Interactive Robot for Playing Russian Checkers

Human\u2013robot interaction in board games is a rapidly developing field of robotics. This paper presents a robot capable of playing Russian checkers designed for entertaining, training, and research purposes. Its control program is based on a novel unsupervised self-learning algorithm inspired by AlphaZero and represents the first successful attempt of using this approach in the checkers game. The main engineering challenge in mechanics is to develop a board state acquisition system non-sensitive to lighting conditions, which is achieved by rejecting computer vision and utilizing magnetic sensors instead. An original robot face is designed to endow the robot an ability to express its attributed emotional state. Testing the robot at open-air multiday exhibitions shows the robustness of the design to difficult exploitation conditions and the high interest of visitors to the robot

Rational Approximation Method for Stiff Initial Value Problems

While purely numerical methods for solving ordinary differential equations (ODE), e.g., Runge–Kutta methods, are easy to implement, solvers that utilize analytical derivations of the right-hand side of the ODE, such as the Taylor series method, outperform them in many cases. Nevertheless, the Taylor series method is not well-suited for stiff problems since it is explicit and not A-stable. In our paper, we present a numerical-analytical method based on the rational approximation of the ODE solution, which is naturally A- and A(α)-stable. We describe the rational approximation method and consider issues of order, stability, and adaptive step control. Finally, through examples, we prove the superior performance of the rational approximation method when solving highly stiff problems, comparing it with the Taylor series and Runge–Kutta methods of the same accuracy order

Integrate-and-Differentiate Approach to Nonlinear System Identification

In this paper, we consider a problem of parametric identification of a piece-wise linear mechanical system described by ordinary differential equations. We reconstruct the phase space of the investigated system from accelerometer data and perform parameter identification using iteratively reweighted least squares. Two key features of our study are as follows. First, we use a differentiated governing equation containing acceleration and velocity as the main independent variables instead of the conventional governing equation in velocity and position. Second, we modify the iteratively reweighted least squares method by including an auxiliary reclassification step into it. The application of this method allows us to improve the identification accuracy through the elimination of classification errors needed for parameter estimation of piece-wise linear differential equations. Simulation of the Duffing-like chaotic mechanical system and experimental study of an aluminum beam with asymmetric joint show that the proposed approach is more accurate than state-of-the-art solutions

Audio Encryption With Computational Chaotic System Error

This paper proposes a novel method of chaos-based encryption for audio. Our method outperformed the minimal requirement of speed for real time audio transfers while maintaining its high security features. The paper exploits finite errors derived from the computation of chaotic systems. The cipher is built on the lower bound error, which is computed by means of two interval extensions of a chaotic system. It was found that the method was effective, and required little computational power in order to be completed, proving to be faster and still reliable compared to other works

New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes

Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems

Adaptive Chaotic Maps in Cryptography Applications

Chaotic cryptography is a promising area for the safe and fast transmission, processing, and storage of data. However, many developed chaos-based cryptographic primitives do not meet the size and composition of the keyspace and computational complexity. Another common problem of such algorithms is dynamic degradation caused by computer simulation with finite data representation and rounding of results of arithmetic operations. The known approaches to solving these problems are not universal, and it is difficult to extend them to many chaotic systems. This chapter describes discrete maps with adaptive symmetry, making it possible to overcome several disadvantages of existing chaos-based cryptographic algorithms simultaneously. The property of adaptive symmetry allows stretching, compressing, and rotating the phase space of such maps without significantly changing the bifurcation properties. Therefore, the synthesis of one-way piecewise functions based on adaptive maps with different symmetry coefficients supposes flexible control of the keyspace size and avoidance of dynamic degradation due to the embedded technique of perturbing the chaotic trajectory

Improving chaos-based pseudo-random generators in finite-precision arithmetic

One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined by the chaotic orbits. In this study, we show that the results obtained using such an approach are very prone to rounding errors and discretization effects. Thus, it appears that the generated sequences are close to random even when parameters correspond to non-chaotic oscillations. In this study, we confirm that the actual source of pseudo-random properties of bits in a binary representation of numbers can not be chaos, but computer simulation. We propose a technique for determining the maximum number of bits that can be used as the output of a pseudo-random sequence generator including chaos-based algorithms. The considered approach involves evaluating the difference of the binary representation of two points obtained by different numerical methods of the same order of accuracy. Experimental results show that such estimation can significantly increase the performance of the existing chaos-based generators. The obtained results can be used to reconsider and improve chaos-based cryptographic algorithms

Improving Chaotic Image Encryption Using Maps with Small Lyapunov Exponents

Chaos-based encryption is one of the promising cryptography techniques that can be used. Although chaos-based encryption provides excellent security, the finite precision of number representation in computers affects decryption accuracy negatively. In this paper, a way to mitigate some problems regarding finite precision is analyzed. We show that the use of maps with small Lyapunov exponents can improve the performance of chaotic encryption scheme, making it suitable for image encryption

The choice between delta and shift operators for low-precision data representation

Low-precision data types for embedded applications reduce the power consumption and enhance the price-performance ratio. Inconsistence between the specified accuracy of a designed filter or controller and an imprecise data type can be overcome using the δ-operator, an alternative to the traditional discrete-time z-operator. Though in many cases it significantly increases accuracy, sometimes it shows no advantage over the shift operator. So the problem of choice between delta and shift operator arises. Therefore, a study on δ-operator applicability bounds is needed to solve this problem and provide δ-operator efficient practical use. In this paper we introduce a concept of the δ-operator applicability criterion. The discrete system implementation technique with discrete-time operator choice is given for the low-precision machine arithmetic

A reliable chaos-based cryptography using Galois field

Chaos-based image encryption schemes have been extensively employed over the past few years. Many issues such as the dynamical degradation of digital chaotic systems and information security have been explored, and plenty of successful solutions have also been proposed. However, the impact of finite precision in different hardware and software setups has received little attention. In this work, we have shown that the finite precision error may produce distinct cipher-images on different devices. In order to overcome this problem, we introduce an efficient cryptosystem, in which the chaotic logistic map and the Galois field theory are applied. Our approach passes in the ENT test suite and in several cyberattacks. It also presents an astonishing key space of up to 24096. Benchmark images have been effectively encrypted and decrypted using dissimilar digital devices