This article deals with methods of navigation and mapping of mobile robots in an indoor environment, for example, laboratories, building corridors, and so on. It explains the proposed solution of global navigation in more detail through the application of potential field method and its transformation into the topological map. Two separate software tools were designed for simulation of wheeled mobile robot behavior in the authors’ workplace. The first software uses the metric form of space representation and it can simulate tactic level of global navigation, while the second one deals with its transformation into the topological map and can be used for strategic level of global navigation. This is how we can get the so-called multilayer map system suitable for different tasks of mobile robot navigation and path planning.

Calculation of the moving mechanism on a trajectory described by a planar differentiable curve is challenging. The difficulty arises in compliance with high-precision movement. The new method of calculation based on the intrinsic properties of the plane is proposed. The method is based on mathematical linguistics and relational algebra. First, these disciplines are applied to analyze the intrinsic properties of the Euclidean plane. Calculation of classic and new methods for moving point for the flat rod is shown for comparison. Analytical formulas for Jordan curves can be obtained in some cases. The experiments in the areas of geometric modeling and control of a robot are listed briefly. The analytic solution was obtained by nontraditional methods not only for centrally symmetric conic sections but also for Jordan curves.

This paper introduces novel research into specific mechanical properties of composites produced by 3D printing using Continuous-Fiber Fabrication (CFF). Nylon (Onyx) was used as the composite base material, while carbon constituted the reinforcement element. The carbon fiber embedment was varied in selected components taking values of 0°, 45°, 90°, and 135° for parts undergoing tensile testing, while one specific part type was produced combining all angles. Carbon-fiber-free components with 100% and 37% fillings were also produced for comparison purposes. Parts undergoing the Charpy impact test had the fibers deposited at angles of 0° and 90°, while one part type was also produced combining the four angles mentioned before. Carbon-fiber-free parts with 100% and 37% fillings were also produced for comparison purposes as with the first part. The Markforged MARK TWO 3D printer was used for printing the parts. These were subsequently scanned in the METROTOM 1500 computed tomography and submitted to the tensile and impact tests. The results showed that adding carbon fiber to the base material increased the volume of defects in the samples as a result of the porosity increase. Although the tensile testing manifested an overall increase in tensile strength Rm of up to 12 times compared to the sample without reinforcement, it was proven that an improper fiber orientation significantly diminished the strength and that combining the four selected angles did not lead to the highest strength values. Finally, the impact tests also showed that fiber-reinforced parts implied up to 2.7 times more work to fracture, and that an improved fiber orientation also led to strength reduction.

The paper deals with the investigation of 3D digitizing of small parts specifically by optical 3D scanner GOM ATOS TripleScan. The paper shortly illustrates the general concept of Reverse Engineering, which includes also the 3D scanning. The paper also describes the optical 3D scanner GOM ATOS TripleScan and a three-dimensional model obtaining procedure by means of this scanner. In the main part of the paper the concrete 3D scanning process of chosen individual objects is described (clips, ball nose end mill, screw drill, coin). Their shape and size were specific and distinct, therefore it was possible to test and compare particular digitizing attributes. The problems that occurred during 3D digitizing of individual parts are step by step discussed and solved.