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We present a historical commentary together with an English translation of a mathematical-philosophical paper by the Czech differential geometer and later proponent of a geometrized unified field theory Vaclav Hlavatý (1894–1969). The paper was published in 1924 at the height of interpretational debates about recent advancements in differential geometry triggered by the advent of Einstein's general theory of relativity. In the paper he argued against a naive generalization of analogical reasoning valid for curves and surfaces in three-dimensional Euclidean space to the case of higher-dimensional curved Riemannian spaces. Instead, he claimed, the only secure ground to arrive at results is analytical calculation. We briefly discuss the biographical circumstances of the composition of the paper and characterize its publication venue the journal Ruch filosofický. We also give a discussion of the mathematical background for Hlavatý's argument.

In this paper, we study the existence and the numerical estimates of solutions for a specific types of fractional differential equations. The nonlinear part of the problem, however, presupposes certain hypotheses. Particularly, for exact localization of the parameter, the existence of a non-zero solution is established, which requires the sublinearity of the nonlinear part at the origin and infinity. We also take into consideration several theoretical and numerical examples. One of the main novelties of this paper is to use the variational method to investigate the properties of solutions of boundary values problems involving Atangana–Baleanu fractional derivative for the first time.

The aim of this paper is to present some results concerning the problem of minimal projections and extensions. Let X be a reflexive Banach space and let Y be a closed subspace of X of codimension one. Let W be a finite-dimensional Banach space. We present a new sufficient condition under which any minimal extension of an operator A ∈ L ( Y , W ) is strongly unique. In this paper we show (in some circumstances) that if 1 λ ( Y , X ) , then a minimal projection from X onto Y is a strongly unique minimal projection. Moreover, we introduce and study a new geometric property of normed spaces. In this paper we also present a result concerning the strong unicity of best approximation.

Though the boundary layer formation in the chemotactic process has been observed in experiment (cf. [63] ), the mathematical study on the boundary layer solutions of chemotaxis models is just in its infant stage. Apart from the sophisticated theoretical tools involved in the analysis, how to impose/derive physical boundary conditions is a state-of-the-art in studying the boundary layer problem of chemotaxis models. This paper will proceed with a previous work [24] in one dimension to establish the convergence of boundary layer solutions of the Keller–Segel model with singular sensitivity in a two-dimensional space (half-plane) with respect to the chemical diffusion rate denoted by e ≥ 0 . Compared to the one-dimensional boundary layer problem, there are many new issues arising from multi-dimensions such as possible Prandtl type degeneracy, curl-free preservation and well-posedness of large-data solutions. In this paper, we shall derive appropriate physical boundary conditions and gradually overcome these barriers and hence establish the convergence of boundary layer solutions of the singular Keller–Segel system in the half-plane as the chemical diffusion rate vanishes. Specially speaking, we justify that the boundary layer converges to the outer layer (solution with e = 0 ) plus the inner layer as e → 0 , where both outer and inner layer profiles are precisely derived and well understood. By doing this, the structure of boundary layer solutions is clearly characterized. We hope that our results and methods can shed lights on the understanding of underlying mechanisms of the boundary layer patterns observed in the experiment for chemotaxis such as the work by Tuval et al. [63] , and open a new window in the future theoretical study of chemotaxis models.

The complexities of nature have pushed humankind to construct complex mathematical formula that can be used to capture such natural occurrence. Very recently the concept differential and integral operators with fractional order and fractal dimension were introduced. The concept has opened new doors for investigations. In this paper, we present a step forward, where the constant fractal dimension is replaced by variable dimension. We present in detail some properties of this new operators, we suggested a new numerical approach that can be used to solve differential and integral equations associate to this operators. We presented some examples and simulations are presented to underpin the strength of the new operators. We strongly believe that this paper will open many new doors of investigation toward modeling real world problems.

In this paper, we firstly extend the Fourier neural operator (FNO) to discovery the soliton mapping between two function spaces, where one is the fractional-order index space $\{\epsilon|\epsilon\in (0, 1)\}$ in the fractional integrable nonlinear wave equations while another denotes the solitonic solution function space. To be specific, the fractional nonlinear Schr\"{o}dinger (fNLS), fractional Korteweg-de Vries (fKdV), fractional modified Korteweg-de Vries (fmKdV) and fractional sine-Gordon (fsineG) equations proposed recently are studied in this paper. We present the train and evaluate progress by recording the train and test loss. To illustrate the accuracies, the data-driven solitons are also compared to the exact solutions. Moreover, we consider the influences of several critical factors (e.g., activation functions containing Relu$(x)$, Sigmoid$(x)$, Swish$(x)$ and $x\tanh(x)$, depths of fully connected layer) on the performance of the FNO algorithm. We also use a new activation function, namely, $x\tanh(x)$, which is not used in the field of deep learning. The results obtained in this paper may be useful to further understand the neural networks in the fractional integrable nonlinear wave systems and the mappings between two spaces., Comment: 17 pages, 20 figures

Let $R$ be the homogeneous coordinate ring of the Grassmannian $\mathbb{G}=Gr(2,n)$ defined over an algebraically closed field $k$ of characteristic $p \geq \max\{n-2,3\}$. In this paper we give a description of the decomposition of $R$, considered as graded $R^{p^r}$-module, for $r \geq 2$. This is a companion paper to our earlier paper, where the case $r=1$ was treated, and taken together, our results imply that $R$ has finite F-representation type (FFRT). Though it is expected that all rings of invariants for reductive groups have FFRT, ours is the first non-trivial example of such a ring for a group which is not linearly reductive. As a corollary, we show that the ring of differential operators $D_k(R)$ is simple, that $\mathbb{G}$ has global finite F-representation type (GFFRT) and that $R$ provides a noncommutative resolution for $R^{p^r}$., Comment: 52 pages

In this paper, we improve the algorithms of Lauder-Wan \cite{LW} and Harvey \cite{Ha} to compute the zeta function of a system of $m$ polynomial equations in $n$ variables over the finite field $\FF_q$ of $q$ elements, for $m$ large. The dependence on $m$ in the original algorithms was exponential in $m$. Our main result is a reduction of the exponential dependence on $m$ to a polynomial dependence on $m$. As an application, we speed up a doubly exponential time algorithm from a software verification paper \cite{BJK} (on universal equivalence of programs over finite fields) to singly exponential time. One key new ingredient is an effective version of the classical Kronecker theorem which (set-theoretically) reduces the number of defining equations for a "large" polynomial system over $\FF_q$ when $q$ is suitably large.

Customization of manipulator configurations using modularity and reconfigurability aspects is receiving much attention. Modules presented so far in literature deals with the conventional and standard configurations. This paper presents the 3D printable, light-weight and unconventional modules: MOIRs' Mark-2, to develop any custom `n'-Degrees-of-Freedom (DoF) serial manipulator even with the non-parallel and non-perpendicular jointed configuration. These unconventional designs of modular configurations seek an easy adaptable solution for both modular assembly and software interfaces for automatic modeling and control. A strategy of assembling the modules, automatic and unified modeling of the modular and reconfigurable manipulators with unconventional parameters is proposed in this paper using the proposed 4 modular units. A reconfigurable software architecture is presented for the automatic generation of kinematic and dynamic models and configuration files, through which, a designer can design, validate using visualization, plan and execute the motion of the developed configuration as required. The framework developed is based upon an open source platform called as Robot Operating System (ROS), which acts as a digital twin for the modular configurations. For the experimental demonstration, a 3D printed modular library is developed and an unconventional configuration is assembled, using the proposed modules followed by automatic modeling and control, for a single cell of the vertical farm setup.

Different authors have addressed a number of problems in the area of distributed control proposing convincing solutions to specific problems such as static coverage, dynamic coverage/exploration, rendezvous, flocking, formation control. However, a major limitation of problem-specific approaches is a fundamental lack of flexibility when the group meets unexpected conditions and has to change its goal on the fly. In this paper, we show that a large class of distributed control problems can be cast into a general framework based on the adoption of the Lloyd methodology. The adoption of a unified framework enables efficient solutions for the specific problems guaranteeing at the same time important safety and functional properties and a large degree of flexibility in the execution of group tasks. The paper sets the theoretical basis for this development and proves the efficacy of the proposed solutions through extensive simulations and experimental results.

This paper proposes a novel nature-inspired method, so-called ripple-spreading algorithm (RSA) for multi-objective path optimization problem (MOPOP). Unlike most existing methods mainly capable of finding partial or approximated Pareto front, this paper focuses on calculating the complete Pareto front. This is achieved by taking advantage of the optimality principle in natural ripple-spreading phenomenon. Basically, the proposed RSA carries out a one-off ripple relay race in the route network, and then the complete Pareto front will be identified with guaranteed optimality by backtracking those Pareto non-dominated ripples (PNDRs) which reached the destination node. Theoretical analyses and comprehensive experiments show that all complete Pareto fronts of a one-to-all MOPOP can also be found in just a single run of ripple relay race, and the reported method can be further extended to calculate all Pareto optimal paths in dynamical networks, which have rarely been touched by existing MOPOP methods. Since many real-world application problems can be converted into MOPOP, the reported method has a great potential of applications.

This paper continues the program initiated in the works by the authors [60], [61] and [62] and by the authors with Li [51] and [52] to establish higher order Poincar\'e-Sobolev, Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on real hyperbolic spaces using the method of Helgason-Fourier analysis on the hyperbolic spaces. The aim of this paper is to establish such inequalities on the Siegel domains and complex hyperbolic spaces. Firstly, we prove a factorization theorem for the operators on the complex hyperbolic space which is closely related to Geller' operator, as well as the CR invariant differential operators on the Heisenberg group and CR sphere. Secondly, by using, among other things, the Kunze-Stein phenomenon on a closed linear group $SU(1,n)$ and Helgason-Fourier analysis techniques on the complex hyperbolic spaces, we establish the Poincar\'e-Sobolev, Hardy-Sobolev-Maz'ya inequality on the Siegel domain $\mathcal{U}^{n}$ and the unit ball $\mathbb{B}_{\mathbb{C}}^{n}$. Finally, we establish the sharp Hardy-Adams inequalities and sharp Adams type inequalities on Sobolev spaces of any positive fractional order on the complex hyperbolic spaces. The factorization theorem we proved is of its independent interest in the Heisenberg group and CR sphere and CR invariant differential operators therein., Comment: 51 pages

Behavior Trees (BTs) were invented as a tool to enable modular AI in computer games, but have received an increasing amount of attention in the robotics community in the last decade. With rising demands on agent AI complexity, game programmers found that the Finite State Machines (FSM) that they used scaled poorly and were difficult to extend, adapt and reuse. In BTs, the state transition logic is not dispersed across the individual states, but organized in a hierarchical tree structure, with the states as leaves. This has a significant effect on modularity, which in turn simplifies both synthesis and analysis by humans and algorithms alike. These advantages are needed not only in game AI design, but also in robotics, as is evident from the research being done. In this paper we present a comprehensive survey of the topic of BTs in Artificial Intelligence and Robotic applications. The existing literature is described and categorized based on methods, application areas and contributions, and the paper is concluded with a list of open research challenges.

Goulden, Jackson and Vakil observed a polynomial structure underlying one-part double Hurwitz numbers, which enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification profile over $\infty$, a unique preimage over 0, and simple branching elsewhere. This led them to conjecture the existence of moduli spaces and tautological classes whose intersection theory produces an analogue of the celebrated ELSV formula for single Hurwitz numbers. In this paper, we present three formulas that express one-part double Hurwitz numbers as intersection numbers on certain moduli spaces. The first involves Hodge classes on moduli spaces of stable maps to classifying spaces; the second involves Chiodo classes on moduli spaces of spin curves; and the third involves tautological classes on moduli spaces of stable curves. We proceed to discuss the merits of these formulas against a list of desired properties enunciated by Goulden, Jackson and Vakil. Our formulas lead to non-trivial relations between tautological intersection numbers on moduli spaces of stable curves and hints at further structure underlying Chiodo classes. The paper concludes with generalisations of our results to the context of spin Hurwitz numbers., Comment: 20 pages. Some corollaries are added in the second version, and software numerical checks are performed

Highlights • A compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention policies. • Short-term projection results have been illustrated for Bangladesh and India. • All necessary graphical simulations have been performed with the help of Caputo-Fabrizio fractional derivatives. • Optimal control problem for fractional system has been designed and the existence of unique solution has also been showed by using Picard-Lindelof technique., When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention strategies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Bangladesh and India. Control reproduction numbers (Rc) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. Nevertheless, as the pandemic is not over in any country, it is highly recommended to use efficacious face coverings and maintain strict physical distancing in public gatherings. All necessary graphical simulations have been performed with the help of Caputo-Fabrizio fractional derivatives. In addition, optimal control strategies for fractional system have been designed and the existence of unique solution has also been showed using Picard-Lindelof technique. Finally, unconditional stability of the fractional numerical technique has been proved.

This paper presents semantic-based methods for the understanding of human movements in robotic applications. To understand human movements, robots need to first, recognize the observed or demonstrated human activities, and secondly, learn different parameters to execute an action or robot behavior. In order to achieve that, several challenges need to be addressed such as the automatic segmentation of human activities, identification of important features of actions, determine the correct sequencing between activities, and obtain the correct mapping between the continuous data and the symbolic and semantic interpretations of the human movements. This paper aims to present state-of-the-art semantic-based approaches, especially the new emerging approaches that tackle the challenges of finding generic and compact semantic models for the robotics domain. Finally, we will highlight potential breakthroughs and challenges for the next years such as achieving scalability, better generalization, compact and flexible models, and higher system accuracy.

In this paper, we discuss the omni-directional gait of a passive-spine hexapod robot, which consists of three body segments connected by passive body joints. To design the turning and rotating gaits for this robot, firstly, we analyze a geometric model to demonstrate how segment rotation can result from abduction of the legs. Next, we obtain the principle of the rotation and direction of the body segments, which are analyzed by determining the geometric features of different configurations. The turning and rotating gaits are then attained by varying only the duration of the transition sequence of the passive-spine hexapod robot. The capability of sideways motion is also given in this paper. Finally, this proposed method for designing the omni-directional gait of a passive-spine hexapod is demonstrated by simulations and experiments.

Chatter between devices becomes a primary concern in actual engineering problems since it may cause the reduction of efficiency. Due to random factors and non-smooth properties, difficulties rest in deriving the analytical results and such systems are generally investigated with simplified approximate methods. In this context, the present paper pioneers the response analysis of three-dimensional hydraulic relief valve impact systems under stochastic excitations. In order to retain the non-smooth characteristics of the systems under consideration, no non-smooth transformation is imposed on the original system. A procedure in which the stochastic trajectories start from the contact surface and return to the contact surface for the next time is constructed. Probability density functions (PDFs) of the random trajectories returning to the contact surface at any time can be obtained, and the proposed procedure is proved accurate and efficient using Monte Carlo (MC) simulations in this paper. Moreover, we find that the flow rate of the systems can lead to the stochastic P-bifurcation on the contact surface. Further discussion indicates that the proposed procedure can substantially reflect the complicated dynamic behaviors of the high-dimensional vibro-impact systems.

This paper assesses some of the key legal and regulatory questions arising from the integration of physical robotic systems with cloud-based services, also called “cloud robotics.” The literature on legal and ethical issues in robotics has a strong focus on the robot itself, but largely ignores the background information processing. Conversely, the literature on cloud computing rarely addresses human–machine interactions, which raise distinctive ethical and legal concerns. In this paper, we investigate, from a European legal and regulatory perspective, the growing interdependence and interactions of tangible and virtual elements in cloud robotics environments. We highlight specific problems and challenges in regulating such complex and dynamic ecosystems and explore potential solutions. To illustrate practical challenges, we consider several examples of cloud robotics ecosystems involving multiple parties, various physical devices, and various cloud services. These examples illuminate the complexity of interactions between relevant parties. By identifying pressing legal and regulatory issues in relation to cloud robotics, we hope to inform the policy debate and set the scene for further research.

Stefan Kempisty był polskim matematykiem zajmujacym sie funkcjami zmiennej rzeczywistej, teoria mnogosci, całkami, funkcjami przedziału i teoria pola powierzchni. W 1919 roku obronił prace doktorska ,,O funkcjach nawpołciagłych" na Uniwersytecie Jagiellonskim w Krakowie, a promotorem był Kazimierz Zorawski. W grudniu 1924 roku habilitował sie na Uniwersytecie Warszawskim i w latach 1920--1939 pracował na Uniwersytecie Stefana Batorego w Wilnie. Opublikował ponad czterdziesci prac naukowych i trzy podreczniki z analizy rzeczywistej oraz jedna monografie. Reprezentował w swoich pracach i na seminariach szkołe warszawska. Nazwisko Kempistego w matematyce pojawia sie w zwiazku z definicja funkcji quasi-ciagłej, roznymi ciagłosciami funkcji wielu zmiennych, klasyfikacja funkcji Baire'a, Younga i Sierpinskiego, funkcjami przedziału oraz całkami Denjoy'a i Burkilla. Zainteresowalismy sie Kempistym ze wzgledu na jego dorobek naukowy, pewne niewyjasnione informacje osobiste oraz 125 rocznice urodzin przypadajaca w 2017 roku. Przedstawiamy wiec jego biografie, udział w konferencjach, sylwetki zony Eugenii i corki Marii oraz jego dorobek naukowy. Wszystkie informacje o nim pochodza z wielu zrodeł. Stefan Jan Kempisty was a Polish mathematician, working in the theory of real functions, set theory, integrals, interval functions and the thory of surface area. In 1919 he defended his Ph.D. thesis ``On semi-continuous functions" at the Jagiellonian University in Krakow under supervision of Kazimierz Zorawski. In December 1924 he did habilitation at the Warsaw University and from 1920 to 1939 he worked at the Stefan Batory University in Vilnius. He published over forty scientific papers, three textbooks and one monograph. He represented in his papers and on seminars the Warsaw school. Kempist's name in mathematics appears in connection with the definition of quasi-continuous functions, different kind of continuity of functions of several variables, the classification of Baire, Young and Sierpinski functions, interval functions and Denjoy and Burkill integrals. We took interest in Kempisty because of his academic achievements, some unexplained personal information, and his 125th birthday in 2017. So we present his biography, participation in conferences, the silhouette his wife Eugenia and daughter Maria, and his scientific achievements. All information about it comes from several sources. Validerad;2018;Nivå 1;2018-04-17 (andbra)

Harmony Search (HS) is a metaheuristic optimisation algorithm inspired by musical improvisation. So far it has been applied to various optimisation problems, and there are several application-oriented review papers. However, this review paper tries to focus on the historical development of algorithm structure instead of applications. This paper explains the original HS algorithm along with a selection of modified and hybrid HS methods: adaption of original operators of the basic harmony search, parameter adaption, hybrid methods, handling multi-objective optimisation problems and constraint handling.

With the rapid development of cloud manufacturing (CMfg) technology in Industrial Internet based on the concept of manufacturing as a service, how to effectively and quickly implement manufacturer scheduling in a cloud manufacturing environment has aroused widespread attention of researchers. Manufacturers in the cloud manufacturing environment are virtualized and digitized, and then aggregated in the form of cloud data. As a direct provider of cloud manufacturing services, manufacturers shift the service mode from the traditional decentral type to a centralized type. However, in practice, manufacturers can't respond promptly to the needs of customer. The scheduling of manufacturers will directly affect the quality of cloud manufacturing services. This paper research the problem of manufacturer scheduling in the cloud manufacturing environment and analyzes the factors that affect the manufacturer resource scheduling in five categories including task load degree, task reliability, manufacturing efficiency, manufacturing resource richness and Internet of Things (IoT) match degree. At the same time, we establishes the scheduling index and the objective function model. The Chaos Optimization Algorithm (COA) is used to solve the objective function and achieve scheduling of manufacturers under different scheduling tasks. The simulation results show that the proposed scheduling index is comprehensive and effective. Based on the math model of manufacturer scheduling, all the factors that influence the manufacturer scheduling in the cloud manufacturing environment can be merged together, and the complicated scheduling problem also can be transformed into the mathematical problem to solve. In this paper, the manufacturer scheduling algorithm based on Chaos Theory can finish the scheduling of manufacturers under various tasks and make the cloud manufacturing platform provide manufacturing services to users in time.

The production planning and control of aircraft remanufacturing system is becoming a critical issue with the development and application of reusable aircraft parts. With the unpredictable demands of remanufactured products, the aircraft parts remanufacturing system (APRS) operates with various disruptions, which could seriously influence the system's efficiency. To generate timely and efficient response towards the frequent disruptions in APRS, an adaptive rescheduling policy is presented in this paper with a trigger and a re-scheduler. The trigger evaluates the system performance loss caused by the disruptions with a specific Relative Performance Deviation Index (RPDI) and determines when the re-scheduler is activated to re-optimize the schedule. The re-scheduler then intelligently selects the optimal rescheduling method by an improved random forest (IRF) based on the system status described by a set of reduced but important features. In order to deal with the data imbalance in different classes in the remanufacturing system, this paper develops a problem-oriented conditional generative adversarial networks (CGAN) for data augmentation. Aiming to demonstrate the effectiveness of the proposed method, an experiment is conducted with three commonly used classification approaches. And, the results show the competitiveness of the proposed approach in reducing the rescheduling trigger times and the rescheduling performance improvement.

This paper proposes a novel scalable multimodal multiobjective test problem suite. The proposed test problems have various properties, such as presence of local Pareto optimal set (PS), scalable number of PSs, nonuniformly distributed PSs, discrete Pareto front (PF), and scalable number of variables and objectives. All of the test problems proposed in this paper are continuous optimization problems. Therefore, they can be used to measure different capacities of multimodal multiobjective continuous optimization algorithms. Moreover, a landscape visualization method for multiobjective problems is proposed to show the properties of the multimodal multiobjective test problems. Based on the landscapes, the characteristics of these problems are analyzed and characterized. Furthermore, the existing multimodal multiobjective optimization algorithms and several popular multiobjective algorithms are tested and compared with the novel test problem suite. Then, a discussion on the desired properties of multimodal multiobjective optimization algorithms and future works on multimodal multiobjective optimization are presented.

Whale Optimization Algorithm (WOA) is an optimization algorithm developed by Mirjalili and Lewis in 2016. An overview of WOA is described in this paper, rooted from the bubble-net hunting strategy, besides an overview of WOA applications that are used to solve optimization problems in various categories. The best solution has been determined to make something as functional and effective as possible through the optimization process by minimizing or maximizing the parameters involved in the problems. Research and engineering attention have been paid to Meta-heuristics for purposes of decision-making given the growing complexity of models and the needs for quick decision making in the engineering. An updated review of research of WOA is provided in this paper for hybridization, improved, and variants. The categories included in the reviews are Engineering, Clustering, Classification, Robot Path, Image Processing, Networks, Task Scheduling, and other engineering applications. According to the reviewed literature, WOA is mostly used in the engineering area to solve optimization problems. Providing an overview and summarizing the review of WOA applications are the aims of this paper.

Our main purpose in this paper is to establish the existence and nonexistence of extremal functions (also known as maximizers) and symmetry of extremals for several Trudinger-Moser type inequalities on the entire space R n , including both the critical and subcritical Trudinger-Moser inequalities (see Theorems 1.1, 1.2, 1.3, 1.4, 1.5). Most of earlier works on existence of maximizers in the literature rely on the complicated blow-up analysis of PDEs for the associated Euler-Lagrange equations of the corresponding Moser functionals. The new approaches developed in this paper are using the identities and relationship between the supremums of the subcritical Trudinger-Moser inequalities and the critical ones established by the same authors in [25] , combining with the continuity of the supremum function that is observed for the first time in the literature. These allow us to establish the existence and nonexistence of the maximizers for the Trudinger-Moser inequalities in different ranges of the parameters (including those inequalities with the exact growth). This method is considerably simpler and also allows us to study the symmetry problem of the extremal functions and prove that the extremal functions for the subcritical singular Truddinger-Moser inequalities are symmetric. Moreover, we will be able to calculate the exact values of the supremums of the Trudinger-Moser type in certain cases. These appear to be the first results in this direction.

A crucial requirement for imparting autonomy to the fish-inspired robots is the trajectory planning capability that can generate obstacle-free and optimal trajectories to a commanded goal location. Research in the area of dynamics-aware trajectory planning, especially in the presence of environmental disturbances, for fish-inspired robots is scarce. Trajectory-following for fish-inspired robots, which is different from trajectory planning, has been well explored wherein feedback controllers that reject disturbances are employed to follow the pre-specified waypoints. This paper reports an optimal trajectory planning approach for Anguilliform-inspired robots based on model predictive planning framework. The robot’s dynamics constraints, as well as its interaction with the surrounding flow conditions, are captured via dynamics simulations and are expressed using discretized motion primitives. The motion primitives are then used for generating a search-tree and an A*-based algorithm is used for searching the optimal trajectory. We developed a simulation-based admissible heuristic function that is used for improving the computational performance of the developed trajectory planner. The developed simulation-based heuristic function provided a computational speed-up by a factor of up to 10.3 with respect to that of the Euclidean heuristic for test cases comprising of a variety of obstacle densities, ambient flow conditions, and goal locations. The trajectories generated by the developed approach have been found to be dynamically feasible, collision-free, and optimal for the experiments reported in this paper. We believe that the developed approach can impart autonomy to the Anguilliform-inspired robots that, due to their slender and hyper-redundant structures, can perform autonomous inspection and maintenance of sub-sea structures having narrow regions, obstacles, and ambient flow and can be useful in various civil and defense applications.

This paper investigates a hypothesis that in case of hard optimization problems, selection of the proper search space is more relevant than the choice of the solving algorithm. Dynamic Vehicle Routing Problem is used as a test problem and the hypothesis is verified experimentally on the well-known set of benchmark instances. The paper compares Particle Swarm Optimization (PSO) and Differential Evolution (DE) operating in two continuous search spaces (giving in total four distinctive approaches) and a state-of-the art discrete encoding utilizing Genetic Algorithm (GA). The advantage of selected continuous search space over a discrete one is verified on the basis of quality of the final solution and stability of intermediate partial solutions. During stability analysis it has been observed that practical level of uncertainty, resulting from the dynamic nature of the problem, is lower than could be expected from a popular degree of dynamism measure. In order to challenge that issue, benchmark problems have been solved also with a higher level of dynamism and an empirical degree of dynamism has been proposed as an additional measure of the amount of uncertainty of the problem. The results obtained by both continuous algorithms outperform those of state-of-the-art algorithms utilizing discrete problem representation, while the performance differences between them (PSO and DE) are minute. Apart from higher numerical efficiency in solving DVRP, the use of continuous problem encoding proved its advantage over discrete encoding also in terms of intermediate solutions stability. Requests-to-vehicles assignment sequences generated by the proposed approach were approximately 40% more accurate with respect to the final solution than their counterparts generated with a discrete encoding. Analysis of these sequences of intermediate solutions for several benchmark sets resulted in designing a penalty term taking into account a specific dynamic nature of the optimized problem. An addition of this penalty term improved the above-mentioned stability of partial solutions by another 10%.

One of the main current applications of Intelligent Systems are Recommender systems (RS). RS can help users to find relevant items in huge information spaces in a personalized way. Several techniques have been investigated for the development of RS. One of them are Swarm Intelligence (SI) techniques, which are an emerging trend with various application areas. Although the interest in using Computational Intelligence in web personalization and information retrieval fostered the publication of some survey papers, these surveys so far focused on different application domains, e.g., clustering, or were too broadly focused and incorporated only a handful of SI approaches. This study provides a comprehensive review of 77 research publications applying SI in RS. The study focus on five aspects we consider relevant for such: the recommendation technique used, the datasets and the evaluation methods adopted in their experimental parts, the baselines employed in the experimental comparison of proposed approaches and the reproducibility of the reported results. At the end of this review, we discuss negative and positive aspects of these papers, as well as point out opportunities, challenges and possible future research directions. To the best of our knowledge, this survey is the most comprehensive review of approaches using SI in RS. Therefore, we believe this review will be a relevant material for researchers interested in either of the domains.

Due to high degrees-of-freedom of humanoids and induced redundancy, there are multiple ways of performing a given manipulation task. Finding optimal ways of performing tasks is one desirable property of any motion planning framework. This includes optimizing both the path with respect to a certain objective function and also the final pre-grasp or goal position. Additionally, a variety of constraints need to be satisfied such as stability, self-collision and collision with objects in the environment and also kinematic loop-closure formed during the task. In this paper, an asymptotically optimal sampling based approach for generating motion plans is presented. A novel constraint solver extension to the bidirectional Fast Marching Trees (BFMT*) algorithm in the form of a way-point generator is proposed such that it can be applied for whole-body motion planning of humanoids. Moreover, a comparison of the performance of the proposed extension of BFMT* and the state-of-art RRT* based motion planner is shown. A gradient based inverse kinematics solver has also been implemented in combination with an optimization technique to generate goal configurations in order to ensure optimality in the pre-grasp position. The efficacy of the proposed approach is evaluated in a simulation environment on Hubo+ robot model. The results show a significant improvement in path costs, as well as overall optimality of given tasks for the proposed approach. Additionally, rigorous analysis over the choice of planning algorithms considered in this paper is present for the considered scenarios.

In this paper, we study the impact of geodesic vector fields (vector fields whose trajectories are geodesics) on the geometry of a Riemannian manifold. Since, Killing vector fields of constant lengths on a Riemannian manifold are geodesic vector fields, leads to the question of finding sufficient conditions for a geodesic vector field to be Killing. In this paper, we show that a lower bound on the Ricci curvature of the Riemannian manifold in the direction of geodesic vector field gives a sufficient condition for the geodesic vector field to be Killing. Also, we use a geodesic vector field on a 3-dimensional complete simply connected Riemannian manifold to find sufficient conditions to be isometric to a 3-sphere. We find a characterization of an Einstein manifold using a Killing vector field. Finally, it has been observed that a major source of geodesic vector fields is provided by solutions of Eikonal equations on a Riemannian manifold and we obtain a characterization of the Euclidean space using an Eikonal equation.

The sphere-pipe intersecting curve is a kind of spatial complex curve, which is controlled by robot in the sphere-pipe welding. In this paper, a discrete method for robot welding by offline programming is put forward. To move the robot with the specified curve trajectory, it need to be discretized to generate the robot motion instructions. As the core innovation of this paper, a discrete method of sphere-pipe intersecting curve is given according to the chord error limit and principle of equal arc length, which guarantees the accuracy of robot welding. To achieve this goal, this paper has done the following related works. First, the geometrical model of the sphere-pipe intersection is established, which can cover most of the intersection modes. Second, this paper gives the parameter equations in two different coordinate systems because the expression is very complex. This operation will simplify the subsequent calculations. Although the curve expression is simplified, it is very complicated to find the maximum based on the definition of curvature. After experimental analysis, this paper presents a simple and effective algorithm for the calculation of maximum curvature. Finally, this paper takes the Puma560 robot for simulation, and the simulation results are used to verify the feasibility and effectiveness of our method.

Accurate, time-effective calibration and decoupling procedures of multi-axis Force/Moment (F/M) sensors are critical to the implementation of these sensors. Recently, many decoupling methods have been proposed by researchers, but the inherent coupling relationship among components of multi-axis F/M sensors has not been taken into account. In this paper, we thus proposed a novel Sparse Voltage Maximum Inter-class Variance (SVMIV) algorithm, which took advantage of the inherent relationship nature. Furthermore, a novel nonlinear decoupling method based on the Parallel Voltage-Extreme Learning Machine (PV-ELM) was also presented. To demonstrate the utility of the proposed approach, extensive comparisons were made between the proposed PV-ELM decoupling method and several conventional decoupling approaches such as Least Square (LS), Support Vector Regression (SVR), Back Propagation Neural Network (BPNN), and Extreme Learning Machine (ELM). Results of real decoupling experiments demonstrated that the proposed the PV-ELM decoupling algorithm outperforms linear decoupling algorithms for six-axis F/M sensors. In addition, it was also proved that the PV-ELM decoupling method can decouple the outputs of six-axis F/M sensors with higher precision, faster speed, improved robustness, and faster convergence than the state-of-the-art nonlinear decoupling algorithms such as SVR, BP and ELM. Overall, this paper proposed a novel way to deal with the inherent coupling relationship of six-axis F/M sensors, and the experimental results demonstrated that the maximum I-type and II-type errors were below 0.356% and 0.270%, respectively, of full scale in all measured variables.

Transforming the manufacturing environment from manually operated production units to unsupervised robotic machining centres requires a presence of reliable in-process monitoring system. In this paper, we demonstrate a technique for automatic endpoint detection of weld seam removal in a robotic abrasive belt grinding process with the help of a vision system using deep learning. The paper presents the results of the first investigative stage of semantic segmentation of weld seam removal states using encoder-decoder convolutional neural networks (EDCNN). An experimental investigation using four different weld seam states on mild steel work coupon are trained using the VGG-16 network based on encoder-decoder architecture. The results demonstrate the potential of the developed vision based methodology as a tool for endpoint prediction of the weld seam removal in real time during a compliant abrasive belt grinding process. The prediction system based on semantic segmentation is able to monitor weld profile geometry evolution taking into account the varying belt grinding parameters during machining which will allow further process optimisation. National Research Foundation (NRF) This work was conducted within the Rolls-Royce@NTU Corporate Lab with support from the National Research Foundation (NRF) (Grant No. M-RT1.1 M4061298) Singapore under the Corp Lab@University Scheme.

In this paper, we propose a multi-agent based art production framework. In existing artwork creation systems, images were generated using artificial life and evolutionary computation approaches. In artificial life, swarm intelligence or Boids model, and in evolutionary computation, genetic algorithm or genetic programming are commonly used to create images. These automated artwork creation systems make it easy to create artistic images even if the users are not professional artists. Despite the high possibility of these creation systems, however, much research has not been done so far. In this paper, we propose an art production framework that generates images using multi-agents with chaotic dynamics features. Agents act on the canvas following the three rules of Boids model. In addition, each agent possesses a chaotic neural network which trained by differential evolution algorithm, so that colors can be evolved to represent a better style. As a result, we propose an art production framework for generating processing artworks that contain highly complex dynamics. Finally, we created the glitch artworks using the proposed framework, which shows a new glitch style.

This paper proposes a universal control strategy and novel haptic interface for the International Thermonuclear Experimental Reactor (ITER) welding/machining robot. The developed method implements a reliable position control and sense between the human and the robot as well as between the robot and the task environment in which provides highly accurate position control based on joystick inputs with real-time haptic capabilities. The proposed control structure has the characteristics of a universal technique independent of the actual control algorithm and it can be applied with other suitable control methods as a real-time control strategy. One of the contributions of this paper is that the proposed control method combines a directed random search method and real-time simulation to develop an intelligent controller in which each generation of parameters is tested on-line by the real-time simulator before being applied to the real process. The controller was evaluated on a hydraulic position servo system where the simulator of the hydraulic system was built based on Markov chain Monte Carlo (MCMC) method. A Particle Swarm Optimization (PSO) algorithm combined with the foraging behavior of E. coli bacteria was utilized as the directed random search engine. PSO is influenced by the simulation of social behavior in which each individual agent of the possible solution population, benefits from its history and its interactions with other agents within the population. This sharing of knowledge helps facilitate faster convergence to an optimal solution. From the other side, the effect of Bacterial Foraging Optimization (BFO) of E. coli is that the agent is making a decision to which position to move. The agent does this with attention to the previous data stored in the memory as the best past position. These selection behaviors of particles help to avoid poor foraging and improve foraging strategies. In conclusion, the proposed control and haptic strategy allows the operator to be kinetically plugged into the work environment and simultaneously provides force feedback sense with high controllability without neglecting the system dynamics. Post-print / Final draft

Diaconis and Griffiths (2014) study the multivariate Krawtchouk polynomials orthogonal on the multinomial distribution. In this paper we derive the reproducing kernel orthogonal polynomials Q n ( x , y ; N , p ) on the multinomial distribution which are sums of products of orthonormal polynomials in x and y of fixed total degree n = 0 , 1 , … , N . The Poisson kernel ∑ n = 0 N ρ n Q n ( x , y ; N , p ) arises naturally from a probabilistic argument. An application to a multinomial goodness of fit test is developed, where the chi-squared test statistic is decomposed into orthogonal components which test the order of fit. A new duplication formula for the reproducing kernel polynomials in terms of the 1-dimensional Krawtchouk polynomials is derived. The duplication formula allows a Lancaster characterization of all reversible Markov chains with a multinomial stationary distribution whose eigenvectors are multivariate Krawtchouk polynomials and where eigenvalues are repeated within the same total degree. The χ 2 cutoff time, and total variation cutoff time is investigated in such chains. Emphasis throughout the paper is on a probabilistic understanding of the polynomials and their applications, particularly to Markov chains.

This paper describes the design of a regional observer-based controller for the locally Lipchitz nonlinear systems, which can be employed successfully to attain both monitoring and control of a wide range of systems. An observer-based control approach has been employed to attain advantages of the traditional state feedback along with the state estimation through an observer. A lot of work has been accomplished for the globally Lipchitz nonlinear systems. However, a less conservative continuity, called the generalized ellipsoidal Lipchitz condition, has been applied in this paper to consider the locally Lipchitz systems. This condition is then incorporated to attain convex routines for computing the local controller and observer gains. The focus of the present study is to investigate conditions for simultaneous design of observer and controller under locally Lipchitz nonlinearities for systems with norm-bounded disturbances that not only guarantees the stabilization and true state estimation but also robustness against external perturbations. Furthermore, the decoupling of the observer and controller design conditions has been worked out for obtainment of a simple design method. Since the resultant control approach applies to a general class of systems, it can be straightforwardly employed to the globally Lipschitz nonlinear systems as a specific case. The approach is tested via a chaotic system and simulation results are provided to validate the effectiveness of resultant control schemes for the locally Lipschitz systems.

It makes great economic losses and bad social influence for our country about some accidental drinking water contamination and vicious attacks to water distribution networks. In terms of solving the problems of drinking water contamination caused by accidental contaminant event in water supply network, used the techniques just like sensor network which could determinate the source location to isolate the contaminated area and minimized its hazards. Previous studies have shown that the contamination source determination problem model can be utilized to convert the contamination source determination problem to an unimodal function optimization problem. However, we notice that it is a multimodal function optimization problem in essence and the number of its solution has non-uniqueness feature. In this paper, we first modified the problem model with formulate the threshold value based on the previous works and proposed the niching genetic algorithm calculate multiple contamination sources, and provide the possibility for screening the true contamination source. Furthermore, this paper applies different distribution networks verify the validity after the threshold formulation as well as the effectiveness of algorithm from various aspects.

Research findings have shown that evolution equations containing non-integer order derivatives can lead to some useful dynamical systems which can be used to describe important physical scenarios. This paper deals with numerical simulations of multicomponent symbiosis systems, such as the parasitic predator-prey model, the commensalism system, and the mutualism case. In such models, we replace the classical time derivative with either the Caputo fractional derivative or the Atangana-Baleanu fractional derivative in the sense of Caputo. To guide in the correct choice of parameters, we report the models linear stability analysis. Numerical examples and results obtained for different instances of fractional power α are provided for non-spatial models as well as the spatial case in one and two dimensions in other to justify our theoretical findings which include the chaotic phenomena, spatiotemporal and oscillatory patterns, multiple steady states and other spatial pattern processes. This paper further suggest an alternative approach to incessant killing of wildlife animals for pattern generation and decorative purposes.

An epidemic is a typical public health emergency that refers to the occurrence and rapid spread of disease. A good epidemic transmission model plays a crucial role in preventing an epidemic. The epidemic transmission model is largely similar to the model of sentiment analysis and transmission on social media. Therefore, this paper intend to use the method of deep learning to explore the key issues of theme and sentiment analysis from the perspective of public opinion analysis. In order to fully extract the features automatically, we combine the following methods: multi-channel inputs, multi-granularity convolution kernels, direct connection with high-speed channels, and this paper proposes the multi-channel and multi-kernel (MCMK) model. Furthermore, we leverage generative adversarial nets to combine several single tasks, called Joint-MCMK model, which achieves information sharing and improves the training speed and model accuracy. To verify the validity of our proposed models, this paper experimented with the short text topic classification dataset TREC [1] and the sentiment analysis dataset IMDB [2] . Results achieved 98.6% and 92.6% respectively, which are superior to the highest existing industry benchmark (96.1% and 92.58%). In addition, this paper compared the training spread differences between the joint-MCMK model and MCMK model, which shows that the joint-MCMK model has better performance at training speed. Finally, the control variable method was used to analyze the multiple effects of the different factors. The optimal value of some relevant parameters in our models were verified by several experiments.

Computer numerical control (CNC) systems are becoming multi-functional as the requirements for manufacturing quality, efficiency and product diversity are becoming more rigorous. The reconfigurability and scalability property of CNC are important for reducing manufacturing costs and functional redundancy and shortening manufacturing time. However, in current CNC systems, functions are closely coupled in a real-time operation environment. This has been a main obstacle for implementing a scalable and reconfigurable CNC system. This paper proposes a new type of CNC system named invisible numerical control (INC) system to simplify CNC architecture and improve CNC architecture reconfigurability and function reusability. INC system consists of three sub-systems, namely project center, motor controller and mobile terminal. The functions of the sub-systems are machine control instructions generation, execution of machine control instructions and process control respectively. The sub-systems are organized in loosely coupled manner. This is enabled by current computer/information resources and technologies such as high speed data transmission, large capacity and high speed storage, standard communication protocols and compiled operation of machining programs. By configuring different functions in project center, it can generates uniform machine control instructions for multiple and different types of machine tools. Therefore, reconfigurability and function reusability are achieved. This paper illustrates the functions, architecture and information model of INC and builds an INC prototype. Case studies show that by using current off-the-shelf hardware, INC can be implemented to undertake different manufacturing tasks.

In this paper stiffness of cable-driven parallel robots (CDPRs) is analyzed in detail and based on this analysis, the stiffness-feasible workspace is introduced. This workspace includes all stable poses which increasing the internal forces can modify the total stiffness of the robot. It has been shown that in the CDPRs, the concept of the internal forces can be applied for keeping cables in tension and increasing stiffness. However, it should be noted that increasing the internal forces may decrease the overall stiffness of the mechanism and it is only applicable in stabilizable poses of the workspace. Therefore, stiffness-feasible workspace determines the allowable internal forces range which can increase the stiffness and it will guarantee that in this range of the internal forces, the structure of the robot is stable. In this paper, by employing this criterion and evolutionary algorithms, a CDPR is optimally designed, and a set of answers is presented. In this design, in addition to the stiffness-feasible workspace, another criterion as stiffness number is presented which is useful for specifying the distribution of the stiffness and stiffness-feasibility of the robot.

Use of sensors in robotic welding for controlling the weld quality leads to replacement of manual welding operation in dangerous work environment in presence of high temperature and fumes even in small or medium scale enterprises. The seam tracking operation is very essential for extracting weld seam position which can be fed to robot controller for instructing robot along the weld seam path. The seam tracking operation can be executed by different types of sensors having their own merits and demerits. In this paper, different sensors and techniques used for seam tracking task in robotic welding have been discussed in detail. Each sensor has different method or technology of weld seam feature extraction which have been described by different authors in different ways. The chief tasks for seam tracking have been found to be weld starting and end point detection, weld edge detection, joint width measurement and weld path position determination with respect to robot co-ordinate frame. Thus sensors have a very important role in robotic welding for fully automating the system with in process real time monitoring of weld process parameters with the sensor feedback. In further discussion the practical use of different sensors in industries with a comparison of their advantages and disadvantages have been discussed. This Paper presents the role of sensors in robotic welding and a detail study of methodologies of weld seam position and geometry feature extraction by different sensors typically used for weld seam tracking.

This paper presents a robust method for generic obstacle detection and collision warning in Advanced Driver Assistance Systems (ADAS). The highlight of our method is the ability to detect all obstacles without prior knowledge and detect partially occluded obstacles including the obstacles that have not completely appeared in the frame (truncated obstacles). Our results show an improvement of 90% more true positives per frame compared to one of the state-of-the-art methods. Our proposed method is robust to variations in illumination and to a wide variety of vehicles and obstacles that are encountered while driving. Distortions are introduced when Inverse Perspective Mapping (IPM) projects the camera image onto the road surface plane. In this paper, we first show that the angular distortion in the IPM domain belonging to obstacle edges varies as a function of their corresponding 2D location in the camera plane. We use this information to perform proposal generation. We propose a novel proposal assessment method based on fusing statistical properties from both the IPM image and the camera image to perform robust outlier elimination and false positive reduction. We also present an annotated obstacle detection dataset derived from various source videos that can serve as a benchmark for the evaluation of future obstacle detection algorithms. The source videos containing diverse illumination and traffic conditions are derived from multiple publicly available datasets.

This paper attempts to address the problem of online modulation of virtual impedance for an assistive robot based on real-time gait and activity measurements to personalize the assistance for different users at different states. In this work, smart shoes and inertial sensors are introduced to measure ground contact forces and knee joint kinematics, respectively. An automatic impedance tuning (AIT) approach is presented for a knee assistive device (KAD) based on real-time activity recognition and gait phase detection. The activities considered in this paper are level, uphill, and downhill walking. A Gaussian mixture model (GMM) is employed to map the fuzzy likelihood of various activities and gait phases to the desired virtual impedance of the KAD. The prior estimate of virtual impedance is defined using human knee impedance identified with the walking data collected on different users. The AIT approach is integrated into the high-level impedance-based controller of the KAD for assistance during the stance phase. Finally, to evaluate the benefit of the proposed algorithm in stance phase, an EMG sensor is placed on the vastus medialis muscle group of three participants. The proposed approach is compared with two baseline approaches: constant impedance and finite state machine, and the results demonstrate that the profiles of impedance parameters and robot assistive torque are smoother and the muscle activity of vastus medialis is reduced. It is also noticed that the participants reduce their step lengths and increase walking cadence with assistance from the KAD.

Target searching in an unknown environment is a traditional research issue in the multiagent area. In some real cases, the agents do not only discover the targets; instead, they have subsequent tasks that must be completed before a deadline. In this paper, these cases are abstracted as the agents searching for target locations in an unknown environment and then occupying these target locations within a limited time. The agents can obtain rewards by occupying the target locations, and the goal of this problem is to maximize net income, defined as total reward minus the moving cost of the agents. This problem can be transformed into the traditional problems, and then be solved by previous related algorithms. However, this approach is not optimal. In this paper, we present a method that combines previous algorithms and a decision-making algorithm. The experiments demonstrate that the method containing our decision-making algorithm can lead to higher net income than simply using previous algorithms. This work was supported by the National Natural Science Foundation of China (61472079, 61807008 and 61806053), the Natural Science Foundation of Jiangsu Province of China (BK20171363, BK20180356, BK20180369).

Modern manufacturing systems require increased levels of automation for fast and low-cost production, but also high levels of flexibility and adaptability to dynamic production requirements. Human-robot interaction allows for closer collaboration in assembly tasks that require increased productivity by combining the performance of robotic systems with the flexibility and dexterity of human workers. However, the main challenge is establishing human safety while performing near to robots. Towards enabling safe human-robot collaboration several physical and software systems should be combined. In this paper, a cyber-physical system for enabling and controlling safe human-robot collaborative assembly operations is discussed. The approach considers a shared fenceless working space where humans, industrial robots, or other moving objects, such as auto-guided vehicles, may operate. The working space is monitored by optical sensors. In this context, human safety is the major challenge. The paper focuses on a Cyber-Physical System for enabling human-robot collaboration based on real-time evaluation of safety distance and a closed-loop control for triggering collision preventive actions. An initial implementation is evaluated in a specific use case in a laboratory machine shop with an industrial robot, and its results are compared regarding the use of one or more sensors. The comparison is performed in terms of system response time to detect human presence within a predefined safety zone.

Vessels constitute one of the most cost effective ways of transporting goods around the world. Despite the efforts, maritime accidents still occur, with catastrophic consequences. For this reason, vessels are submitted to periodical inspections for the early detection of cracks and corrosion. These inspections are nowadays carried out at a great cost. In order to contribute to make ship inspections safer and more cost-efficiently, this paper presents a novel framework to turn a Micro-Aerial Vehicle (MAV) into a flying camera that can virtually teleport the human surveyor through the different structures of the vessel hull. The system architecture has been developed to be reconfigurable so that it can fit different sensor suites able to supply a proper state estimation, being at the same time compatible with the payload capacity of the aerial platform and the operational conditions. The control software has been designed following the Supervised Autonomy paradigm, so that it is in charge of safety related issues such as collision avoidance, While the surveyor, within the main control loop, is supposed to supply motion commands while he/she is concentrated on the inspection at hand. In this paper, we report on an extensive evaluation of the platform capabilities and usability, both under laboratory conditions and on board a real vessel, during a field inspection campaign., This is a preprint version of publication with DOI: https://doi.org/10.1016/j.rcim.2018.09.009. This work is partially supported by FEDER funding, by the European Social Fund through Ph.D. scholarship FPI10-43175042V (Conselleria d'Educacio, Cultura i Universitats, Govern de les Illes Balears), by project nr. AAEE50/2015 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears).

One of the important classes of coupled systems of algebraic, differential and fractional differential equations (CSADFDEs) is fractional differential algebraic equations (FDAEs). The main difference of such systems with other class of CSADFDEs is that their singularity remains constant in an interval. However, complete classifying and analyzing of these systems relay mainly to the concept of the index which we introduce in this paper. For a system of linear differential algebraic equations (DAEs) with constant coefficients, we observe that the solvability depends on the regularity of the corresponding pencils. However, we show that in general, similar properties of DAEs do not hold for FDAEs. In this paper, we introduce some practical applications of systems of FDAEs in physics such as a simple pendulum in a Newtonian fluid and electrical circuit containing a new practical element namely fractors. We obtain the index of introduced systems and discuss the solvability of these systems. We numerically solve the FDAEs of a pendulum in a fluid with three different fractional derivatives (Liouville–Caputo’s definition, Caputo–Fabrizio’s definition and with a definition with Mittag–Leffler kernel) and compare the effect of different fractional derivatives in this modeling. Finally, we solved some existing examples in research and showed the effectiveness and efficiency of the proposed numerical method.