The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

Ultra-wideband (UWB) technology is one of the most promising wireless communication technologies. Examples of UWB applications include, among others, radiocommunication devices and location systems, due to their operating range, ability to work in outdoor environments, and resistance to multipath effects. This article focuses on the use of UWB technology in constructing a guide localization system for an unmanned ground vehicle (UGV), which is one of the stages of implementing a “follow me” system. This article describes the complete process of UWB signal processing from its acquisition, methods of filtering, and obtained results, to determining the location of the guide. This article examines the possibility of using modified versions of localization algorithms for determining the guide’s location, including trilateration, methods of nonlinear programming, and a geometric algorithm proposed by us. The innovation of this study consists in the implementation of an algorithm that changes the selection of equations (mathematical model) for determining location based on the number of available measurements from UWB sensors.

As a result of ever-growing energy demands, motor vehicles are among the largest contributors to overall energy consumption. This has led researchers to focus on fuel consumption, which has important implications for the environment, the economy, and geopolitical stability. This article presents a comprehensive analysis of various fuel consumption modeling methods, with the aim of identifying parameters that significantly influence fuel consumption. The scientific novelty of this article lies in its use of low-cost technology, i.e., an OBD-II interface paired with a mobile phone, combined with modern mathematical modeling methods to create an accurate model of the fuel consumption of a vehicle. A vehicle test drive was performed, during which variations in selected parameters were recorded. Based on the obtained data, a model of the vehicle’s fuel consumption was built using three forecasting methods: a multivariate regression model, decision trees, and neural networks. The results show that the multivariate regression model obtained the lowest MSE, MAR, and MRSE coefficients, indicating that this was the best forecasting method among those tested. Sufficient forecast error results were obtained using neural networks, with increases of approximately 73%, 10%, and 131% in MSE, MAE, and MRAE, respectively, compared to regression results. The worst results were obtained with the decision tree model, with increases of approximately 163%, 21%, and 92% in MSE, MAE, and MRAE compared to the regression results.

One of the technologies used for localization is GNSS (Global Navigation Satellite Systems), which is exposed to many phenomena, i.e., the occurrence of terrain covers, reflections of the radio waves, and the multipath nature of the radio waves in the propagation environment. To increase the resistance to environmental phenomena, special types of antennas are used, which include, among others, choke ring antennas. The article describes the design and construction of the choke ring antenna and the impact of the mentioned device on the quality of GNSS positioning. The accuracy of the constructed antenna (based on selected accuracy measures: DRMS, 2DRMS, SEP, MRSE, SAE) is calculated together with positioning errors determined for two types of antennas: choke ring antenna and the dedicated antenna supplied by the manufacturer in RTK mode. The results confirm that the designed choke ring antenna can be used for positioning without significantly losing accuracy in the RTK mode.

The article describes the issues of transport of bulk materials. The knowledge of this process has a key impact on the rational planning of transport tasks. It is necessary to have knowledge about the transport services market and the competition that exists in it. In order to achieve a competitive advantage on the market, enterprises should analyze data on the implementation of transport tasks on an ongoing basis. It is also important that the costs incurred from the conducted activity are minimized, while increasing the quality of services and taking into account the sustainable development of the enterprise. The study analyzes data from a few selected motor vehicles in the period of 3 years of operation, coming from an enterprise specializing in the transport of bulk materials. Moreover, a global sensitivity analysis was performed based on a neural model describing the impact of the analyzed factors on the company’s profit. The results show that the most important factors influencing the company’s profit are the fuel consumption of individual vehicles, the driver (driving style) and the month (average temperature, weather conditions).

The work presents the dynamic equations of motion of a unmanned six-wheeled vehicle with mecanum wheels for rescue applications derived with the of Lagrange equations of the second kind with multipliers. Analysed vehicle through using mecanum wheels has three degrees of freedom and can move on a flat ground in any direction with any configuration of platform’s frame. In order to derive dynamic equations of motion of mentioned object, kinetic potential of the system and generalized forces affecting the system are determined. The results of a solution of inverse dynamics problem are also published.