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This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.

The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.

We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S²ⁿ⁺¹ and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to Eⁿ⁺¹ × Sⁿ(4) in higher dimension.

All results are novel and generalizations of previously obtained results.

To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

As supply chain excellence matters, designing an appropriate health-care supply chain is a great consideration to the health-care providers worldwide. Therefore, the purpose of this paper is to benchmark several potential health-care supply chains to design an efficient and effective one in the presence of mixed data.

To achieve this objective, this research illustrates a hybrid algorithm based on data envelopment analysis (DEA) and goal programming (GP) for designing real-world health-care supply chains with mixed data. A DEA model along with a data aggregation is suggested to evaluate the performance of several potential configurations of the health-care supply chains. As part of the proposed approach, a GP model is conducted for dimensioning the supply chains under assessment by finding the level of the original variables (inputs and outputs) that characterize these supply chains.

This paper presents an algorithm for modeling health-care supply chains exclusively designed to handle crisp and interval data simultaneously.

The outcome of this study will assist the health-care decision-makers in comparing their supply chains against peers and dimensioning their resources to achieve a given level of productions.

A real application to design a real-life pharmaceutical supply chain for the public ministry of health in Morocco is given to support the usefulness of the proposed algorithm.

The novelty of this paper comes from the development of a hybrid approach based on DEA and GP to design an appropriate real-life health-care supply chain in the presence of mixed data. This approach definitely contributes to assist health-care decision-makers design an efficient and effective supply chain in today’s competitive word.

In order to improve the computation efficiency of the four-point rainflow algorithm, a new fast four-point rainflow cycle counting algorithm (FFRA) using a novel loop iteration mode is proposed.

In this new algorithm, the loop iteration mode is simplified by reducing the number of iterations, tests and deletions. The high efficiency of the new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.

The extensive simulation results show that the extracted cycles by the new FFRA are the same as those by the four-point rainflow cycle counting algorithm (FRA) and the three-point rainflow cycle counting algorithm (TRA). Especially, the simulation results indicate that the computation efficiency of the FFRA has improved an average of 12.4 times compared to the FRA and an average of 8.9 times compared to the TRA. Moreover, the equivalence of cycle extraction results between the FFRA and the FRA is proved mathematically by utilizing some fundamental properties of the rainflow algorithm. Theoretical proof of the efficiency improvement of the FFRA in comparison to the FRA is also given.

This merit makes the FFRA preferable in online monitoring systems of structures where fatigue life estimation needs to be accomplished online based on massive measured data. It is noticeable that the high efficiency of the FFRA attributed to the simple loop iteration, which provides beneficial guidance to improve the efficiency of existing algorithms.

The purpose of this study is a numerical simulation and an analytical analysis about the low-velocity impact on a functionally graded porous plate with porosity distribution in the thickness direction. In this article, polymethyl methacrylate is used for matrix, and single-walled carbon nanotube (CNTs) (10,10) with consideration agglomeration sizes and lumping of CNT inside the agglomerations is applied for reinforcement.

In analytical formulation, the non-linear Hertz contact law is applied for interaction between projectile and plate surface. High-order shear deformation plate theory is developed, and energy of the system for impactor and plate is written. The governing equations are derived using Ritz method and Lagrange equations and are solved using the fourth-order Runge–Kutta method. Also, ABAQUS finite element model of functionally graded porous plate with all edges simply supported and reinforced by CNT under low-velocity impact is simulated and is compared with those is achieved in the present analytical approach.

In parametric studies, the influence of porosity distribution patterns include uniform, non-uniform symmetric and non-uniform asymmetric on the histories of contact force and impactor displacement of simply supported plate reinforced by CNT are presented. Eventually, the effects of porosity coefficient, impactor initial velocity, impactor radius and CNTs lumping inside agglomerations for non-uniform symmetric distribution patterns are discussed in impact event in detail.

In this paper, the effect of combination of polymethyl methacrylate and CNTs with consideration agglomeration sizes and lumping of CNTs inside the agglomerations in the form of a functionally graded porous plate is studied in the problem of low-velocity impact analysis.

This study aims to investigate the most effective approach for governments and enterprises to combat desertification by considering the governance cycle. The focus is on understanding how the government can incentivize enterprises to actively engage in desertification combat efforts.

Both the government and the enterprise are treated as rational entities, making strategic choices for joint participation in combating desertification. Recognizing the dynamic nature of the desertification combat area, differential game models are employed to identify the optimal mode for combating desertification.

The findings underscore the significant influence of the governance cycle duration on the selection of desertification combat modes for government and enterprise. A cooperative mode is best suited to a short governance cycle, while an ecological subsidy mode is optimal for a longer cycle. Enhancing governance technology and shortening the governance cycle are conducive to combating desertification. Reducing taxes alone may not be an effective control strategy; rather, the government can better motivate enterprises by adopting tax rate policies aligned with the chosen governance mode.

This research contributes by elucidating the impact mechanism of the government cycle’s length on the desertification combat process. The results may offer valuable insights for governments in formulating strategies to encourage corporate participation in combating desertification and provide theoretical support for selecting optimal desertification combat modes.

The authors propose to estimate a varying coefficient panel data model with different smoothing variables and fixed effects using a two-step approach. The pilot step estimates the varying coefficients by a series method. We then use the pilot estimates to perform a one-step backfitting through local linear kernel smoothing, which is shown to be oracle efficient in the sense of being asymptotically equivalent to the estimate knowing the other components of the varying coefficients. In both steps, the authors remove the fixed effects through properly constructed weights. The authors obtain the asymptotic properties of both the pilot and efficient estimators. The Monte Carlo simulations show that the proposed estimator performs well. The authors illustrate their applicability by estimating a varying coefficient production frontier using a panel data, without assuming distributions of the efficiency and error terms.

Autonomous mobile robots (AMRs) play a crucial role in industrial and service fields. The paper aims to build a LiDAR-based simultaneous localization and mapping (SLAM) system used by AMRs to overcome challenges in dynamic and changing environments.

This research introduces SLAM-RAMU, a lifelong SLAM system that addresses these challenges by providing precise and consistent relocalization and autonomous map updating (RAMU). During the mapping process, local odometry is obtained using iterative error state Kalman filtering, while back-end loop detection and global pose graph optimization are used for accurate trajectory correction. In addition, a fast point cloud segmentation module is incorporated to robustly distinguish between floor, walls and roof in the environment. The segmented point clouds are then used to generate a 2.5D grid map, with particular emphasis on floor detection to filter the prior map and eliminate dynamic artifacts. In the positioning process, an initial pose alignment method is designed, which combines 2D branch-and-bound search with 3D iterative closest point registration. This method ensures high accuracy even in scenes with similar characteristics. Subsequently, scan-to-map registration is performed using the segmented point cloud on the prior map. The system also includes a map updating module that takes into account historical point cloud segmentation results. It selectively incorporates or excludes new point cloud data to ensure consistent reflection of the real environment in the map.

The performance of the SLAM-RAMU system was evaluated in real-world environments and compared against state-of-the-art (SOTA) methods. The results demonstrate that SLAM-RAMU achieves higher mapping quality and relocalization accuracy and exhibits robustness against dynamic obstacles and environmental changes.

Compared to other SOTA methods in simulation and real environments, SLAM-RAMU showed higher mapping quality, faster initial aligning speed and higher repeated localization accuracy.

The purpose of this study is to explore numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction.

The two fluids micropolar and Walters-B liquid are considered to start flowing from the slot to the stretching sheet. A magnetic field of constant strength is imposed on their flow transversely. The problems on heat and mass transport are set up with thermal, chemical reaction, heat generation, etc. to form partial differential equations. These equations were simplified into a dimensionless form and solved using spectral homotopy analysis method (SHAM). SHAM uses the basic concept of both Chebyshev pseudospectral method and homotopy analysis method to obtain numerical computations of the problem.

The outcomes for encountered flow parameters for temperature, velocity and concentration are presented with the aid of figures. It is observed that both the velocity and angular velocity of micropolar and Walters-B and thermal boundary layers increase with increase in the thermal radiation parameter. The decrease in velocity and decrease in angular velocity occurred are a result of increase in chemical reaction. It is hoped that the present study will enhance the understanding of boundary layer flow of micropolar and Walters-B non-Newtonian fluid under the influences of thermal radiation, thermal conductivity and chemical reaction as applied in various engineering processes.

All results are presented graphically and all physical quantities are computed and tabulated.

The rapid development of the Internet has led to an increasingly significant role for E-commerce business. This study examines how the green supply chain (GSC) operates on the E-commerce online channel (resell mode and agency mode) and the traditional offline channel with information sharing under demand uncertainty.

This study builds a multistage game model that considers the manufacturer selling green products through different channels. On the traditional offline channel, the competing retailers decide whether to share demand signals. Regarding the resale mode of E-commerce online channel, just E-tailer 1 determines whether to share information and decides the retail price. In the agency mode, the manufacturer decides the retail price directly, and E-tailer 2 sets the platform rate.

This study reveals that information accuracy is conducive to information value and profits on both channels. Interestingly, the platform fee rate in agency mode will inhibit the effect of a positive demand signal. Information sharing will cause double marginal effects, and price competition behavior will mitigate such effects. Additionally, when the platform fee rate is low, the manufacturer will select the E-commerce online channel for operation, but the retailers' profit is the highest in the traditional channel.

This research explores the interplay between different channel structures and information sharing in a GSC, considering price competition and demand uncertainty. Besides, we also considered what behaviors and factors will amplify or transfer the effect of double marginalization.