## 2 Materials and Methods
### The Voxel Grid and the Approach to Capture Data
This is not dissimilar to downsizing, but, rather than an average of the points' locations, it is the mode of where more points fall in the world space voxel grid. Using the above methods, the agent has a system in which to recreate an SLAM system using frame-to-frame alignment. However, as stated at the start of this paper, the world is already a fixed grid of voxels; understanding the relationship between the perceived sensor data and that voxel grid links these data points together. The agent must now update that world space coordinate with the information it can gain. One might look at this approach and ponder on the differences between the SLAM system, or, indeed, other mapping systems that align 3D point clouds of data. The response is that with the voxel grid system, the world state does not move with new alignments; that is to say that when an agent revisits an area and the coordinate is perceived as different, the map the agent has generated is not moved or aligned, but, rather, the information is fed into the voxel at the new coordinate. An example of this is shown in Figure 2

First, a more transitional way of aligning and registering mapping data will be examined. For simplicity, the example will be limited to 2D. Figure 2: The figure shows the origin can be set arbitrarily when the agent first starts recording a new environment..

As can be seen in the above Figure 3, as the data from the agent become misaligned, the data are reconciled to the new location relative to the first frame. This, in effect, relocalises the environment to the new frame, and the information about the \"incorrect\" data is lost. In Figure 4, we can see that the data are still being realigned; however, the information about the previous records is kept, and over time, this will provide a greater probability for a given voxel to contain the ground truth information. Figure 4: Figure showing object overlay increasing the probability of a voxel containing an object. Figure 3: Figure illustrating an agent initializing two different sets of voxels based on the position of the environment. _The voxel_-- A voxel is a unit of graphic information that defines a point in three-dimensional space. For use in this paper, the information contained inside is extended from just a simple X,Y, Z, and colour, to the storage of information that will help define the world's complex nature. The agent should store information pertaining to its observation of the environment, for example, heat or sound data. Figure 5 shows this in more detail. In this paper, some assumptions are made about the data that are recorded and stored inside the voxel; however, there is no necessity to limit the recorded information. The below shows the definition of the voxel grid utilized in this paper. \(w\) = The size of the world

Time \(t\) is an arbitrary, but consistent, timestep that is defined by the agent. \(\text{g}=\{\,v_{1},\ldots,v_{w}\,\}\)

v = {x,y,z,d}

where {X,Y,Z} \(\in\mathbb{R}\)

and represents the position of an arbitrary point in Cartesian space. \(\text{d}=\{\,h_{1}\ldots h_{t}\}\)

\(\text{d}=\{\,\text{e},\,\text{r},\text{b},\,\}\)

\(\text{j}=\{\,o_{1}\ldots o_{s}\,\}\) Where \(s\) is the number of objects discovered in any given frame

\(\text{o}=\{\,\text{i},\,\text{p}\,\}\)

\(\text{p}=\text{The probability of a given object being in that voxel at time t}\)

\(\text{e}=\text{Agent Experience}\)

\(\text{r}=\text{Reliability of agents}\)

\(\text{b}=\text{Agent Bias}\)

_Object detection from a recognised set_--A key aspect identified in the hypothesis is that of object recognition under occlusion. That is, it is difficult to identify objects that are partially obscured, by either other items within the environment or perhaps poor viewing angles. The voxel grid can address these issues by allowing the object being identified to be reconciled with a template for the given object to be found, over multiple orientations and scales.