# Kinematic Analysis of an Omnidirectional Tracked Vehicle
## 5 Conclusions  
The article presents a kinematic model of a pair of tracks of an omnidirectional vehicle. This model represents a separate component of an omni-track vehicle. If needed, it can be extended to analyze the motion of any type of omni-track vehicles, consisting of a larger number of pairs of tracks, which is a novelty in relation to most existing works. The model enables the determination of the vehicle body's displacements relative to the ground for any orientation of the free rollers, based on the predefined displacements of the tracks relative to the body. This article presents the body of the vehicle, obtained on the basis of this model, for the selected orientation angles of the free rolls and the preset speeds of individual tracks. A numerical model of the omni-track vehicle was also developed, allowing the dynamic simulation of motion. This model includes mass properties and ground contact forces acting on the rollers, enabling a realistic simulation of the vehicle's movement. A comparative study between numerical simulation results and those obtained from the kinematic model showed that the kinematic approach accurately reflects the real dynamic behaviour of the vehicle. Therefore, it provides a solid foundation for controlling a real omni-track system. Thanks to the compact and simple structure of the proposed kinematic model, it is possible to implement it on units with relatively low computational power, especially for typical roller angles of 45\({}^{\circ}\) and 135\({}^{\circ}\). Using the proposed model to control a vehicle with a different roller orientation is still possible, but the errors between the theoretical and actual vehicle trajectory will be higher.  
In parallel with the work described in this article, experimental research was conducted on a real prototype of an omni-track vehicle. Experimental studies, not included in this article, have shown that changing the ground on which the robot moves can worsen the driving properties of an uncorrected driving system by an order of magnitude. The conceptof implementing the presented kinematic model is based on the use of on-board sensors, such as the IMU orientation sensor, which will enable the real-time reading of the vehicle's angular orientation relative to its initial position. Thanks to this, using the proposed kinematic model, it will be possible to determine corrective values for the control system, which will enable restoring the set direction of movement; for example, using the PID controller and feedback of the current orientation angle. Going a step further, sensor fusion can be used. Based on data from the encoders of individual running systems, accelerometer and gyroscope readings, as well as the orientation sensor, one can try to recreate the actual trajectory of the omni-tracked vehicle. This operation should be possible regardless of the external forces acting on it or the surface irregularities, without the need to use external positioning systems such as GPS or cameras and markers. A detailed description of this experimental research and its results will be published in a separate publication. The further research will include the verification of the control system's effectiveness during real-world vehicle operation--both in translational motion and in motion involving changes in angular orientation.  
This research was funded by Grants-in-Aid from the Wroclaw University of Science and Technology, Faculty of Mechanical Engineering, Poland (K61--no. 825 1050 500).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The author declares no conflicts of interest.