## 2 Hardware and Software Solutions
### Representation of Space  
The space being described can be represented as continuous or discrete. In the real world, the environment is continuous, which complicates the solution in finding the optimal route, as continuous space is described by a set of infinite possible states. For simplicity, the continuous environment is divided into a finite set of states. This process is called environmental discretization. Finding a path then means searching for a sequence of states leading to the destination state. The state represents a point in space. The basic types of space representations can be divided according to [21], into metric, topological, and hybrid, see Figure 4. In each variant, localization in space is a basic problem, but of a different nature. The represented environment is often called the environment map. Based on what part of the environment the map represents, it is divided into a local or global map. They focus locally on the robot's close surroundings, while global maps focus on the entire area. Metric maps represent objects in the environment based on their geometric properties. Two variants are most often used. The first is based on the calculation of Cartesian coordinates of the environment. Kalman filtration is often used here, using a fusion of odometric data and data from environmental sensors. The second variant takes the form of a grid map of occupancy. These maps are made from cells, which represent an estimate of the occupancy of individual cells in the environment [21]. The way cells are divided and formed is dealt with by the cellular decomposition of the medium [22]. The advantage of the metric map is the ability to create a detailed representation of the environment. However, higher demands on recording capacity and computing capacity are also related to this. However, the biggest disadvantage of this approach is that it does not provide a  
Figure 3: Division of methods path planning.  
system for representing symbolic entities such as tables and doors. In a topological map, the environment is represented on the basis of its significant properties. This type of map takes the form of a graph, where nodes represent significant properties and edges represent relationships between properties. When creating a map, the uncertainty in determining the position of the mobile robotic system does not affect it. One of the problems with this approach is identifying the significant features and nodes in the environment that are used to create the map. The advantage of this map is considered to be fault tolerance in determining the position of the system in Cartesian coordinates, as it is not a priority when creating the map. A hybrid map is a combination of metric and topological, consisting of nodes and edges similar to a topological map. However, both edges and nodes can be described in the metric form of a map. This way of representing space uses the advantages of both mentioned forms. The metric description provides greater map detail, and the topological description increases resilience to localization errors. The problem arises when switching from one form of representation to another [21].  
The standard that deals with the data format for the needs of robotic system navigation, i.e., the map format, is called IEEE 1873-2015 [23]. This standard defines the concept of a global map, which consists of local maps. A local map can consist of a metric map, a topological map, or a combination of both. In the context of the standard, grid maps and geometric maps are included in metric maps. A geometry map contains a list of contiguous geometric elements (such as points and lines). Topological maps already consist of the mentioned nodes and edges. Edges represent a direct (single jump) connection between adjacent nodes. In metric maps, the distance between two elements must be calculated, while in topological maps, this only applies to some elements. The output of the map defined by the IEEE 1873-2015 standard is in XML format. In our case, we decide to use grid map.