## 1 Introduction  
Nowadays, robotics has several areas, each of which is closely related. The area of robotics that we focus on in our workplace is called Simultaneous Localization and Mapping (SLAM). In solving this problem, the robotic system is in an unknown environment, and the initial position is known. The main goals of the SLAM solution are to obtain the most accurate model of the mapped environment and to monitor the exact position of the robotic system in the environment. This task does not seem very difficult when considering an ideal environment where various noises and measurement errors do not occur. Unfortunately, this kind of environment can only be achieved on a theoretical level. Various types of methods and algorithms are used to overcome these shortcomings. The sequence of individual steps is generally still the same and independent of the type of algorithm used. The steps are as follows: initialization, data association, extraction of landmarks, estimation of the state of the mobile robotic system and the state of landmarks, updating the status of the mobile robotic system, and updating the status of landmarks. For each of the mentioned steps, it is possible to use different solution methods, which are already linked to the specific algorithm used. SLAM can be used in a variety of environments, whether on land, in water, or in the air. Currently, one of the most popular techniques in this area is called ASLAM. It is often referred to in the scientific literature as automatic SLAM [1], autonomous SLAM [2], or SPLMA (Simultaneous Planning, Localization and Mapping) [3]. All these mentioned names have the same destination and thus is active motion selection. Using ASLAM, the autonomous movement of the mobile robotic system is solved in order to obtain a map. In the obtained map, various areas of our interest can be defined, such as unexplored areas, areas of irregular shapes, and areas with narrow alleys. The topic of autonomous vehicles is very wide. If we wanted to focus on the field of road transport, we could have achieved it as the author in [4] did, where he chose to use LAS (Lane Assistant System) technology. If we wanted to transfer such an application to the field of industry, it is possible to cite the deployment of an Autonomous Ground Vehicle (AGV) in an industrial hall as an example. It is usually necessary to map the space before deployment (this depends on the technology used), and it is possible to use active SLAM for this. Such mapping is often performed during working hours and the customer cannot always afford to be absent from the workforce, with the result that there may be a dynamic object in the mapped environment in the form of moving people. This can result in defects in the map and collisions of the robotic system with a dynamic object. We considered these mentioned complications to be crucial from our point of view, so we tried to find a solution. ASLAM with a combination of dynamic object detection to avoid collisions can significantly reduce the time required to map the environment. When operating a mobile robotic system, the detection of dynamic objects in the environment is an important aspect that increases the safety of the entire system. However, detection alone is often not enough to provide reliable navigation in a complex environment. The ideal situation is if the robotic system can predict the shape and trajectory of the movement in order to avoid collisions. The combination of dynamic object motion detection and prediction can be considered a particularly challenging task if we consider the variability of dynamic object patterns. Taking into account as an example two objects: a man and a car, two different types of motion arise. The person moves nonlinearly and without significant restrictions when changing direction, while the car has a smoother movement and reaches a much higher speed, which can cause a problem when tracking it.