## 2 State of the Art Review  
### Modeling of Wheeled Mobile Robots  
The modeling of wheeled mobile robots covers kinematics and dynamics issues. From the point of view of robot control, it is important to solve the inverse kinematics problem, which allows us to determine what the wheel motion parameters should be for the desired robot motion parameters. This problem can be unambiguously solved assuming no wheel slip during robot movement. In the case of skid-steered robots that typically move in wheel-slipping conditions, this solution is subject to error. The real movement parameters can then be estimated based on the robot dynamics model, which takes into account the interaction of the wheels with the ground and the phenomenon of wheel slip. The basics of the modeling and testing of automotive vehicles, taking into account the wheel slip phenomenon, are presented in the book by [PERSON], 2005 [2]. In turn, the basics of soil mechanics and the modeling of off-road vehicles on various grounds, i.e., terramechanics, are formulated in the book by [PERSON], 1960 [3]. Therefore, depending on whether the wheeled vehicle is traveling on paved or unpaved ground, a partially different approach should be used. Various formalisms can be used to determine the dynamic equations of motion. The most frequently used are the Newton-Euler formalism and formalisms based on the Lagrange equations, an example of which is the work of [PERSON] and [PERSON], 2004 [4]. The article by [PERSON] et al., 2023 [5] is devoted to a review of mathematical models of wheeled and tracked vehicles, which discusses selected issues of kinematics and dynamics. In the field of wheeled vehicles, the car-like kinematic structure and a variant of this structure with independently steered four wheels, as well as the skid-steered structure are considered. In turn, the work by [PERSON] et al., 2022 [6] contains a review of mathematical models of the service robots. The kinematics and dynamics of these robots are taken into account, including the phenomenon of wheel slip. The review covers differentially driven, skid-steered, and car-like kinematic structures with various numbers of wheels. Additionally, models of tracked robots as well as legged and snake robots are discussed. The article by [PERSON] et al., 2021 [7] concerns the issues of the modeling and control of a six-wheeled skid-steered robot. This work focuses on the issues of the driving force distribution and control strategy of such a robot, which aim to improve the vehicle maneuverability and stability. It also contains the results of experimental studies of the robot using the analyzed solutions of the control system. When modeling the movement of wheeled mobile robots, it is usually assumed that they move on horizontal ground. However, one can also find fewer works that take into account the case of sloped terrain, an example of which is the article by [PERSON] et al., 2012 [8]. In such a case, the robot dynamics model is more complex, but more general and allows for taking into account additional phenomena resulting from the slope of the terrain. In order to obtain the actual parameters of the dynamic system, an identification process is carried out based on the measurement of the excitations and responses of the object. This process can take place both offline, as in the paper by [PERSON], 2023 [9], and online, as in the work by [PERSON] and [PERSON], 2014 [10], where the parameters of the object are determined in real time. The first approach allows for a more comprehensive analysis, while the second has the advantage that, in the event of a change in the parameters of the robot's model, e.g., related to a change in the type of ground or the transported mass, information about the current parameters can be used by the control system. The robot's parameters can also be estimated by the control system if an adaptive control strategy based on the known structure of the object model is applied.