Search Results (121)

Humanoid robots have attracted considerable attention for their anthropomorphic structure, extended workspace, and versatile capabilities. This paper presents a novel humanoid upper-body robotic system comprising a pair of 8-degree-of-freedom (DOF) arms, a 3-DOF head, and a 3-DOF torso—yielding a 22-DOF architecture inspired by human biomechanics and implemented via standardized hollow joint modules. To overcome the critical reliance of zeroing neural network (ZNN)-based trajectory tracking on the Jacobian matrix derivative, we propose an integration-enhanced matrix derivative observer (IEMDO) that incorporates nonlinear feedback and integral correction. The observer is theoretically proven to ensure asymptotic convergence and enables accurate, real-time estimation of matrix derivatives, addressing a fundamental limitation in conventional ZNN solvers. Workspace analysis reveals that the proposed design achieves an 87.7% larger total workspace and a remarkable 3.683-fold expansion in common workspace compared to conventional dual-arm baselines. Furthermore, the observer demonstrates high estimation accuracy for high-dimensional matrices and strong robustness to noise. When integrated into the ZNN controller, the IEMDO achieves high-precision trajectory tracking in both simulation and real-world experiments. The proposed framework provides a practical and theoretically grounded approach for redundant humanoid arm control. Full article

Background: Gait kinematics address the analysis of joint angles and segment movements during walking. Although there is work in the literature to solve the problems of forward (FK) and inverse kinematics (IK), there are still problems related to the accuracy of the estimation of Cartesian and joint variables, singularities, and modeling complexity on gait analysis approaches. Objective: In this work, we propose a framework for two-dimensional gait analysis addressing the singularities in the estimation of the joint variables using quaternion-based kinematic modeling. Methods: To solve the forward and inverse kinematics problems we use the dual quaternions’ composition and Damped Least Square (DLS) Jacobian method, respectively. We assess the performance of the proposed methods with three gait patterns including normal, toe-walking, and heel-walking using the RMSE value in both Cartesian and joint spaces. Results: The main results demonstrate that the forward and inverse kinematics methods are capable of calculating the posture and the joint angles of the three-DoF kinematic chain representing a lower limb. Conclusions: This framework could be extended for modeling the full or partial human body as a kinematic chain with more degrees of freedom and multiple end-effectors. Finally, these methods are useful for both diagnostic disease and performance evaluation in clinical gait analysis environments. Full article

A method for configuration synthesis of a reconfigurable decoupled parallel mechanical leg is proposed. In addition, a configuration evaluation index is proposed to evaluate the synthesized configurations and select the optimal one. Kinematic analysis and performance optimization of the selected mechanism’s configuration are carried out, and the motion mode of the robot’s reconfigurable mechanical leg is selected according to the task requirements. Then, the robot’s gait in walking mode is planned. Firstly, based on bionic principles, the motion characteristics of a mechanical leg based on a mammalian model and an insect model were analyzed. The input and output characteristics of the mechanism were analyzed to obtain the reconfiguration principle of the mechanism. Using type synthesis theory for the decoupled parallel mechanism, the configuration synthesis of the chain was carried out, and the constraint mode of the mechanical leg was determined according to the constraint property of the chain and the motion characteristics of the moving platform. Secondly, an evaluation index for the complexity of the reconfigurable mechanical leg structure was developed, and the synthesized mechanism was further analyzed and evaluated to select the mechanical leg’s configuration. Thirdly, the inverse position equations were established for the mechanical leg in the two motion modes, and its Jacobian matrix was derived. The degrees of freedom of the mechanism are completely decoupled in the two motion modes. Then, the workspace and motion/force transmission performance of the mechanical leg in the two motion modes were analyzed. Based on the weighted standard deviation of the motion/force transmission performance, the global performance fluctuation index of the mechanical leg motion/force transmission is defined, and the structural size parameters of the mechanical leg are optimized with the performance index as the optimization objective function. Finally, with the reconfigurable mechanical leg in the insect mode, the robot’s gait in the walking operation mode is planned according to the static stability criterion. Full article

This paper presents a novel four-dimensional autonomous conservative model characterized by an infinite set of equilibrium points and an unusual algebraic structure in which all eigenvalues of the Jacobian matrix are zero. The linearization of the proposed model implies that classical stability analysis is inadequate, as only the center manifolds are obtained. Consequently, the stability of the system is investigated through both analytical and numerical methods using Lyapunov functions and numerical simulations. The proposed model exhibits rich dynamics, including hyperchaotic behavior, which is characterized using the Lyapunov exponents, bifurcation diagrams, sensitivity analysis, attractor projections, and Poincaré map. Moreover, in this paper, we explore the model with fractional-order derivatives, demonstrating that the fractional dynamics fundamentally change the geometrical structure of the attractors and significantly change the system stability. The Grünwald–Letnikov formulation is used for modeling, while numerical integration is performed using the Caputo operator to capture the memory effects inherent in fractional models. Finally, an analog electronic circuit realization is provided to experimentally validate the theoretical and numerical findings. Full article

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

AI-powered health assistants offer promising opportunities to enhance health management among older adults. However, real-world uptake remains limited, not only due to individual hesitation, but also because of complex interactions among users, platforms, and public policies. This study investigates the dynamic behavioral mechanisms behind adoption in aging populations using a tripartite evolutionary game model. Based on replicator dynamics, the model simulates the strategic behaviors of older adults, platforms, and government. It identifies evolutionarily stable strategies, examines convergence patterns, and evaluates parameter sensitivity through a Jacobian matrix analysis. Results show that when adoption costs are high, platform trust is low, and government support is limited, the system tends to converge to a low-adoption equilibrium with poor service quality. In contrast, sufficient policy incentives, platform investment, and user trust can shift the system toward a high-adoption state. Trust coefficients and incentive intensity are especially influential in shaping system dynamics. This study proposes a novel framework for understanding the co-evolution of trust, service optimization, and institutional support. It emphasizes the importance of coordinated trust-building strategies and layered policy incentives to promote sustainable engagement with AI health technologies in aging societies. Full article

The digital economy presents multiple challenges to the promotion of green technologies, including behavioral uncertainty among firms, heterogeneous technological choices, and disparities in policy incentive strength. This study develops a tripartite evolutionary game model encompassing government, production enterprises, and technology suppliers to systematically explore the strategic evolution mechanisms underlying green technology adoption. A three-dimensional nonlinear dynamic system is constructed using replicator dynamics, and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is applied to identify key cost and benefit parameters for firms. Simulation results exhibit a strong match between the estimated parameters and simulated data, highlighting the model’s identifiability and explanatory capacity. In addition, the stability of eight pure strategy equilibrium points is examined through Jacobian analysis, revealing the evolutionary trajectories and local stability features across various strategic configurations. These findings offer theoretical guidance for optimizing green policy design and identifying behavioral pathways, while establishing a foundation for data-driven modeling of dynamic evolutionary processes. Full article

This study explores analytical soliton solutions for the cubic–quintic time-fractional nonlinear non-paraxial pulse transmission model. This versatile model finds numerous uses in fiber optic communication, nonlinear optics, and optical signal processing. The strength of the quintic and cubic nonlinear components plays a crucial role in nonlinear processes, such as self-phase modulation, self-focusing, and wave combining. The fractional nonlinear Schrödinger equation (FNLSE) facilitates precise control over the dynamic properties of optical solitons. Exact and methodical solutions include those involving trigonometric functions, Jacobian elliptical functions (JEFs), and the transformation of JEFs into solitary wave (SW) solutions. This study reveals that various soliton solutions, such as periodic, rational, kink, and SW solitons, are identified using the complete discrimination polynomial methods (CDSPM). The concepts of chaos and bifurcation serve as the framework for investigating the system qualitatively. We explore various techniques for detecting chaos, including three-dimensional and two-dimensional graphs, time-series analysis, and Poincarè maps. A sensitivity analysis is performed utilizing a variety of initial conditions. Full article

This study presents an integrated stiffness modeling and evaluation framework for an orthopedic surgical robot, aiming to enhance cutting accuracy and operational stability. A comprehensive stiffness model is developed, incorporating the stiffness of the end-effector, cutting tool, and force sensor. End-effector stiffness is computed using the virtual joint method based on the Jacobian matrix, enabling accurate analysis of stiffness distribution within the robot’s workspace. Joint stiffness is experimentally identified through laser tracker-based displacement measurements under controlled loads and calculated using a least-squares method. The results show displacement errors below 0.3 mm and joint stiffness estimation errors under 1.5%, with values more consistent and stable than those reported for typical surgical robots. Simulation studies reveal spatial variations in operational stiffness, identifying zones of low stiffness and excessive stiffness. Compared to prior studies where stiffness varied over 50%, the proposed model exhibits superior uniformity. Experimental validation confirms model fidelity, with prediction errors generally below 5%. Cutting experiments on porcine femurs demonstrate real-world applicability, achieving average stiffness prediction errors below 3%, and under 1% in key directions. The model supports stiffness-aware trajectory planning and control, reducing cutting deviation by up to 10% and improving workspace stiffness stability by 30%. This research offers a validated, high-accuracy approach to stiffness modeling for surgical robots, bridging the gap between simulation and clinical application, and providing a foundation for safer, more precise robotic orthopedic procedures. Full article

The Stewart-platform-based bumper plays a critical role in shipborne strap-down inertial navigation systems (SINSs), effectively mitigating shock-induced disturbances to ensure measurement accuracy. Dynamic modeling for the bumper under a huge impact is a key issue in predicting the shock isolation performance of the bumper. In this paper, the dynamic modeling of shock isolation performance for Stewart-platform-based bumpers under huge impacts is proposed and validated experimentally. Firstly, a model of a Stewart-platform-based bumper is established considering the geometric configuration and dynamic parameters of the bumper by calculating the Jacobian matrix, stiffness matrix, damping matrix and mass matrix. Secondly, an analytic simulation of the impact is presented based on the measured impact acceleration, and the impact force on the load is derived according to the non-displacement assumption in the impact stage. Then, the Lagrangian formulation was systematically applied to establish governing equations characterizing the six-degree-of-freedom (DOF) dynamics of the bumper, incorporating both inertial coupling effects and nonlinear shock energy dissipation mechanisms. Afterwards, dynamic equations were solved via the Runge–Kutta method to obtain the theoretical results. Finally, the proposed dynamic modeling and shock isolation performance analysis method was validated via impact experiments for the bumper. Full article

Harmonic functions are renowned for their application in the analysis of minimal surfaces. These functions are also very important in applied mathematics. Any harmonic function in the open unit disk $\mathbb{U}=\left\{z\in \mathbb{C}:\left|z\right|<1\right\}$ can be written as a sum $f=h+\overline{g}$, where h and g are analytic functions in $\mathbb{U}$ and are called the analytic part and the co-analytic part of f, respectively. In this paper, the harmonic shear $f=h+\overline{g}\in S_{\mathcal{H}}$ and its rotation $f^{\mu }$ by $\mu \left(\mu \in \mathbb{C},\left|\mu \right|=1\right)$ are considered. Bounds are established for this rotation $f^{\mu }$, specific inequalities that define the Jacobian of $f^{\mu }$ are obtained, and the integral representation is determined. Full article

The river chief system (RCS) has been progressively integrated into rural river governance, resulting in notable improvements in river environments. However, the governance involves multiple stakeholders with conflicting interests and challenges, including low efficiency in collaborative governance. Based on evolutionary game theory, this paper explores the strategy evolution mechanism of multiple stakeholders in rural river governance under the RCS. A four-party evolutionary game model is constructed, involving the government, rural river chiefs, functional organizations, and villagers. By employing phase diagrams, Jacobian matrices, and Lyapunov’s first method, we investigate the evolutionary process of the four-party game and analyze its asymptotic stability. The study identifies the following two evolutionary stable strategies: lenient supervision, no patrol, governance, and participation and lenient supervision, no patrol, governance, and non-participation. Then, numerical simulation analysis is conducted using MATLAB 2024b to validate the scientific rigor and effectiveness of the evolutionary game model and analyze the impact of key parameters’ changes on the strategy choices of each stakeholder. The findings provide guidance for improving the efficiency of multi-stakeholder collaboration in rural river governance and the smooth implementation of the RCS in rural areas. Full article

In this paper, we study the optimality conditions and perform a stability analysis for the second-order cone constrained variational inequalities (SOCCVI) problem. The Lagrange function and Karush–Kuhn–Tucker (KKT) condition of the SOCCVI problem is given, and the optimality conditions for the SOCCVI problem are studied. Then, the second-order sufficient condition satisfying the constrained nondegenerate condition is proved. The strong second-order sufficient condition is defined. And the nonsingularity of Clarke’s generalized Jacobian of the KKT point, the strong regularity of the KKT point, the uniform second-order growth condition, the strong stability of the KKT point, and the local Lipschtiz homeomorphism of the KKT point for the SOCCVI problem are proved to be equivalent to each other. Then, the stability theorem of the SOCCVI problem is obtained. Full article

The local convergence analysis of a two-step vectorial method of accelerators with order five has been shown previously. But the convergence order five is obtained using Taylor series and assumptions on the existence of at least the fifth derivative of the mapping involved, which is not present in the method. These assumptions limit the applicability of the method. Moreover, a priori error estimates or the radius of convergence or uniqueness of the solution results have not been given. All these concerns are addressed in this paper. Furthermore, the more challenging semi-local convergence analysis, not previously studied, is presented using majorizing sequences. The convergence for both analyses depends on the generalized continuity of the Jacobian of the mapping involved, which is used to control it and sharpen the error distances. Numerical examples validate the sufficient convergence conditions presented in the theory. Full article

The planar parallel robots are widely employed in industrial applications due to simple geometry, few linkage interferences, and a large, reachable workspace. The symmetric geometry can bring significant convenience to parallel robots. The complexity of the mathematic models can be simplified since only one calculation method can be proposed to deal with various kinematic limbs in a parallel manipulator. The symmetric geometry can ease the assembly and maintenance procedures due to the modular design of linkages/joints. A novel 2-translation and 1-rotation (2T1R) parallel robot with symmetric geometry is proposed in this research. There is one closed loop in each kinematic limb, and 18 revolute joints are applied in its planar structure. Both the inverse and direct kinematic models are explored. The first-order relationship between robot inputs and outputs are constructed. Various singularity configurations are obtained based on the Jacobian matrix. The reachable workspace is resolved by the discrete spatial searching methodology, followed by the impacts originating from various linkages. The dexterity analysis of the parallel robot is conducted. Full article