# Measurement of Wheel Radius in an Automated Guided Vehicle
## 1 Introduction  
The use of an automated guided vehicle (AGV) is becoming more and more common. In many cases, the routes implemented by these vehicles are subject to constant changes and are adapted to the currently assigned task. The basic navigation system for most of these vehicles is odometry. The navigation process using odometry assumes the constancy of parameters such as rolling radii and wheelbases. Slips are also not included in this process. In real conditions, when working with different loads and on different surfaces, these parameters change their values and slides occur. Not taking these changes into account in the navigation algorithm leads to errors in determining the position. An extensive review regarding odometry errors is included in papers [1, 2]. There are several types of errors that affect the accuracy of the positioning process. These include systematic and unsystematic errors. The systematic errors that arise in determining the current position during the movement of the vehicle are aggregated [1, 3]. Depending on the type of surface, the share of the systematic and the unsystematic errors in the error of position determination may be different. In addition, odometry errors can be caused by the same movement equations [4]. These equations describe any trajectory through a series of short sections. The accuracy of this approximation depends on the sampling frequency and vehicle speed. Many methods are used to correct errors. The first works related to error correction concern systematic errors. Correction of these errors and calibration of the system takes place after traveling the preset route section and measuring the error of the final position [1, 2, 5, 6, 7, 8]. Modern measurement techniques enable online measurements. A variety of techniques may be used for measurements, a brief review of which is contained in [9, 10, 11]. In most solutions usingadditional measurement systems, extensive filtration methods are applied. These can be online methods such as at work [12; 13; 14] or offline as at work [15]. All the aforementioned works assume that the wheel and ground are rigid, cooperation between the wheel and the road takes place at one point and there is no slip. In recent years, there have been works including changes in rolling radius and occurrence of wheel slip [16; 17; 18; 19; 20; 21]. Such changes in the rolling radius have been taken into account in the navigation process of the vehicle presented in Sec. 4.1 and intended for the carriage of loads. The shape of the route and the mass of the cargo carried during the operation of the vehicle is subject to change [22]. It depends on the currently assigned task. In the case of a change in the mass of the transported load or its position on the vehicle, the loads of individual wheels change. Along with these changes, the rolling radii of the vehicle wheels are subject to change. Failure to take this fact into account in the calculation algorithm will lead to errors. In order to reduce these errors, it is necessary to enter into the calculation algorithm appropriate values of rolling radii taking into account the current wheel load. This operation will be possible only after examining and determining the dependence of the rolling radius on the wheel load. As part of the article, it was decided to describe the measurement methodology as well as the course of experimental research aimed at determining the dependence of the rolling radius on the wheel load in the vehicle under consideration. The paper is organized as follows. Section 2 presents a research object and its characteristics and information about the wheel and its properties. Section 3 presents an overview of selected measurement methods. As part of the review, errors resulting from failure to maintain ideal measuring conditions were indicated. Taking into account the measurement capabilities and existing environmental conditions, the most adequate measurement method for the further stage of experimental research was indicated.