Pub Date : 2024-10-05DOI: 10.1016/j.apm.2024.115740
In this research, a total Lagrangian Galerkin free element method (GFrEM) is proposed for the analysis of finite deformation in hyperelastic materials. This method derives the total Lagrangian formulation using the initial configuration as the reference. The mechanical behavior of hyperelastic materials is modeled by the non-Hookean strain energy function. Since Lagrangian isoparametric elements are freely formed in GFrEM by collocation nodes with their surrounding nodes, intrinsic boundary conditions can be imposed simply as in the finite elements method. In addition, the Galerkin method was used to ensure the stability of the results when constructing the equations for each collocation node. The validity and convergence of the proposed method are verified by several two- and three-dimensional numerical examples that include bending, compression, and torsion of hyperelastic materials. The example of nearly incompressible material shows that GFrEM remains highly accurate even with large deformations where the FEM cannot converge.
{"title":"A total Lagrangian Galerkin free element method for finite deformation in hyperelastic materials","authors":"","doi":"10.1016/j.apm.2024.115740","DOIUrl":"10.1016/j.apm.2024.115740","url":null,"abstract":"<div><div>In this research, a total Lagrangian Galerkin free element method (GFrEM) is proposed for the analysis of finite deformation in hyperelastic materials. This method derives the total Lagrangian formulation using the initial configuration as the reference. The mechanical behavior of hyperelastic materials is modeled by the non-Hookean strain energy function. Since Lagrangian isoparametric elements are freely formed in GFrEM by collocation nodes with their surrounding nodes, intrinsic boundary conditions can be imposed simply as in the finite elements method. In addition, the Galerkin method was used to ensure the stability of the results when constructing the equations for each collocation node. The validity and convergence of the proposed method are verified by several two- and three-dimensional numerical examples that include bending, compression, and torsion of hyperelastic materials. The example of nearly incompressible material shows that GFrEM remains highly accurate even with large deformations where the FEM cannot converge.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-05DOI: 10.1016/j.apm.2024.115731
This work focuses on investigating the optimal design of composite sandwich plates (FCSPs) with a viscoelastic square honeycomb core (VSHC). Firstly, using the cross-fill theory, the complex modulus technique, the first-order shear deformation theory, the minimum strain energy principle, and the Newmark-β method, a theoretical model of the VSHC-FCSPs under half-sine pulse excitation is formulated to calculate the inherent frequencies, the peak and vibration decay time of the transient response in time domain. The peak and vibration decay time are taken as the indexes of the anti-vibration performance. Considering an index of structural stiffness performance, the average value of the inherent frequencies is adopted to calculate the overall stiffness. After a set of literature validations and optimization validations, the multi-objective genetic algorithm is employed to study the optimization issue of VSHC-FCSPs. The optimization objectives are to minimize the three design variables of the transient response peak, vibration decay time, and reciprocal of overall stiffness. Then, the fiber laying angle of each layer, the core thickness ratio and the modulus ratio are assumed as optimization variables. Finally, the results with good vibration resistance and structural stiffness in the Pareto front are chosen as references, and these corresponding variations of the design variables and optimization objectives are obtained. The optimization results have revealed that the optimization variables corresponding to the intermediate points should be selected as references to improve the anti-vibration capacity and ensure the structural stiffness performance.
{"title":"Optimal design of vibration resistance of fiber-reinforced composite sandwich plates embedded in a viscoelastic square honeycomb core","authors":"","doi":"10.1016/j.apm.2024.115731","DOIUrl":"10.1016/j.apm.2024.115731","url":null,"abstract":"<div><div>This work focuses on investigating the optimal design of composite sandwich plates (FCSPs) with a viscoelastic square honeycomb core (VSHC). Firstly, using the cross-fill theory, the complex modulus technique, the first-order shear deformation theory, the minimum strain energy principle, and the Newmark-<em>β</em> method, a theoretical model of the VSHC-FCSPs under half-sine pulse excitation is formulated to calculate the inherent frequencies, the peak and vibration decay time of the transient response in time domain. The peak and vibration decay time are taken as the indexes of the anti-vibration performance. Considering an index of structural stiffness performance, the average value of the inherent frequencies is adopted to calculate the overall stiffness. After a set of literature validations and optimization validations, the multi-objective genetic algorithm is employed to study the optimization issue of VSHC-FCSPs. The optimization objectives are to minimize the three design variables of the transient response peak, vibration decay time, and reciprocal of overall stiffness. Then, the fiber laying angle of each layer, the core thickness ratio and the modulus ratio are assumed as optimization variables. Finally, the results with good vibration resistance and structural stiffness in the Pareto front are chosen as references, and these corresponding variations of the design variables and optimization objectives are obtained. The optimization results have revealed that the optimization variables corresponding to the intermediate points should be selected as references to improve the anti-vibration capacity and ensure the structural stiffness performance.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-04DOI: 10.1016/j.apm.2024.115729
Objective
This paper addresses the carrier landing affected by airwake, parametric uncertainties, and carrier deck motion, its main target being the design of a novel sliding mode based automatic carrier landing system to obtain accurate tracking of the reference trajectory, robustness in terms of disturbances and uncertainties, as well as excellent touchdown accuracy.
Approach
For an aircraft nonlinear dynamics, written under a four-stage cascaded strict feedback form, the design of the novel landing control architecture involves the design of a guidance subsystem, robust sliding mode controllers (for the control of the heading angle, attitude angles, and angular rates), an approach power compensation system, adaptive control laws suppressing the uncertainties and disturbances, a Kalman filter for deck motion prediction, a block computing the reference trajectory, a tracking differentiator block for deck motion compensation, and first-order command filters.
Main results
The software validation process proves the effectiveness of the sliding mode based control scheme and the suppression of the uncertainties and disturbances. Also, the comparison between the performances of the sliding mode control based carrier landing system and the ones associated to other automatic carrier landing systems shows the superiority of the sliding mode based control scheme, as well as its better touchdown accuracy and landing success rate.
Significance
This study innovatively transforms the general carrier landing problem into a time-varying tracking control problem for cascaded strict feedback dynamics with disturbances and uncertainties. The new designed automatic carrier landing system is the first control architecture in the literature employing the sliding mode control augmented by adaptive control laws for carrier landing, subjected to airwake, deck motion, and uncertainties.
{"title":"Four-stage cascaded adaptive sliding mode control for automatic carrier landing with airwake disturbances and uncertainties","authors":"","doi":"10.1016/j.apm.2024.115729","DOIUrl":"10.1016/j.apm.2024.115729","url":null,"abstract":"<div><h3>Objective</h3><div>This paper addresses the carrier landing affected by airwake, parametric uncertainties, and carrier deck motion, its main target being the design of a novel sliding mode based automatic carrier landing system to obtain accurate tracking of the reference trajectory, robustness in terms of disturbances and uncertainties, as well as excellent touchdown accuracy.</div></div><div><h3>Approach</h3><div>For an aircraft nonlinear dynamics, written under a four-stage cascaded strict feedback form, the design of the novel landing control architecture involves the design of a guidance subsystem, robust sliding mode controllers (for the control of the heading angle, attitude angles, and angular rates), an approach power compensation system, adaptive control laws suppressing the uncertainties and disturbances, a Kalman filter for deck motion prediction, a block computing the reference trajectory, a tracking differentiator block for deck motion compensation, and first-order command filters.</div></div><div><h3>Main results</h3><div>The software validation process proves the effectiveness of the sliding mode based control scheme and the suppression of the uncertainties and disturbances. Also, the comparison between the performances of the sliding mode control based carrier landing system and the ones associated to other automatic carrier landing systems shows the superiority of the sliding mode based control scheme, as well as its better touchdown accuracy and landing success rate.</div></div><div><h3>Significance</h3><div>This study innovatively transforms the general carrier landing problem into a time-varying tracking control problem for cascaded strict feedback dynamics with disturbances and uncertainties. The new designed automatic carrier landing system is the first control architecture in the literature employing the sliding mode control augmented by adaptive control laws for carrier landing, subjected to airwake, deck motion, and uncertainties.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.apm.2024.115747
The contact impact problem in planar multibody systems can be efficiently solved by formulating it as the linear complementarity problem, which requires a complex modeling process. To simplify the process, a recursive algorithm for the dynamics of planar multibody systems with frictional unilateral constraints is proposed based on the reduced multibody system transfer matrix method. Firstly, the contact forces of frictional unilateral constraints are integrated into the recurrence relations of system components using Lagrange multipliers. Subsequently, the relative motion equations of the contact positions are discretized in time, which are then utilized to describe the linear complementarity problem for systems. The dynamics of the system is solved by the Moreau time-stepping method with the recursive method. Finally, the proposed algorithm was validated using the woodpecker toy and used to model a slider-crank mechanism with clearance, which shows its characteristics of facilitating modeling, universal, and highly programmable. This recursive algorithm provides an effective tool for solving non-smooth planar multibody systems while extending the application of the multibody system transfer matrix method.
{"title":"A recursive algorithm for dynamics of planar multibody systems with frictional unilateral constraints","authors":"","doi":"10.1016/j.apm.2024.115747","DOIUrl":"10.1016/j.apm.2024.115747","url":null,"abstract":"<div><div>The contact impact problem in planar multibody systems can be efficiently solved by formulating it as the linear complementarity problem, which requires a complex modeling process. To simplify the process, a recursive algorithm for the dynamics of planar multibody systems with frictional unilateral constraints is proposed based on the reduced multibody system transfer matrix method. Firstly, the contact forces of frictional unilateral constraints are integrated into the recurrence relations of system components using Lagrange multipliers. Subsequently, the relative motion equations of the contact positions are discretized in time, which are then utilized to describe the linear complementarity problem for systems. The dynamics of the system is solved by the Moreau time-stepping method with the recursive method. Finally, the proposed algorithm was validated using the woodpecker toy and used to model a slider-crank mechanism with clearance, which shows its characteristics of facilitating modeling, universal, and highly programmable. This recursive algorithm provides an effective tool for solving non-smooth planar multibody systems while extending the application of the multibody system transfer matrix method.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.apm.2024.115735
The general solution of elasticity for plane anisotropic beams with arbitrary constraints at ends and arbitrary normal and tangential distributed loads on surfaces is derived, which consists of internal forces (i.e., bending moment, shearing force, axial force) and their integrals and derivatives of different orders and load-independent polynomial function sequences of longitudinal coordinates. The method for determining the function sequences is established by resolving the governing equation and boundary conditions of the stress function method. For beams with an elastic symmetry plane, a method for directly determining explicit expressions for all terms of function sequences is provided. Particular solutions of examples are solved using general solution formulas, and the results align excellently with existing exact solutions. Finally, the errors in EBT and TBT when applied to beams made of different materials are analysed.
{"title":"Exact solutions for anisotropic beams with arbitrary distributed loads","authors":"","doi":"10.1016/j.apm.2024.115735","DOIUrl":"10.1016/j.apm.2024.115735","url":null,"abstract":"<div><div>The general solution of elasticity for plane anisotropic beams with arbitrary constraints at ends and arbitrary normal and tangential distributed loads on surfaces is derived, which consists of internal forces (i.e., bending moment, shearing force, axial force) and their integrals and derivatives of different orders and load-independent polynomial function sequences of longitudinal coordinates. The method for determining the function sequences is established by resolving the governing equation and boundary conditions of the stress function method. For beams with an elastic symmetry plane, a method for directly determining explicit expressions for all terms of function sequences is provided. Particular solutions of examples are solved using general solution formulas, and the results align excellently with existing exact solutions. Finally, the errors in EBT and TBT when applied to beams made of different materials are analysed.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.apm.2024.115736
Existing deep nonnegative matrix factorization-based approaches treat shallow and deep layers equally or with similar strategies, neglecting the heterogeneous physical structures between the shallow and progressively deeper layers, thus failing to explore the latent different sub-manifold structures in the hyperspectral image. In this paper, we propose a deep nonnegative matrix factorization model with bidirectional constraints to achieve hyperspectral unmixing. The sub-manifold structures in hyperspectral image are fully exploited by filtering and penalizing the shallow abundance layer with a denoised regularizer and a manifold regularizer. In contrast to the shallow abundance layer, the remaining layers are constrained by an extremely common regularizer to avoid over-denoising and maintain fidelity. In this way, the fine cues between different substances are exploited to a large extent. Additionally, the overall reconstruction error can be well controlled because the performance of the designed feedback mechanism can be fine-tuned by the inverse hierarchical constraints. Finally, we employ Nesterov's optimal gradient method to solve the optimization problem effectively. Experiment results are conducted on both synthetic datasets and real datasets, and all results show that the proposed method is superior to recent canonical unmixing methods.
{"title":"Deep bidirectional hierarchical matrix factorization model for hyperspectral unmixing","authors":"","doi":"10.1016/j.apm.2024.115736","DOIUrl":"10.1016/j.apm.2024.115736","url":null,"abstract":"<div><div>Existing deep nonnegative matrix factorization-based approaches treat shallow and deep layers equally or with similar strategies, neglecting the heterogeneous physical structures between the shallow and progressively deeper layers, thus failing to explore the latent different sub-manifold structures in the hyperspectral image. In this paper, we propose a deep nonnegative matrix factorization model with bidirectional constraints to achieve hyperspectral unmixing. The sub-manifold structures in hyperspectral image are fully exploited by filtering and penalizing the shallow abundance layer with a denoised regularizer and a manifold regularizer. In contrast to the shallow abundance layer, the remaining layers are constrained by an extremely common regularizer to avoid over-denoising and maintain fidelity. In this way, the fine cues between different substances are exploited to a large extent. Additionally, the overall reconstruction error can be well controlled because the performance of the designed feedback mechanism can be fine-tuned by the inverse hierarchical constraints. Finally, we employ Nesterov's optimal gradient method to solve the optimization problem effectively. Experiment results are conducted on both synthetic datasets and real datasets, and all results show that the proposed method is superior to recent canonical unmixing methods.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-02DOI: 10.1016/j.apm.2024.115734
In recent years, there has been a lot of interest in exploiting the bistable behavior of snap-through systems to harvest energy from vibration sources. The efficient operation of any bistable VEH depends on its ability to exhibit large-amplitude interwell motion. Under weak ambient excitation, bistable VEH performs marginally because of the confinement of motion to a single well. Frequency up-conversion, multi-stability, and adaptive techniques are some of the performance enhancement strategies suggested for bistable-VEH. Considering the VEH's space constraints, the above designs are hard to implement in practical cases. This study introduces an inertial amplification mechanism (IAM) as a simple passive strategy to enhance the performance of a snap-through VEH, a concept not explored in previous studies. The addition of IAM increases the effective mass without increasing the physical mass and thereby enhances energy harvesting, especially from weak ambient excitation sources. The dynamics and performance of the enhanced snap-through VEH are investigated analytically and numerically under harmonic and random excitations. The harmonic balance method (HBM) derives the frequency-amplitude relationship, which shows a hardening behavior and an increase in bandwidth. The effective potential method provides a closed-form expression for the joint probability density function (Joint PDF), which is governed by the Fokker-Planck equation. The joint PDF shows a transition from bimodal to unimodal with an increase in the value of the geometrical parameter. The stochastic averaging method is employed to obtain the stationary probability density function, which defines the long-term dynamics of the VEH. The effects of noise intensity, mass ratio, and inertial amplifier angle on the dynamics are investigated. Finally, the performance of the proposed VEH is compared with a conventional snap-through VEH, an equivalent linear VEH, and a multistable VEH under harmonic and random excitation conditions. The findings suggest that the snap-through VEH with the IAM has advantages over the linear and multistable nonlinear VEH in terms of extracting energy from low-intensity harmonic and random excitation sources. This simple augmentation strategy preserves the original system's bistability, eliminating the need for the complex design of a multistable VEH.
{"title":"Inertial amplification as a performance enhancement method for snap-through vibration energy harvester","authors":"","doi":"10.1016/j.apm.2024.115734","DOIUrl":"10.1016/j.apm.2024.115734","url":null,"abstract":"<div><div>In recent years, there has been a lot of interest in exploiting the bistable behavior of snap-through systems to harvest energy from vibration sources. The efficient operation of any bistable VEH depends on its ability to exhibit large-amplitude interwell motion. Under weak ambient excitation, bistable VEH performs marginally because of the confinement of motion to a single well. Frequency up-conversion, multi-stability, and adaptive techniques are some of the performance enhancement strategies suggested for bistable-VEH. Considering the VEH's space constraints, the above designs are hard to implement in practical cases. This study introduces an inertial amplification mechanism (IAM) as a simple passive strategy to enhance the performance of a snap-through VEH, a concept not explored in previous studies. The addition of IAM increases the effective mass without increasing the physical mass and thereby enhances energy harvesting, especially from weak ambient excitation sources. The dynamics and performance of the enhanced snap-through VEH are investigated analytically and numerically under harmonic and random excitations. The harmonic balance method (HBM) derives the frequency-amplitude relationship, which shows a hardening behavior and an increase in bandwidth. The effective potential method provides a closed-form expression for the joint probability density function (Joint PDF), which is governed by the Fokker-Planck equation. The joint PDF shows a transition from bimodal to unimodal with an increase in the value of the geometrical parameter. The stochastic averaging method is employed to obtain the stationary probability density function, which defines the long-term dynamics of the VEH. The effects of noise intensity, mass ratio, and inertial amplifier angle on the dynamics are investigated. Finally, the performance of the proposed VEH is compared with a conventional snap-through VEH, an equivalent linear VEH, and a multistable VEH under harmonic and random excitation conditions. The findings suggest that the snap-through VEH with the IAM has advantages over the linear and multistable nonlinear VEH in terms of extracting energy from low-intensity harmonic and random excitation sources. This simple augmentation strategy preserves the original system's bistability, eliminating the need for the complex design of a multistable VEH.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.apm.2024.115727
This study focuses on achieving optimal consensus control based on the state-dependent Riccati equation (SDRE) in multi-agent systems (MASs) characterized by the interconnectivity of multiple sub-systems with physical interconnections. The objective is to establish a suitable communication topology among the MAS controllers that considers both local and global objectives while ensuring stability through distributed control. To address this, an innovative extension of leader-follower and leaderless consensus control methodologies is proposed, accompanied by stability analysis employing the Lyapunov method. Additionally, the paper explores consensus control for dynamically interconnected MASs handling suspended load transportation, such as multi-lift systems. By utilizing the principles of virtual work by D'Alembert and Gauss's principle of least constraint, a constrained multibody system model is developed, incorporating the Udwadia-Kalaba motion equation approach. Simulation results and theoretical analysis validate the efficiency and performance of the proposed consensus controller structure.
本研究的重点是在多智能体系统（MAS）中实现基于状态相关里卡提方程（SDRE）的最优共识控制，该系统的特点是多个子系统具有物理互连性。目标是在 MAS 控制器之间建立合适的通信拓扑结构，既考虑局部目标和全局目标，又通过分布式控制确保稳定性。为此，本文提出了领导者-追随者和无领导者共识控制方法的创新扩展，并利用 Lyapunov 方法进行了稳定性分析。此外，论文还探讨了处理悬挂负载运输的动态互联 MAS（如多电梯系统）的共识控制。利用达朗贝尔的虚拟工作原理和高斯的最小约束原理，结合 Udwadia-Kalaba 运动方程方法，建立了一个约束多体系统模型。仿真结果和理论分析验证了所提出的共识控制器结构的效率和性能。
{"title":"Optimal consensus control of dynamically interconnected multi-agent systems: A SDRE approach for efficient and stable operation","authors":"","doi":"10.1016/j.apm.2024.115727","DOIUrl":"10.1016/j.apm.2024.115727","url":null,"abstract":"<div><div>This study focuses on achieving optimal consensus control based on the state-dependent Riccati equation (SDRE) in multi-agent systems (MASs) characterized by the interconnectivity of multiple sub-systems with physical interconnections. The objective is to establish a suitable communication topology among the MAS controllers that considers both local and global objectives while ensuring stability through distributed control. To address this, an innovative extension of leader-follower and leaderless consensus control methodologies is proposed, accompanied by stability analysis employing the Lyapunov method. Additionally, the paper explores consensus control for dynamically interconnected MASs handling suspended load transportation, such as multi-lift systems. By utilizing the principles of virtual work by D'Alembert and Gauss's principle of least constraint, a constrained multibody system model is developed, incorporating the Udwadia-Kalaba motion equation approach. Simulation results and theoretical analysis validate the efficiency and performance of the proposed consensus controller structure.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.apm.2024.115737
The wheel-legged robots combine efficient and fast wheeled locomotion with the terrain-adaptive legged locomotion. Inspired by reinforcement learning and adaptive dynamic programming, a novel dynamic optimal balance control method is proposed for wheel-legged robots on uneven terrains. First, the virtual leg length is solved according to the kinematics model of the five-link closed-chain mechanism. In addition, a simplified wheel-legged spring-loaded inverted pendulum model is established to determine the linear state-space expression of the floating-base, virtual leg, and driving wheel. Second, a fast iterative algorithm built upon adaptive dynamic programming and optimal gain matrix is introduced. Using the initial gain matrix and an initial state vector, the online policy iteration learns the initial state data set generated by external disturbances, and the steps of policy evaluation and policy improvement are repeatedly implemented by Kleinman's algorithm. Subsequently, the virtual support force is controlled by the composite control framework for the length of the virtual leg with spring-damping characteristics and roll angle. The input torque for each hip joint is calculated using the virtual model control mapping technology. Finally, the robustness and adaptability of the proposed framework are verified through simulations. This paper presents a novel control method for the future application of wheel-legged robot in complex scenarios.
{"title":"A novel adaptive dynamic optimal balance control method for wheel-legged robot","authors":"","doi":"10.1016/j.apm.2024.115737","DOIUrl":"10.1016/j.apm.2024.115737","url":null,"abstract":"<div><div>The wheel-legged robots combine efficient and fast wheeled locomotion with the terrain-adaptive legged locomotion. Inspired by reinforcement learning and adaptive dynamic programming, a novel dynamic optimal balance control method is proposed for wheel-legged robots on uneven terrains. First, the virtual leg length is solved according to the kinematics model of the five-link closed-chain mechanism. In addition, a simplified wheel-legged spring-loaded inverted pendulum model is established to determine the linear state-space expression of the floating-base, virtual leg, and driving wheel. Second, a fast iterative algorithm built upon adaptive dynamic programming and optimal gain matrix is introduced. Using the initial gain matrix and an initial state vector, the online policy iteration learns the initial state data set generated by external disturbances, and the steps of policy evaluation and policy improvement are repeatedly implemented by Kleinman's algorithm. Subsequently, the virtual support force is controlled by the composite control framework for the length of the virtual leg with spring-damping characteristics and roll angle. The input torque for each hip joint is calculated using the virtual model control mapping technology. Finally, the robustness and adaptability of the proposed framework are verified through simulations. This paper presents a novel control method for the future application of wheel-legged robot in complex scenarios.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-30DOI: 10.1016/j.apm.2024.115730
Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an “interface-enlarging” phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations.
近几十年来，多孔复合材料受到越来越多的关注。本研究开发了一种在规定应力约束下的并行多尺度拓扑优化（CMTO）方法，用于设计具有多域微结构的多孔复合材料。首先，为了解决在整个优化过程中由于微结构类型的变化而导致的局部应力预测困难，提出了一种连续可微的应力测量方法，以有效逼近局部应力。其次，开发了一种基于等几何分析（IGA）的反均质化方法，以提高应力预测的准确性，然后将其集成到基于离散材料优化（DMO）插值方案开发的 CMTO 中。第三，提出了一种与宏观和微观设计变量都可微分的应力约束，以实现宏观结构配置、微观结构配置和分布的应力约束并行优化。第四，建立了一种新颖的后处理方法，以实现具有布局的单元尺寸轮廓的平滑和体积保全。最后，在全局应力约束下，使用所提出的 CMTO 实现了两个基准设计实例，即 l 型支架和裂缝问题，以证明所提方法的有效性。结果表明，所提出的方法可以通过三种设计方式（即宏观结构配置、微观结构配置和分布）有效降低应力集中。此外，在应力约束考虑的情况下，还有趣而合理地发现了 "界面扩大 "现象。
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