## 2 Materials and Methods
### The Voxel Grid and the Approach to Capture Data  
Navigating unknown environments poses a significant challenge in robotics, given the complexity, dynamics, and diversity of real-world spaces [20; 21]. To overcome this challenge, agents need a more universal view of the world to comprehend and represent the data they perceive, allowing for a common ground for information sharing and representation of surroundings in a simple and relatable manner. This approach has been explored in previous research, demonstrating the benefits of shared understanding of the environment for multiagent systems [13; 22]. To enable agents to comprehend and represent the environment, various techniques have been developed, such as voxel-based representation learning [13; 23] and semantic RGB-D SLAM [21]. Other studies have investigated deep loop closure detection and point cloud registration for LiDAR SLAM [24], fast and compact loop closure detection using 3D point clouds for indoor mobile mapping [25], and a lightweight LiDAR-inertial SLAM system with loop closing [26]. These techniques enable agents to represent the environment more accurately and efficiently, leading to better navigation and mapping performance. Navigating unknown environments is a challenging problem in robotics, but various techniques have been developed to provide agents with a more universal view of the world, enabling them to comprehend and represent the data they perceive. To reconcile the various approaches described above, this paper proposes an approach that aims to standardise environmental representations. To achieve this goal, it is necessary to adopt a standard form for representing complex environmental data, such as an occupancy grid. Occupancy grids offer a representation of the world as evenly spaced fields of probabilities. Initially set to zero, these probabilities are typically instantiated upon observation, allowing any unexplored location to be sampled and referenced relative to other grid locations. In a traditional occupancy grid approach, the grid represents the probability of observing an object. To generalise this concept, the proposed approach transforms the variable \(z\), a measurement observation, into a set of measurements \(z=\) set and applies Bayesian inference to reason with this set. This approach levels the playing field for all heterogeneous agents, given that there is an agreed-upon set of descriptions (coordinates) to commonly address the environment. However, for our purposes, a 2D or 3D coordinate system does not sufficiently capture the complex nature of the data that needs to be represented. As an alternative, we propose using a 3D voxel grid, which contains the measurement and observation data inside each voxel. This voxel grid offers a rich representation of the environment, allowing agents to reason about the occupancy of different regions and the likelihood of objects existing within them. This approach has been used in previous research, such as in voxel-based representation learning for place recognition [13] and semantic RGB-D SLAM for rescue robot navigation [21] These studies demonstrate the effectiveness of using voxel grids to represent complex environmental data and the benefits of doing so. The world can be perceived as a set of probabilities that remain fixed, such as the likelihood of a region being occupied or containing a particular object. As time passes, this set of probabilities is updated, and information is stored together with a timestamp. Consequently, every voxel in the grid represents a collection of past observations regarding the environment. This approach enables agents to reason about different areas' occupancy and the likelihood of objects being present, even if the objects are in motion. By capturing data over time within a fixed space, the probability of an object's location becomes more certain as agents explore, while still retaining the data's validity despite dynamic and moving objects.