# Kinematic Analysis of an Omnidirectional Tracked Vehicle
## 1 Introduction
The second demonstrator was a full-sized vehicle with dimensions of 2.5 \(\times\) 3.5 m and the same track arrangement. The publication details a number of tests to which the vehicle in question was subjected and presents possible concepts for the industrial use of the proposed chassis. The most comprehensive study to date was published in 2020 [23], focusing on the numerical and experimental studies of a full-sized omni-tracked vehicle--a 5t forklift equipped with a symmetrical, non-overlapping track system. The paper provides a mathematical model of the kinematics for the selected chassis type and an analysis of how roller orientation affects movement speed. The numerical model of the vehicle in question is then presented, and the results of the simulations of the different variants of motion are presented. In the section on bench tests, an analysis of current consumption during different types of movement is presented, as well as the results of the measurement of the drive speed. Another study from the last five years [24] described centre-point steering models for omni-track vehicles in typical track systems. The authors introduced the phenomenon of slippage between the track roller and the ground in the steering models. In addition, they proposed a mechanism for correcting the angular velocity of the vehicle body during movement. They conducted a series of numerical simulations, as well as experimental tests, demonstrating significant improvements in handling properties for specific chassis. More of the latest research [25] describes the experimental testing of a lightweight prototype omni-tracked robot in a parallel, fully overlapping track system. It describes the robot's construction process and proposes an algorithm for static directional correction, the effectiveness of which was confirmed by experimental studies. Last year's study [26] deals with experimental research on the prototype of an omni-track robot in a parallel, fully overlapping tracks system. It contains a description of the construction of the prototype, as well as the results of the experimental testing of the dynamic direction correction module. This module, on the basis of the current driving  
Figure 4: Schemes of omni-tracked vehicles with free rollers with parallel tracks. From (**left**) fully non-overlapping, (**center**) partially overlapping, and (**right**) fully overlapping. parameters, allows for the determination of corrective values, enabling the robot to more accurately follow a predetermined trajectory. In omni-track vehicles, the direction of movement is achieved by controlling the individual tracks' drives. In the direction parallel to the direction of the axis of the free roller in contact with the ground, there is much greater resistance to movement than in the perpendicular direction. Thanks to this, combined with the relative motion of individual tracks, it is possible to achieve omnidirectional mobility. In order to properly control an omni-track vehicle, it is necessary to be able to induce body motion in the selected direction. For this purpose, a kinematic analysis of the omni-track vehicle is necessary. A kinematic analysis of the other types of omnidirectional vehicles can be found in articles [27; 28]. The first article deals with the kinematic analysis of a vehicle equipped with four omnidirectional wheels. The wheels in the analyzed platform are oriented to each other at an angle of 90\({}^{\circ}\). The second article focuses on both the kinematic and dynamic modelling of a vehicle equipped with four Mecanum wheels. In both cases, the methodology presented is based on the analysis of each wheel (reduced to a free roll having contact with the ground at a given moment) separately. The analysis of a typical tracked vehicle is considered in [29], using the example of an autonomous tracked vehicle. This work presents a comprehensive control scheme for tracked vehicles, including both kinetic and dynamic models during movement in difficult terrain.