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In this paper, we present real-time collision-free inverse kinematics (RCIK) that accurately performs consecutively provided six-degrees-of-freedom commands in environments containing static and dynamic obstacles. Our method is based on an optimization-based IK approach to generate IK candidates with high feasibility for the command. While checking various constraints (e.g., collision and joint velocity limits), we select the best configuration among generated IK candidates through our objective function, considering the continuity of joints and collision avoidance with obstacles. To avoid dynamic obstacles efficiently, we propose a novel, collision-cost prediction network (CCPN) that estimates collision costs using an occupancy grid updated from sensor data in real-time. We evaluate our method in three dynamic problems using a real robot, the Fetch manipulator, and four static problems using three different configurations of robots. We show that the proposed method successfully performs the consecutively given commands in real-time, mainly thanks to the collision cost prediction network, while avoiding dynamic and static obstacles. The results of tested problems are available in the accompanying video.

A novel predictor–corrector explicit scheme is presented to solve structural dynamic problems. It is a three sub-steps method, in which the previous two sub-steps are set as predictors and the last sub-step is regarded as correctors. The explicit scheme is third-order accuracy and can achieve forth-order accuracy in the absent of physical damping. The stability limit of the proposed scheme is much larger than the existing methods. Also, the numerical dissipation and dispersion of the explicit scheme can be controlled through the different algorithm parameters. The explicit scheme not only possesses adequate numerical dissipation and dispersion in high-frequency responses, but also gets small numerical errors in the whole frequency domain for dynamic system. These performances of the proposed explicit scheme are further highlighted in comparison with other typical explicit schemes.

We show how the interpolation step of numerical integration can be pre-compiled in partial equilibrium stochastic dynamic problems. We display the pre-compilation’s sufficient conditions and document its speed gains using a consumption-savings model with a discrete labour choice, wage uncertainty and stochastic non-labour income.

The formation of multi-quadrotor UAVs (QUAVs) in long flights will encounter many constraints and obstacles in the flight process, so it is necessary to change the formation shape to avoid these constraints. When the flight path of QUAVs is individually optimized, multiple individual dynamic problems will be faced, making the solution complicated and spending a long time. In this paper, as a whole instead of individuals considering the QUAVs, the formation is regarded as a rigid body using the Voronoi graph theory method in the flight process. The constraints of the followed QUAVs are transformed into the constraints of leader QUAV. Therefore, the formation is transformed for different constraints by changing the virtual rigid body structure or shape. A time-varying model is established to facilitate the use of optimization. The energy consumption of the leader UAV within the specified time is minimized as the trajectory optimization objective. The optimization improvement of the end heading and height constraints is proposed. A trajectory optimization method for the leader QUAV based on Gauss pseudospectral method is proposed, transforming the original optimal control problem into the nonlinear programming one. The simulation results demonstrate and verify the proposed method.

This paper is concerned with new formulations of local meshfree numerical method, for the solution of dynamic problems in linear elasticity, Integrated Local Mesh Free (ILMF) method. The key attribute of local numerical methods is the use of a modeling paradigm based on a node-by-node calculation, to generate the rows of the global system of equations of the body discretization. In the local domain, assigned to each node of a discretization, the work theorem is kinematically formulated, leading thus to an equation of mechanical equilibrium of the local node, that is used by local meshfree method as the starting point of the formulation. The main feature of this paper is the use of a linearly integrated local form of the work theorem. The linear reduced integration plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy. As a consequence, the derived meshfree and finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as computational efficiency of numerical methods is concerned. The cantilever beam was analyzed with this technique, in order to assess the accuracy and efficiency of the new local numerical method for dynamic problems with regular and irregular nodal configuration. The results obtained in this work are in perfect agreement with Mesh-Free Local Petrov-Galerkin (MLPG) and the Finite Element Method (FEM) solutions.

Rock dynamic constitutive model plays an important role in understanding dynamic response and addressing rock dynamic problems. Based on elastoplastic mechanics and damage mechanics, a dynamic constitutive model of rock coupled with elastoplastic damage is established. In this model, unified strength theory is taken as the yield criterion; to reflect the different damage evolution law of rocks under tension and pressure conditions, the effective plastic strain and volumetric plastic strain are used to represent the compressive damage variable and the equivalent plastic strain is used to represent the tensile damage variable; the plastic hardening behavior and strain rate effect of rocks are characterized by piecewise function and dynamic increase factor function, respectively; Fortran language and LS-DYNA User-Defined Interface (Umat) are used to numerically implement the constitutive model; the constitutive model is verified by three classical examples of rock uniaxial and triaxial compression tests, rock uniaxial tensile test, and rock ballistic test. The results show that the constitutive model can describe the dynamic and static mechanical behavior of rock comprehensively.

We present a dynamic algorithm for the recognition of proper circular-arc (PCA) graphs, that supports the insertion and removal of vertices (together with its incident edges). The main feature of the algorithm is that it outputs a minimally non-PCA induced subgraph when the insertion of a vertex fails. Each operation cost O ( log ⁡ n + d ) time, where n is the number vertices and d is the degree of the modified vertex. When removals are disallowed, each insertion is processed in O ( d ) time. The algorithm also provides two constant-time operations to query if the dynamic graph is proper Helly (PHCA) or proper interval (PIG). When the dynamic graph is not PHCA (resp. PIG), a minimally non-PHCA (resp. non-PIG) induced subgraph is obtained.

An improved explicit time integration method is proposed for linear and nonlinear dynamics. Its calculation procedure is obtained with cubic B-spline interpolation approximation and weighted residual method. In the formulation, a momentum corrector is used to improve actual computation accuracy, especially for some special discontinuous loads. Analytical solutions of the local truncation errors, algorithmic damping and period elongation have been deduced to obtain the influence of algorithmic parameters on these basis algorithmic properties. The proposed method possesses at least second-order accuracy and can achieve at most third-order accuracy for no physical damping case. With free algorithmic parameters, the proposed method has controllable stability and numerical dissipation. Some demonstrative numerical examples are tested to confirm high efficiency of the proposed method for a variety of dynamic problems such as, dynamic response analysis of linear systems under various representative applied loads, finite element analysis (FEA) for dynamic response of engineering structures, and nonlinear dynamic analysis for strong nonlinear system.

In this study, two novel stochastic models are introduced to solve the dynamic sectorization problem, in which sectors are created by assigning points to service centres. The objective function of the first model is defined based on the equilibration of the distance in the sectors, while in the second one, it is based on the equilibration of the demands of the sectors. Both models impose constraints on assignments and compactness of sectors. In the problem, the coordinates of the points and their demand change over time, hence it is called a dynamic problem. A new solution method is used to solve the models, in which expected values of the coordinates of the points and their demand are assessed by using the Monte Carlo simulation. Thus, the problem is converted into a deterministic one. The linear and deterministic type of the model, which is originally non-linear is implemented in Python's Pulp library and in this way the generated benchmarks are solved. Information about how benchmarks are derived and the obtained solutions are presented.

Time-history analysis is a versatile tool for studying structural dynamic behaviors. The run-time is, however, considerable. A Step-Enlargement-Based Time-History Analysis Acceleration Technique (SEB THAAT) was proposed in 2008 for structural dynamic problems when the excitation is in a digitized format. Many successful tests were carried out on the technique, and some are in progress. In this paper, for the first time, it is demonstrated, via four seismic examples, that the technique can reduce the analysis run-time, when the damping is non-classical. A general rule is also developed that explains the observations and can anticipate the technique’s performance when applied to analysis of non-classically damped structural dynamics. Accordingly, the performance is well, provided a slight condition on the integration scheme. The achievement is significant, because of reasons, such as the fact that non-classical damping is more realistic than classical damping and that the additional requirement is not very restrictive.

No-wait Integrated Scheduling Problem (NISP) describes a real-life process of the non-standard products where the consideration is given to the great structure differences, processing parameter differences, no-wait constraint, and the need for further deep processing after assembly of jobs. To deal with the dynamic orders of non-standard products, the scheduling algorithm to be design should be a dynamic algorithm with the ability to deal with the above conditions. At first, the dynamic scheduling problem is transformed to a series of continuous static scheduling problem by adoption of window-based event-driven strategy, thus establishing constraint programming model targeted at minimal total tardiness and thereby proposing a hybrid method of Heuristic Algorithm and Constraint Programming (HA-CP) for the problem. In order to enhance the ability to response the dynamic orders of non-standard products, HA-CP adopts heuristic algorithm to generate a pre-scheduling solution at each dynamic event moment, so that jobs that fall into the window period are labelled as dispatched jobs, while the remaining jobs are labelled as jobs to be dispatched. To improve solution quality, the jobs to be dispatched are mapped into an operation-based constraint programming model, then, during the execution interval of dispatched jobs, constraint programming solver starts to solve the jobs to be dispatched and update the current solution if the solver gets a better solution within the execution interval. The above procedures are repeated until all jobs are scheduled. Finally, the results of simulation experiment show that the proposed algorithm is effective and feasible.

The article considers a numerical method for solving a two-dimensional coupled dynamic thermoplastic boundary value problem based on deformation theory of plasticity. Discrete equations are compiled by the finite-difference method in the form of explicit and implicit schemes. The solution of the explicit schemes is reduced to the recurrence relations regarding the components of displacement and temperature. Implicit schemes are efficiently solved using the elimination method for systems with a three diagonal matrix along the appropriate directions. In this case, the diagonal predominance of the transition matrices ensures the convergence of implicit difference schemes. The problem of a thermoplastic rectangle clamped from all sides under the action of an internal thermal field is solved numerically. The stress-strain state of a thermoplastic rectangle and the distribution of displacement and temperature over various sections and points in time have been investigated.

This paper proposes a two-sub-step time integration method with controllable dissipation to solve nonlinear dynamic problems. The proposed method has second-order accuracy, unconditional stability and zero-order overshoots. In addition, different from most existing time integration methods, the present method is self-starting, and initial acceleration vector is not required. Importantly, the well-known BN-stability theory for first-order nonlinear dynamics is employed to design algorithmic parameters; thus, the present method is BN-stable, or unconditionally stable for nonlinear dynamics. The present method can give stable and accurate predictions for nonlinear problems in which some excellent methods such as the trapezoidal rule and the ρ∞-Bathe method fail. A few representative nonlinear numerical examples show that the proposed method enjoys advantages in accuracy, stability and energy conservation compared with the trapezoidal rule and the ρ∞-Bathe method.

A novel hybrid strategy combining a spiral dynamic algorithm (SDA) and a bacterial foraging algorithm (BFA) is presented in this article. A spiral model is incorporated into the chemotaxis of the BFA algorithm to enhance the capability of exploration and exploitation phases of both SDA and BFA with the aim to improve the fitness accuracy for the SDA and the convergence speed as well as the fitness accuracy for BFA. The proposed algorithm is tested with the Congress on Evolutionary Computation 2013 (CEC2013) benchmark functions, and its performance in terms of accuracy is compared with its predecessor algorithms. Consequently, for solving a complex engineering problem, the proposed algorithm is employed to obtain and optimise the fuzzy logic control parameters for the hub angle tracking of a flexible manipulator system. Analysis of the performance test with the benchmark functions shows that the proposed algorithm outperforms its predecessor algorithms with significant improvements and has a competitive performance compared to other well-known algorithms. In the context of solving a real-world problem, it is shown that the proposed algorithm achieves a faster convergence speed and a more accurate solution. Moreover, the time-domain response of the hub angle shows that the controller optimised by the proposed algorithm tracks the desired system response very well.

The dynamic problem of thermomechanics for a bimetallic layer with plane-parallel boundaries under the action of a homogeneous nonstationary electromagnetic field has been formulated. The thermal s...

In this article, we derive the general explicit linear four-step (ELFS) rule with fifth-order precision systematically, together with a group of specific ELFS rules provided. Afterwards, we formulate and investigate a new and challenging discrete-time dynamic problem with relatively complex structure and future unknownness, which is simply termed future system of bounded inequalities and nonlinear equations (SBINE). With the aid of the general ELFS rule, the general ELFS-type discretized zeroing neural network (DZNN) model is proposed to solve the future SBINE. Moreover, theoretical and numerical results are presented to show the validity and high precision of the proposed general ELFS-type DZNN model. Finally, comparative numerical experiments based on a wheeled mobile robot containing several additional constraints are further performed to substantiate the applicability, validity, and superiority of the proposed general ELFS-type DZNN model.

Domain adaptation aims to improve the performance of the classifier in the target domain by reducing the difference between the two domains. Domain shifts usually exist in both marginal distribution and conditional distribution, and their relative importance varies with datasets. Moreover, there is an influence between marginal distribution distance and conditional distribution distance. However, joint domain adaptation approaches rarely consider those. Existing dynamic distribution alignment methods require a feature discriminator, and they need to train a subdomain discriminator for each class. Besides, they don’t think about the interaction between the two distribution distances. In this article, we propose a dynamic joint domain adaptation approach, namely Joint Domain Adaptation Based on Adversarial Dynamic Parameter Learning (ADPL), to deal with the above problems. Both marginal distribution alignment and conditional distribution alignment can be implemented by adversarial learning. The dynamic algorithm can keep a balance between marginal and conditional distribution alignment with only two domain discriminators. In addition, the dynamic algorithm takes the influence between the two distribution distances into consideration. Compared with several advanced domain adaptation methods on both text and image datasets, all classification experiments and extensive comparison experiments demonstrate that ADPL has higher learning performance of classification and less running time. This reveals that ADPL outperforms the state-of-the-art domain adaptation approaches.

How data became one of the most powerful tools to fight an epidemic is a question that a recent (10 June 2020) The New York Times article poses in its title. Indeed, the spread of COVID-19 involves dynamically evolving hidden data (for example, the number of infected people, the number of asymptomatic people) that must be deduced from noisy and partially observed data (for example, the number of daily deaths, the number of daily hospitalizations, and the number of daily positive tests). The underlying mathematics for posing and solving this and several other partially observed dynamic problems is familiar to control theorists

The study considers the solution of a number of problems of supersonic and hypersonic gas dynamics using a model that takes into account the dissociation and ionization of air. The results of verification and validation of the developed numerical method using various difference schemes (the Roe scheme, Rusanov scheme, AUSM scheme) for discretizing convective flows are presented. The formulation of the mathematical model for high-temperature air uses the presence of equilibrium chemical reactions of dissociation and ionization. For this purpose, at high incoming flow velocities, the Kraiko model is applied, which includes equilibrium chemical reactions in air at high temperatures. To discretize the basic equations, the finite volume method on an unstructured grid is applied. One of the features of the constructed mathematical model is the implementation of the transition between physical and conservative variables. Relationships are given, with the help of which the transition from conservative variables to physical ones and vice versa is carried out when using the high-temperature air model. To ensure the stability of numerical calculations, an entropy correction is introduced. The decrease in entropy in the solution of hyperbolic equations is excluded by introducing an artificial viscosity according to Neumann, as well as by using the Godunov method with an exact solution of the Riemann problem and methods based on the approximate solution of the problem of the decay of an arbitrary discontinuity. A number of problems of supersonic gas dynamics (supersonic flow in a channel with a straight step and supersonic flow around a sphere) are numerically solved taking into account high-temperature effects. The criteria for the accuracy of numerical calculations related to the location of shock-wave structures are discussed. The calculated shock-wave structure of the flow is compared with the data available in the literature, as well as with calculations using the perfect gas model. Some results of numerical calculations are compared with the available experimental data. The shock-wave flow patterns obtained in the framework of the inviscid model, which takes into account the effect of viscosity and its dependence on temperature, and the turbulent flow model are compared. On the basis of numerical simulation data, the influence of viscous effects on the flow characteristics in a channel with a straight step and hypersonic flow around a sphere is considered. The influence of various numerical factors on the shape of the bow shock and the presence of fluctuations in the solution behind the shock is emphasized. As part of the work, a computational module was prepared for the commercial package Ansys Fluent, implemented with the help of user programming tools. The prepared module expands the standard capabilities of commercial software focused on solving computational gas dynamics problems, and is available to Ansys Fluent users for solving hypersonic aerodynamics problems. The developed means of numerical simulation can be useful in the design and optimization of hypersonic aircraft.

To account for the nonlinear dynamic effects of flexible sandwich plates undergoing large deformation, a computational method for dynamic analysis of flexible sandwich plates is studied. According to the characteristics of sandwich plates, a simplified plate model is proposed based on the Kirchhoff plate theory, in which the shear stiffness of the core plate is neglected and the stiffness for the whole plate is derived. For the dynamic problem of flexible multibody systems, a thin plate element has been studied based on the absolute nodal coordinate formulation (ANCF). Meanwhile, a method based on invariant tensors is proposed for calculating elastic forces and their Jacobians, which can be calculated during preprocessing and applied for programmed calculation. Using examples, the proposed computational method is verified to be feasible and accurate. In addition, a benchmark example and a double-pendulum model are used to verify the applicability and feasibility of our analytical method for flexible sandwich plates in flexible multibody systems. Therefore, this method lays a foundation for the study of flexible dynamics problems regarding multibody systems with sandwich plates.

For nonlinear dynamic topology optimization, explicit geometry information cannot be obtained with the currently density-based topology optimization methods. To directly obtain an explicit geometry structure in nonlinear dynamic topology optimization, the moving morphable components method is employed to find the optimal topology by changing geometrical parameters of a series of components. However, nonlinear dynamic topology optimization is extremely resourced-consuming, since the objective function and constraints should be evaluated by solving the dynamic equations in each optimization cycle. To solve this problem, the equivalent static loads method is introduced to convert a nonlinear dynamic problem into a linear static problem. The equivalent static loads are obtained by nonlinear dynamic analysis and used as linear static loading conditions. Then, the linear static optimization is carried out by using the moving morphable components method. The linear static system is continuously approaching the nonlinear dynamic systems. In this procedure, the key time steps are selected to calculate the equivalent static loads, and optimization is not coupled with nonlinear dynamic analysis. To avoid mesh distortion problems and make optimization more efficient, the transformation variable is introduced to transform the optimization results before nonlinear dynamic analysis. In this paper, the objective function is defined as the minimum strain energy, with the constraint of volume fraction. Three numerical examples are presented to verify the effectiveness of this method.

In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multi-body systems. Although the motion of multi-body systems is considered to be a well-studied problem and various methods have been proposed for its solution, a unified approach providing an intuitive interpretation is still pursued. We describe how to build factor graphs to model and simulate multibody systems using both, independent and dependent coordinates. Then, batch optimization or a fixed-lag-smoother can be applied to solve the underlying optimization problem that results in a highly-sparse nonlinear minimization problem. The proposed framework has been tested in extensive simulations and validated against a commercial multibody software. We release a reference implementation as an open-source C++ library, based on the GTSAM framework, a well-known estimation library. Simulations of forward and inverse dynamics are presented, showing comparable accuracy with classical approaches. The proposed factor graph-based framework has the potential to be integrated into applications related with motion estimation and parameter identification of complex mechanical systems, ranging from mechanisms to vehicles, or robot manipulators., 23 pages

The reproducing kernel (RK) approximation based direct collocation method (DCM) requires the complex and time-consuming derivatives calculation of the approximation function, and the DCM has the poor accuracy and stability, which hinder the extensive application of this method. Therefore, in this work, we propose a gradient reproducing kernel (GRK) based stabilized collocation method (SCM) which can manage the computational complexity of the RK derivatives calculation and significantly improve the efficiency by directly constructing the GRK approximations, and handle the accuracy and stability problems of the DCM by employing the SCM. Moreover, the computation cost of the SCM is about the same level of the DCM, which is much more efficient than the Galerkin meshfree methods. The proposed method is particularly suitable for solving the thin beam and plate problems which requests the fourth-order differentiation in the strong form. The implementations of this method for the static and dynamical problems are detailedly exhibited. Numerical examples confirm that the presented algorithm provides high efficiency and good performance for the beam and plate simulations.