks [171]. They were localised using a VICON tracking system [253]. This system can determine the pose of a robot to an accuracy of 1mm.

Accurate knowledge of a robot’s position allows for virtual obstacles to be created, and hence virtual sensing to be implemented. The range of this virtual sensing could easily be changed to allow heterogeneity to be defined between robots. The positions of obstacles are randomly generated in the map. As with the MATLAB simulation, the sensor was taken to be a circle with variable radius about the robot. When an obstacle enters the sensor range of a robot the Euclidian distance to that obstacle is calculated, then Gaussian noise is added to this reading. Sensing is the only virtual parameter used in the embodied simulation; the communication, robots, arena and associated physical noise are all real.

at the beginning of each mapping effort, this is shown in figure 5.5. The arena represents an unknown and cluttered environment; as such, though the experimental environment is simplified, it represents the unknown and cluttered surroundings a robot could encounter when exploring a nuclear cave, and thus allows preliminary conclusions to be drawn about the suitability of the control algorithm. The experiments conducted will be outlined subsequently.

5.4.2 Experimental Methodology

The aim of these experiments was to investigate the suitability of the RVF framework for the exploration and mapping of a nuclear cave environment, and to compare its results on a single robot, a homogeneous swarm, and a heterogeneous swarm. In addition, the effect of the occupancy grid resolution was examined in each case. The hope was that the results in the embodied simulation would verify those acquired in the MATLAB simulation.

In this section the experiments that were run on the single robot, the homogeneous swarm and the heterogeneous swarm will be outlined. In each case 30 experiments were run, in keeping with the guideline put forward by the national institute for standards and testing [115]. This states that thirty experiments give an 80% reliability. This section will detail: the single robot experiments; the homogeneous experiments; and finally, the heterogeneous experiments.

5.4.2.1 Single Robot Experiments

The initial aim of the single robot experiments was to examine the effect of the occupancy grid resolution on the algorithm and mapping time, as well as investigate the performance of the RVF framework on a single robot. When exploring the 1.5x2m test arena, the area was divided into smaller regions defining the occupancy grid to be filled by the robot. To inspect the effect of a varied occupancy grid resolution, the following divisions were used:

1. 13x10 - each grid square is approximately twice the diameter of the robot. 2. 26x20 - each grid square is approximately the diameter of the robot. 3. 52x40 - each grid square is approximately half the diameter of the robot.

These divisions provide a trade-off between computation time and accuracy: as the matrix storing the occupancy grid grows so does the processing time, whilst a finer grid allows a more accurate definition of the location of obstacles.

Each grid resolution was examined with three virtual sensor ranges: 20cm, 40cm and 80cm. This is because robots comprising the heterogeneous swarm would later use these sensor ranges, so it was prudent to have a baseline for comparison on each member.

In each case the robot was initialised at a random location at the edge of the map, to simulate entry into a nuclear cave. The robot then proceeds to map the environment until 80% coverage is reached, at which point the time is recorded and the experiment repeated.

5.4.2.2 Homogeneous Swarm Experiments

The homogeneous experiments were conducted on a group of four E-Puck robots, each given a virtual sensor range of 40cm using the embodied simulation method described earlier. During these tests there were two communication modes explored: local communication and global communication. In the local communication mode, robots were only able to communicate with each other when within their sensory range. In the global communication mode, robots communicated with each other continuously, regardless of the distance between them. Communication was achieved over WiFi, using ROS nodes that published and received [195]. The occupancy grid was the only item being communicated between robots. To do this it was first converted into a one-dimensional matrix, whose elements were transmitted one at a time. This matrix was then converted back into the appropriate occupancy grid form when it was received. The average between the receiving robot’s own occupancy grid and the occupancy grid it was being sent was then found to be the new occupancy grid. If multiple messages were sent at once, due to multiple robots’ being within communication range, they are randomly ordered and resolved based on this order.

Each communication paradigm was examined at the three grid resolutions used in the single robot case: 13x10, 26x20 and 52x40. This was to investigate the effect the grid resolution has on the exploration time, as it was expected the higher communication overhead associated with a finer resolution would cause exploration time to increase.

As with the single robot examinations, each member of the homogeneous swarm was ini- tialised randomly at the edge of the mapping area. The experiments were run until three of the four robots had reached 80% coverage, to match the end condition used in the MATLAB simulations. At this point the experiment was stopped and task completion time was recorded.

5.4.2.3 Heterogeneous Swarm Experiments

The heterogeneous experiments were run on a group of four E-Puck robots. In this case, two robots were given a 40cm sensor range, one a 20cm sensor range and the last robot a 80cm sensor range. In addition, their speeds were limited to 0.07m/s, 0.035m/s and 0.14m/s respectively. This was to allow for virtual heterogeneity to be defined using the homogeneous E-Puck robots. These values were chosen so that the average parameter values of both the heterogeneous and homogeneous swarms were kept the same, to allow for a reasonable comparison. These values also matched those used in the MATLAB simulations to enable verification of the results produced.

The experiments were conducted in the same manner as for the homogeneous swarm. This involved comparing global communication to local communication, over the three occupancy grid resolutions. Communication in the heterogeneous case was achieved in the same way as the homogeneous scenario. The robots were again set at random start locations about the perimeter of the arena. Each experiment was ended when three of the four robots reaches 80% coverage, and the time taken to do so was recorded.

Figure 5.6: A delineation of the experiments conducted in the MATLAB simulation, along with the location of methodology and results within the thesis.

5.5

Results

The experimental methodology used to examine the RVF framework has been detailed in the previous sections. This involved using a MATLAB simulation to rapidly prototype and examine the RVF framework on a homogeneous and a heterogeneous swarm. An embodied simulation was then used to verify the MATLAB simulation results and observe the behaviour on real robots.

This section aims to present the results from the comparative experiments and examine their statistical significance. This section is structured as follows: first, the results from the MATLAB simulations will be presented; second, the results from the embodied simulations will be detailed. In order to delineate the experiments conducted in this chapter, figures 5.6 and 5.7 are provided; these figures detail the sections in which experimental methodology and results can be found for each experiment, for ease of reference.