# Measurement of Wheel Radius in an Automated Guided Vehicle
## 3 An Overview of Selected Measurement methods
### Methodology of Measurements in Rectilinear Motion  
In order to meet the requirements for ensuring the straight-line movement of the vehicle, it is necessary to properly control and drive the vehicle. This can be obtained, for example, by moving along a given reference plane. As shown in Figure 7, as part of this movement, the fixed distance of the selected vehicle point and the assumed reference plane is maintained. Figure 4: An example of a curvilinear route. Figure 5: View of oscillations and interference on a selected fragment. Figure 6: The curve linear run and measurement data, \(R\)—radius of curvature, \(d\), \(d_{n}\) distance between vehicle and reference surface, \(s_{w}\), \(s_{C}\) measured path, 0 middle of the arc, half arc angle \(\phi\). Due to the imperfections of the reference surface and the measuring system, there may be three types of errors. The first of these is related to the nonlinearity of the reference surface. The second error is related to the structure of the reference surface. The third error is related to the accuracy of the measuring device. All three errors affect the measurement data which are used in the control system. This contributes to the formation of vehicle oscillations in relation to the assumed direction of movement. The course of such oscillations is shown in Figure 8a. Some of the errors in measurement data can be eliminated by applying real-time filtering. Excessive deviation from the set path can be partially eliminated by the use of real-time filtration. An example of using an online filter for measurement data entered into the control system is presented in [12]. The benefits of using such a filter are shown in Figure 8b. The application of online filtration has reduced deviations from the set driving path and thus increased the accuracy of the rolling radius determination process. However, it is a big problem to find the appropriate reference surface in real measurement conditions. Some of the surfaces used in the research had discontinuities. The effect of these disturbances is visible peaks in Figures 4, 5 and 8. Assessment of the Influence of Deviation from the Ideal Trajectory on the Value of the Rolling Radius  
In the case of a vehicle with a propulsion system presented in Section 4.1 small errors in the values of the rolling radii and control system errors cause a slight oscillation \(A\) from the set driving path. For the angle of deviation from the given path \(\psi=0\), the vehicle moves along the assumed direction (Figure 9a). For an incorrectly defined initial position of the vehicle in which the deviation angle \(\psi\
eq 0\) the vehicle route deviates from the assumed direction of travel. The distance that can be covered is limited by the width of the corridor and the value of the angle \(\psi\) (Figure 9b). Errors larger in the values of rolling radii cause a strong deviation \(C\) from the assumed trajectory. The actual vehicle movement is carried out in a curve (Figure 9c). In all cases, oscillations coming from the control system are visible on the course of the route. Figure 8: The route of the vehicle with the enlargement of the selected fragment (**a**) before filtration; (**b**) after filtration along. Figure 7: Data recorded during the movement of the vehicle. In order to determine the effect of oscillation and deviation from the target track on measurement accuracy, a series of computer calculations were done. The vehicle moves from the starting point to the endpoint. The direct distance \(L\) between these points is 40 m. Vehicle trajectory is not ideal and deviates from the line connecting the start and endpoints. Therefore, the actual \(L_{r}\) path traveled by the vehicle is greater than the distance \(L\). The first series of calculations concerned the course of motion shown in Figure 9a, while the second series of calculations concerned the course of motion shown in Figure 9c. In both cases, the distance traveled by the vehicle under the assumed traffic conditions, marked \(L_{r}\), was determined.