We examine five setups where an agent (or two agents) seeks to explore unknown environment without any prior information. Although seemingly very different, all of them can be formalized as Reinforcement Learning (RL) problems in hyperbolic spaces. More precisely, it is natural to endow the action spaces with the hyperbolic metric. We introduce statistical and dynamical models necessary for addressing problems of this kind and implement algorithms based on this framework. Throughout the paper we view RL through the lens of the black-box optimization.

Computer graphics, robotics, and physics are one of the many domains where interpolation on the unit sphere S n (often called a unit hypersphere or unit n-sphere) plays a crucial role. In this paper, we introduce a novel approach for achieving smooth and precise interpolation on the unit sphere S n−1 using the n-dimensional generalized Kuramoto model. The proposed algorithm finds the shortest and most direct path between two points on that non-Euclidean manifold. Our simulation results demonstrate that it achieves performance comparable to that of a Spherical Linear Interpolation algorithm. Also, the paper proposes the application of our algorithm in the interpolation of rotations that are presented in the form of four-dimensional data.

Although the technology to automatically score multiple-choice tests has been around for several decades, it is still not as widely available or affordable, especially for paper-based test processing. The main reasons that hinder these processes are the lack of software systems capable of working with contents that are not filled optimally and do not require expensive scanners or other costly equipment. In this study, we present a software system for the automatic reading, storing, and evaluation of scanned assessment sheets. This software system offers a solution that only requires the usual scanned Evaluation Sheets in the form of a not high-resolution image and with the help of specific markers, the system performs reading, storage, and scoring. The user interface is designed to read and display the data from the Evaluation Sheets in detail so that they are very understandable to the user and allow him to quickly spot any errors. The tool has been validated over six years of use and has been continuously improved throughout that period. Thus, this software system achieves a high level of reliability and sensitivity to different levels of the quality of filling out Evaluation Sheets by students.

Averaging data on the unit sphere S d (also called a unit hypersphere) is a common problem in computer vision, robotics and other fields, with applications ranging from motion planning to DNA modelling. In this paper, we introduce a new method for averaging data represented as points on the unit sphere S d−1 using the d-dimensional generalized Kuramoto model. Our method is verified on a range of benchmark data sets and compared with common data averaging algorithms. Also, we showcase the applicability of this method for solving rotation averaging problem.

This paper aims to experimentally and numerically determine the longitudinal modulus of elasticity by the four-point bending method. Samples of wooden beams over which the experimental research was performed were made of silver fir (Abies alba) as prescribed by standard EN 408. The experimental part includes determining bending strength and deformation forces. Experimentally determined bending strength and deflection forces were the input data for evaluating the modulus of elasticity of wooden beams. A numerical analysis of the bending strength by the finite element method was carried out using the ANSYS software package. The numerical model agreed well with the experiments in terms of bending. A numerical model can predict the bending of beams of different sizes. Results showed that the experimental and numerical values are close and usable for further exploitation. Comparison between the experimental and computational force versus the displacement response showed a very good correlation in the results for the fir wood specimens under four-point bending tests.

The development of teleoperation systems, robots, or any physical part of the system can be costly and if something goes wrong it can lead to development overdue. Precisely for these reasons, engineers and scientists today resort to the development of simulated systems before the construction of a real system. Robot Operating System (ROS) is one of the most popular solutions for robot development, manipulation, and simulation. In this paper, we present a web application for remote control of a ROS robot. The robot is controlled via a web application that is used as a virtual Joystick. Also, in this paper, an experimental work analysis of the projected system is performed. Further research possibilities include upgrading the presented web interface, adding certain motion autonomy sensors, or integrating some path planning algorithms.

The construction of smooth interpolation trajectories in different non-Euclidean spaces finds application in robotics, computer graphics, and many other engineering fields. This paper proposes a method for generating interpolation trajectories on the special orthogonal group SO(3), called the rotation group. Our method is based on a high-dimensional generalization of the Kuramoto model which is a well-known mathematical description of self-organization in large populations of coupled oscillators. We present the method through several simulations and visualize each simulation as trajectories on unit spheres S2. In addition, we applied our method to the specific problem of object rotation interpolation.

The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group SO(3), which is known as the non-Abelian Kuramoto model. We have proposed a novel method for finding weighted and unweighted rotation average. In order to verify the correctness of our algorithms, we have compared the simulation results with geometric and projected average using real and random data sets. In particular, we have discovered that our method gives approximately the same results as geometric average.