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Keywords = Lagrangian mechanics

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20 pages, 5352 KB  
Article
Numerical Investigation of the Effect of Bar Design on the Retention Efficiency of Wastewater Bar Screens
by Loubna En-Nabety and El Mostapha Boudi
Eng 2026, 7(5), 229; https://doi.org/10.3390/eng7050229 - 11 May 2026
Viewed by 331
Abstract
Mechanical bar screens serve as the initial treatment stage used to catch insoluble and coarse debris from wastewater flow. They are essential equipment that ensures the protection and efficient operation of downstream facilities. Different parameters affect the performance of bar screens, including particle [...] Read more.
Mechanical bar screens serve as the initial treatment stage used to catch insoluble and coarse debris from wastewater flow. They are essential equipment that ensures the protection and efficient operation of downstream facilities. Different parameters affect the performance of bar screens, including particle size, flow hydraulics, and screen design. Most previous studies have primarily focused on bar screens with rectangular bars and single-phase flow. However, investigating different bar shapes with the presence of waste debris as a second phase is crucial for achieving the optimal design and accurately predicting a bar screen’s efficiency. Therefore, four bar cross-section shapes were examined using 3D simulations of two-phase flow (water and particles). The discrete phase model (DPM) in ANSYS Fluent CFD software was used to represent waste particles in a Lagrangian framework and to evaluate their retention efficiency. The numerical results, validated by a previous study of a wastewater bar screen, indicate that the traditional rectangular bar shape traps a higher rate of debris but results in higher pressure losses. Alternative bar shapes, such as rounded, streamlined, and teardrop cross-sections, have been studied for design improvements. The improved teardrop shape presents significant effectiveness, offering a better balance between pressure loss reduction and enhanced particle separation efficiency. Based on this study, further investigations coupling CFD techniques with the particle tracking method can be carried out for the optimal design of other filtration equipment. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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26 pages, 2766 KB  
Article
Hierarchical Adaptive PID Tuning for Agile Flight: A Safety-Constrained Reinforcement Learning Approach
by Zhong Tian, Sen Hu, Hao Fu, Weiyu Zhu and Bangchu Zhang
Aerospace 2026, 13(5), 446; https://doi.org/10.3390/aerospace13050446 - 9 May 2026
Viewed by 188
Abstract
Multirotor unmanned aerial vehicles (UAVs) suffer from significant control performance degradation during aggressive maneuvers, primarily due to aerodynamic nonlinearities and coupling effects. Conventional fixed-gain PID controllers struggle to simultaneously satisfy performance and robustness requirements across the wide flight envelope. To address this challenge, [...] Read more.
Multirotor unmanned aerial vehicles (UAVs) suffer from significant control performance degradation during aggressive maneuvers, primarily due to aerodynamic nonlinearities and coupling effects. Conventional fixed-gain PID controllers struggle to simultaneously satisfy performance and robustness requirements across the wide flight envelope. To address this challenge, this paper presents a novel hierarchical safety-constrained reinforcement learning (RL) framework for adaptive PID tuning: the inner loop employs fixed gains, the outer loop leverages proximal policy optimization (PPO) for online adaptive gain scheduling, and linear matrix inequality (LMI) constraints delineate robust parameter boundaries for the adaptive exploration. Importantly, the LMI feasibility strictly guarantees theoretical stability for the fixed inner-loop parameters at the linearization vertices within a linear parameter-varying (LPV) framework. Concurrently, the online outer-loop RL stage is protected by safety boundaries and a Lagrangian penalty mechanism acting as an effective engineering safeguard rather than a rigorous global stability proof. Comprehensive high-fidelity simulation benchmarks demonstrate that, compared with a baseline fixed-gain PID controller, the proposed framework reduces overshoot by 18.5% in high-speed step responses and improves the overall mean RMSE by 15.0% across 100 randomized mixed-trajectory trials (with improvements of up to 40.9% in highly dynamic scenarios), yielding consistent gains in trajectory tracking accuracy and disturbance rejection despite uncertain model variations. By seamlessly blending control-theoretic hard constraints with RL-based soft-parameter tuning, the proposed architecture offers a safe and highly adaptive solution for large-envelope flight control, demonstrating strong engineering relevance. Full article
(This article belongs to the Section Aeronautics)
20 pages, 10258 KB  
Article
Humanoid Robot Walking and Grasping Method Using Similarity Reward-Augmented Generative Adversarial Imitation Learning
by Gen-Yong Huang and Wen-Feng Li
Sensors 2026, 26(9), 2756; https://doi.org/10.3390/s26092756 - 29 Apr 2026
Viewed by 460
Abstract
This study aims to enhance the precision of humanoid robots in imitating complex human “walking–grasping” coordinated movements. Addressing limitations in sample efficiency and reward function design in Generative Adversarial Imitation Learning (GAIL), we propose the Similarity Reward-Augmented Generative Adversarial Imitation Learning (SRA-GAIL) framework. [...] Read more.
This study aims to enhance the precision of humanoid robots in imitating complex human “walking–grasping” coordinated movements. Addressing limitations in sample efficiency and reward function design in Generative Adversarial Imitation Learning (GAIL), we propose the Similarity Reward-Augmented Generative Adversarial Imitation Learning (SRA-GAIL) framework. The method integrates plantar thin-film resistive pressure sensors to measure the real-time pressure distribution at four key points on both feet, combined with roll/pitch angle data acquired from JY901S inertial measurement units (IMUs). A Lagrangian constraint optimization strategy is employed to achieve gait stability control based on the zero moment point (ZMP). Simultaneously, a visual similarity evaluation module is established using human demonstration trajectories captured by a Logitech C920E camera, augmented by grip force feedback from flexible thin-film pressure sensors on the hands. This enables the design of a multimodal sensor-fused similarity reward function. By incorporating Lagrangian constraint optimization and a maximum entropy reinforcement learning framework, Similarity Reward-Augmented Generative Adversarial Imitation Learning synchronously optimizes gait stability control—guided by zero moment point (ZMP) and roll/pitch data—and vision-based trajectory similarity evaluation. These components address motion stability constraints and trajectory similarity metrics, respectively, generating biomechanically plausible gait strategies. A spatiotemporal attention mechanism parses human motion trajectory features to drive the end-effector for high-precision trajectory tracking. To validate the proposed method, an imitation learning experimental system was constructed on a physical XIAOLI humanoid robot platform, integrating inertial measurement units (IMUs), plantar pressure sensors, and a vision system. Quantitative evaluations were conducted across multiple dimensions, including robot platform analysis, walking stability, object grasping success rates, and end-effector trajectory similarity. The results demonstrate that, compared to Generative Adversarial Imitation Learning (GAIL) and behavioral cloning, Similarity Reward-Augmented Generative Adversarial Imitation Learning achieves a stable object grasping success rate of 93.7% in complex environments, with a 23.8% improvement in sample efficiency. The method maintains a 96.5% compliance rate for zero moment point (ZMP) trajectories within the support polygon, significantly outperforming baseline approaches. This effectively addresses the bottleneck in robot policies adapting to dynamic changes in real-world environments. Full article
(This article belongs to the Special Issue AI for Sensor-Based Robotic Object Perception)
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26 pages, 11902 KB  
Article
Structural Analysis of Sargassum Floating Net-Barrage
by Frédéric Muttin
J. Mar. Sci. Eng. 2026, 14(9), 803; https://doi.org/10.3390/jmse14090803 - 28 Apr 2026
Viewed by 363
Abstract
Public health suffers from noxious gas emitted by massive beached Sargassum algae. Net-barrages deployed in near-shore seas can contain Sargassum, provided they efficiently resist the additional hydrodynamic pressure induced by the catch. Nowadays, the design and installation of net-barrages are empiric. Structural [...] Read more.
Public health suffers from noxious gas emitted by massive beached Sargassum algae. Net-barrages deployed in near-shore seas can contain Sargassum, provided they efficiently resist the additional hydrodynamic pressure induced by the catch. Nowadays, the design and installation of net-barrages are empiric. Structural breaks and anchor and mooring chain drifts can arise. We provide a mechanical model to evaluate stresses and loads on a structure made of fishing nets and buoy moorings. Hydrodynamic uncertainties occur through catches, fouling and sea current amplitudes appearing in lagoons or sheltered bays. This study presents a non-linear four-node finite-element model for continuous elastic membranes undergoing large displacements and small strains. The model relies on the Lagrangian linearly elastic membrane theory, employing the non-linear Green strain tensor and a non-updated hydrodynamic loading. We study forcings fixed a priori on a netting section of barrage that is 50 m long and 1 m high with double layer, e.g., two net-faces. We consider low and moderate current velocities, 0.05 and 0.35 m∙s−1, while assuming specific vertical and horizontal catch pressures. A barrage installed in the reef lagoon at Le François on Martinique Island that is observable by satellite imagery could benefit of the computed net and mooring tensions. Full article
(This article belongs to the Section Marine Pollution)
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21 pages, 3281 KB  
Article
Moisture Transport and Recycling Shape Wetting and Drying Across China: Implications for Water Sustainability
by Chang Lu, Long Ma, Bolin Sun, Xing Huang and Tingxi Liu
Sustainability 2026, 18(9), 4252; https://doi.org/10.3390/su18094252 - 24 Apr 2026
Viewed by 192
Abstract
Global warming is reshaping the global dry–wet pattern, yet its future trajectory remains uncertain, with important implications for sustainable water resources. China, influenced by both the monsoon system and the mid-latitude westerlies, requires an integrated assessment linking net water balance (precipitation minus evaporation, [...] Read more.
Global warming is reshaping the global dry–wet pattern, yet its future trajectory remains uncertain, with important implications for sustainable water resources. China, influenced by both the monsoon system and the mid-latitude westerlies, requires an integrated assessment linking net water balance (precipitation minus evaporation, PME) to moisture transport. Here we use precipitation, evaporation, and air temperature records for 1981–2023, together with Lagrangian moisture tracking and precipitation recycling diagnostics, to quantify changes in PME across China and to identify the underlying mechanisms. We further assess future evolution under different warming levels (1.5 °C, 2 °C, and 3–4 °C) for 2024–2099 using a CMIP6 multi-model ensemble. China experienced a pronounced warming during the historical period, while precipitation declined overall and evaporation remained nearly stable. As a result, reduced moisture supply strengthened drought sensitivity. Spatially, warming-driven drying is concentrated in the eastern and southern monsoon regions. In contrast, the inland arid and semi-arid Northwest and parts of high-elevation transition zones show a relative shift toward warmer and wetter conditions. Moisture transport diagnostics indicate that China’s moisture supply is jointly sustained by the mid- to high-latitude westerlies and low-latitude oceanic monsoon pathways. These pathways form a continuous transition from the Northwest to the Southeast. Land–atmosphere recycling is stronger in the Southeast, whereas the Northwest depends more on imported moisture, with plateau topography further reshaping the main transport corridors. In the future, PME continues to decline under 1.5 °C warming. Under 2 °C warming, PME enters a transitional state with patchy regional patterns. Under 3–4 °C warming, PME shifts to an overall increase, but uncertainty becomes larger. These results identify a critical turning window at around 2–3 °C warming for China’s PME response, providing a physical basis for sustainable water-resource management and adaptation planning. Full article
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17 pages, 3320 KB  
Article
An Investigation into the Footing Profile Suppression in (110) Si Anisotropic Etching
by Zhishen Wang, Guoliang Xie, Gaowei Xu, Genzi Li, Weihu Zhou, Dongzhi Fu, Lingde Kong, Zhiwen Chen and Sheng Liu
Micromachines 2026, 17(5), 518; https://doi.org/10.3390/mi17050518 - 24 Apr 2026
Viewed by 255
Abstract
Deep Si trenches with vertical sidewalls are critical structures in advanced MEMS sensors and microfluidic devices. (110)-oriented Si is specifically required for this purpose, as its crystallographic geometry inherently provides the nearly 90° vertical {111} planes. However, achieving precise morphology on (110) Si [...] Read more.
Deep Si trenches with vertical sidewalls are critical structures in advanced MEMS sensors and microfluidic devices. (110)-oriented Si is specifically required for this purpose, as its crystallographic geometry inherently provides the nearly 90° vertical {111} planes. However, achieving precise morphology on (110) Si remains challenging due to the formation of unwanted V-shaped footing profiles at the bottom. This study establishes a systematically coupled experimental and numerical framework to investigate the anisotropic wet etching mechanism of (110) Si, quantifying the effects of KOH concentration (10–50 wt.%) and temperature (50–90 °C) on profile evolution. Experimental results demonstrate that 10 wt.% KOH at 70 °C yielded the most favorable morphology within the investigated range, with a minimized footing ratio (<2%). Based on these results, a dual-parameter kinetic regulation mechanism is proposed. Low concentration of KOH can minimize the crystallographic etching rate disparity (γ) between fast-etching {100}/{110} and slow-etching {111} planes, while the selected temperature helps maintain interfacial hydrodynamic stability. Furthermore, an Arbitrary Lagrangian-Eulerian (ALE)-based multiphysics model calibrated with Arrhenius kinetics was developed, which captures the overall trend of trench evolution and the dependence of footing formation on KOH concentration and temperature. This work not only provides a recommended process window for suppressing footing defects but also offers a trend-predictive simulation framework for orientation-dependent Si micromachining. Full article
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21 pages, 10271 KB  
Article
Kinetic Uncertainty in Hydrogen Jet Flames Using Lagrangian Particle Statistics
by Shuzhi Zhang, Vansh Sharma and Venkat Raman
Hydrogen 2026, 7(2), 56; https://doi.org/10.3390/hydrogen7020056 - 22 Apr 2026
Viewed by 374
Abstract
Hydrogen-enriched fuel injection in staged gas-turbine combustors is commonly achieved through jet-in-crossflow (JICF) configurations, where flame stabilization is governed by a local balance between flow-induced strain/mixing and chemical reaction rates. This work investigates turbulent reacting JICF relevant to staged combustion conditions using high-fidelity [...] Read more.
Hydrogen-enriched fuel injection in staged gas-turbine combustors is commonly achieved through jet-in-crossflow (JICF) configurations, where flame stabilization is governed by a local balance between flow-induced strain/mixing and chemical reaction rates. This work investigates turbulent reacting JICF relevant to staged combustion conditions using high-fidelity simulations with adaptive mesh refinement (AMR) and differential-diffusion effects together with Lagrangian particle statistics. Chemistry model uncertainties are incorporated by using a projection method that maps uncertainty estimates from detailed mechanisms into the model used in this work. Results show that the macroscopic flame topology remains in a stable two-branch regime (lee-stabilized and lifted) and is primarily controlled by the jet momentum–flux ratio J. Visualization of the normalized scalar dissipation rate reveals that the flame front resides on the low-dissipation side of intense mixing layers, occupying an intermediate region between over-strained and under-mixed regions. While hydrogen content does not significantly change the global stabilization mode for the cases studied, uncertainty analysis reveals composition-dependent differences that are not apparent in the mean behavior alone. In particular, visualization in Eulerian (χ, T) state-space analysis and particle statistics conditioned on the stoichiometric surface demonstrate that higher-hydrogen cases observe a lower scalar dissipation rate and exhibit substantially reduced variability in OH production under kinetic-parameter perturbations, whereas lower-hydrogen blends experience higher dissipation and amplified chemical sensitivity. These findings highlight that, even in globally similar JICF regimes, the hydrogen content can modify the local response of the flame to kinetic-parameter uncertainty, motivating uncertainty-aware interpretation and design for hydrogen-fueled staging systems. Full article
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23 pages, 5645 KB  
Article
A Theoretical Limit on Power Absorption in Variable-Shape Buoy Wave Energy Converters
by Mohammed Atallah and Ossama Abdelkhalik
J. Mar. Sci. Eng. 2026, 14(8), 737; https://doi.org/10.3390/jmse14080737 - 16 Apr 2026
Viewed by 311
Abstract
Despite the significant potential of ocean wave energy, the high cost of the generated power remains a major challenge. This highlights the need for innovative conceptual designs that enhance energy conversion while maintaining comparable implementation and installation costs. Recently, the concept of Variable-Shape [...] Read more.
Despite the significant potential of ocean wave energy, the high cost of the generated power remains a major challenge. This highlights the need for innovative conceptual designs that enhance energy conversion while maintaining comparable implementation and installation costs. Recently, the concept of Variable-Shape Buoy Wave Energy Converters (VSB WECs) was introduced that uses flexible buoy material. While many studies have demonstrated the improved performance of VSB WECs compared to Fixed-Shape Buoy Wave Energy Converters (FSB WECs) through numerical simulations, analytical validation is essential to support these findings. This paper presents an analytical derivation of the theoretical limit of power absorption for VSB WECs using the complex-conjugate criteria for the heave motion. In this study, a multi-degree-of-freedom (multi-DoF) VSB WEC model is developed using a thin spherical shell representation, incorporating Rayleigh–Ritz and Love approximations under the assumptions of small deformations and axisymmetric vibration. Hydrodynamic coefficients are computed using a Boundary Element Method (BEM) software. The variation in the theoretical power absorption limit with Young’s modulus is analyzed across a range of elastic materials. As a validation step, the derived theoretical limit criterion is applied to the standard reduced-order single-DoF model of an FSBWEC, successfully yielding the exact theoretical limit reported in the literature. Full article
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38 pages, 13650 KB  
Article
Nonlinear Motion Analysis of Floating Bodies in Waves Using the MPS Method
by Xianglong Fu, Di Ren, Jun Soo Park, Xiangxi Han, Junlong Su, Zhanbin Meng and Kunpeng Chen
Water 2026, 18(8), 893; https://doi.org/10.3390/w18080893 - 8 Apr 2026
Viewed by 405
Abstract
This paper develops a two-dimensional fully Lagrangian meshless fluid–structure interaction solver by integrating the Moving Particle Semi-implicit (MPS) method with continuum mechanics to investigate the nonlinear interaction between waves and floating bodies. The stability and accuracy of the proposed model are validated through [...] Read more.
This paper develops a two-dimensional fully Lagrangian meshless fluid–structure interaction solver by integrating the Moving Particle Semi-implicit (MPS) method with continuum mechanics to investigate the nonlinear interaction between waves and floating bodies. The stability and accuracy of the proposed model are validated through several benchmark cases. Furthermore, the solver is employed to analyze the dynamic response of a flat plate floating body in waves. The numerically generated waves exhibit a minimum error of approximately −0.5% and a period consistent with theoretical values, maintaining a smooth and continuous free surface. Due to the inherent limitations of the two-dimensional wave-floating body simulation, the Root Mean Square Error (RMSE) of the interaction results ranges from 5.4% to 15.2%. These findings indicate that the proposed method provides a valuable reference for the design and analysis of floating structures in ocean engineering. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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28 pages, 4866 KB  
Article
Trajectory Optimization with Feasibility Guidance for Agile UAV Path Planning Under Geometric Constraints
by Shoshi Kawarabayashi, Kenji Uchiyama and Kai Masuda
Machines 2026, 14(3), 350; https://doi.org/10.3390/machines14030350 - 20 Mar 2026
Viewed by 619
Abstract
This paper presents a practical optimization framework for improving trajectory feasibility in constrained nonlinear optimal control problems for agile unmanned aerial vehicles (UAVs). The proposed method addresses trajectory optimization problems with non-convex geometric constraints, where gradient-based solvers often fail to converge to feasible [...] Read more.
This paper presents a practical optimization framework for improving trajectory feasibility in constrained nonlinear optimal control problems for agile unmanned aerial vehicles (UAVs). The proposed method addresses trajectory optimization problems with non-convex geometric constraints, where gradient-based solvers often fail to converge to feasible solutions. The framework combines Model Predictive Path Integral (MPPI) control and the Augmented Lagrangian iterative Linear Quadratic Regulator (AL-iLQR). MPPI is employed as a fast sampling-based guidance mechanism to explore feasible regions of the trajectory space, while AL-iLQR is used to efficiently refine locally optimal solutions with high numerical accuracy. By decoupling feasibility exploration from local optimal refinement, the proposed method mitigates the sensitivity of gradient-based trajectory optimization to initialization in highly constrained environments. Numerical simulations involving both simplified two-dimensional dynamics and full quadrotor models demonstrate that the proposed approach significantly improves the probability of converging to feasible and dynamically consistent trajectories compared with AL-iLQR alone. The proposed method does not aim to provide theoretical guarantees of global optimality; instead, it offers a practical and computationally efficient strategy for enhancing feasibility and robustness in real-time UAV trajectory optimization. Full article
(This article belongs to the Special Issue Flight Control and Path Planning of Unmanned Aerial Vehicles)
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35 pages, 1535 KB  
Article
Conditional Sequence Modeling for Safe Reinforcement Learning
by Wensong Bai, Chao Zhang, Qihang Xu, Chufan Chen, Chenhao Zhou and Hui Qian
Mathematics 2026, 14(6), 1015; https://doi.org/10.3390/math14061015 - 17 Mar 2026
Viewed by 397
Abstract
Offline safe reinforcement learning (RL) aims to learn policies from a fixed dataset while maximizing performance under cumulative cost constraints. In practice, deployment requirements often vary across scenarios, necessitating a single policy capable of zero-shot adaptation to different cost thresholds. However, most existing [...] Read more.
Offline safe reinforcement learning (RL) aims to learn policies from a fixed dataset while maximizing performance under cumulative cost constraints. In practice, deployment requirements often vary across scenarios, necessitating a single policy capable of zero-shot adaptation to different cost thresholds. However, most existing offline safe RL methods are trained under a pre-specified threshold, yielding policies with limited generalization and deployment flexibility across cost thresholds. Motivated by recent progress in conditional sequence modeling (CSM), which enables flexible goal-conditioned control by specifying target returns, we propose Return–Cost Regularized Constrained Decision Transformer (RCDT), a CSM-based method that supports zero-shot deployment across multiple cost thresholds within a single trained policy. RCDT is the first CSM-based offline safe RL algorithm that integrates a Lagrangian-style cost penalty with an auto-adaptive penalty coefficient. To avoid overly conservative behavior and achieve a more favorable return–cost trade-off, a reward–cost-aware trajectory reweighting mechanism and Q-value regularization are further incorporated. Extensive experiments on the DSRL benchmark demonstrate that RCDT consistently improves return–cost trade-offs over representative baselines. Full article
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19 pages, 3599 KB  
Article
Integrated Dynamic Modeling and Improved Deviation Coupling Control for Synchronous Motion of Multi-Joint Hydraulic Robotic Arms
by Longmei Zhao, Jianbo Dai, Haozhi Xu, Mingyuan Sun, Xiaoqi Li and Shuren Chen
Machines 2026, 14(3), 326; https://doi.org/10.3390/machines14030326 - 13 Mar 2026
Viewed by 553
Abstract
Multi-joint hydraulic robotic arms are core equipment in intelligent mining, yet their performance is often limited by strong dynamic coupling and nonlinear hydraulic effects. Traditional control methods struggle to achieve high-precision trajectory tracking and coordinated motion under high loads and flow-coupling constraints. To [...] Read more.
Multi-joint hydraulic robotic arms are core equipment in intelligent mining, yet their performance is often limited by strong dynamic coupling and nonlinear hydraulic effects. Traditional control methods struggle to achieve high-precision trajectory tracking and coordinated motion under high loads and flow-coupling constraints. To address these challenges, this paper establishes a coupled hydraulic–mechanical dynamic model for a multi-joint robotic arm. The mechanical dynamics are derived using the Lagrangian formulation, while the hydraulic dynamics account for flow coupling among cylinders. An improved deviation coupling control (IDCC) strategy is proposed, integrating feedforward–feedback compensation, coupling error regulation, and a flow-limiting correction term. Co-simulation in Simulink (2024b) and Amesim (2020) shows that under flow-saturation conditions, the improved strategy reduces the peak trajectory errors by approximately 47.88%, 28.08%, and 49.89% for Joints 1–3, respectively, and shortens the settling time by 27.93%. Experimental results from a three-joint hydraulic test platform confirm error reductions of 10.20–15.58% and a 31.50% decrease in overall adjustment time. The study demonstrates that the proposed control strategy effectively suppresses multi-joint coupling interferences, enhances trajectory tracking accuracy, and improves the adaptability of hydraulic robotic arms under flow-limited conditions, providing a viable solution for high-precision control in intelligent mining applications. Full article
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18 pages, 5358 KB  
Article
Energy Effects of Ground Vortex-Induced Flow Distortion and Foreign Object Ingestion in Aeroengine Intakes
by Longqing Lei, Pengfei Chen, Hua Yang, Zhiyou Liu and Wei Chen
Energies 2026, 19(5), 1317; https://doi.org/10.3390/en19051317 - 5 Mar 2026
Viewed by 405
Abstract
Ground vortex formation beneath aeroengine intakes during near-ground operations represents an energy-related aerodynamic issue, as it degrades inlet flow quality, induces pressure distortion, and reduces the effective utilization of incoming kinetic energy. This study investigates the unsteady characteristics of ground vortex flow under [...] Read more.
Ground vortex formation beneath aeroengine intakes during near-ground operations represents an energy-related aerodynamic issue, as it degrades inlet flow quality, induces pressure distortion, and reduces the effective utilization of incoming kinetic energy. This study investigates the unsteady characteristics of ground vortex flow under headwind conditions and its influence on foreign object ingestion (FOI) in an aeroengine intake. Three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) simulations coupled with a Lagrangian Discrete Phase Model (DPM) are employed to resolve the interaction between intake-induced vortices and dispersed particles near the ground. The results indicate that the ground vortex rapidly develops into a quasi-periodic state, generating significant unsteady total pressure distortion at the intake face, with peak fluctuations reaching approximately 10% of the mean value. This flow non-uniformity reflects a deterioration of inlet energy distribution and is detrimental to downstream compression efficiency. Particle ingestion behavior is strongly dependent on particle density and diameter. Low-density and small particles are more readily entrained into the vortex core and ingested, whereas particles with higher density or larger size exhibit increased inertia and reduced sensitivity to vortex-induced energy transport. The ingestion region is biased toward the lower portion of the intake, consistent with the vortex core location. These findings provide insight into vortex-induced energy distortion and FOI mechanisms, offering guidance for improving aeroengine intake design and energy-efficient operation during near-ground conditions. Full article
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22 pages, 7487 KB  
Article
MPM-Based Computational Mechanics Method for Tendon-Driven Hyperelastic Robots Under Target Deformations
by Manjia Su, Ying Yin, Ruiwei Liu, Shichao Gu and Yisheng Guan
Mathematics 2026, 14(5), 818; https://doi.org/10.3390/math14050818 - 28 Feb 2026
Viewed by 387
Abstract
This work introduces an integrated Material Point Method (MPM) framework for optimizing tendon-driven hyperelastic robots under extreme 3D deformations. To overcome the mesh distortion limitations of the traditional FEM at large strains, we develop a coupled MPM–tendon hyperelastic model that integrates Yeoh constitutive [...] Read more.
This work introduces an integrated Material Point Method (MPM) framework for optimizing tendon-driven hyperelastic robots under extreme 3D deformations. To overcome the mesh distortion limitations of the traditional FEM at large strains, we develop a coupled MPM–tendon hyperelastic model that integrates Yeoh constitutive laws with discrete tendon actuation forces. The model enables robust simulation of anisotropic stress propagation through Lagrangian particle tracking and Eulerian grid discretization, eliminating mesh entanglement artifacts. A strain-gradient-driven tendon path algorithm ensures mechanical efficiency using Fréchet distance-based similarity metrics and curvature smoothness screenin, enforcing spatial continuity in complex topologies. Validation demonstrates: (1) Sub 3 mm geometric errors and about 89% volumetric overlap in worm-inspired deformations; (2) optimal computational efficiency at 0.4–0.6 mm grid densities, balancing accuracy and resource overhead; and (3) projected alignment errors of 0.8 mm (XY), 1.3 mm (XZ), and 2.9 mm (YZ) in multi-view spatial analyses. The framework achieves about 89% ± 2% volumetric overlap in quadrupedal morphing via agonist–antagonist tendon optimization, demonstrating efficacy for extreme 3D deformation control. Full article
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29 pages, 5282 KB  
Article
Spacecraft Safe Proximity Policy Based on Graph Neural Network Safe Reinforcement Learning
by Heng Zhou, Jingxian Wang, Monan Dong, Yong Zhao, Yuzhu Bai and Rong Chen
Aerospace 2026, 13(3), 210; https://doi.org/10.3390/aerospace13030210 - 26 Feb 2026
Viewed by 560
Abstract
Spacecraft safe proximity, as a critical component of on-orbit servicing missions, primarily encounters the following two challenges: the partial observability of the environment surrounding the service spacecraft and the necessity to evade uncertain obstacles. A safe reinforcement learning algorithm based on a graph [...] Read more.
Spacecraft safe proximity, as a critical component of on-orbit servicing missions, primarily encounters the following two challenges: the partial observability of the environment surrounding the service spacecraft and the necessity to evade uncertain obstacles. A safe reinforcement learning algorithm based on a graph neural network is proposed to address the constrained Markov decision problem in partially observable scenarios for spacecraft safe proximity missions. A graph neural network mechanism is introduced to solve the problem of dynamic variations in the quantity and location of obstacles in the observation area of the service spacecraft. The graph attention network is used to facilitate the extraction of feature information from the graph structure, which is then utilized as input for the subsequent reinforcement learning algorithm. The Soft Actor–Critic–Lagrangian algorithm is adopted to deal with the problems of tuning reward function parameters and balancing safety and optimality. By introducing Lagrange multipliers, the constrained optimization problem is transformed into an unconstrained optimization problem. In order to verify the effectiveness of the algorithm proposed in this paper, a spacecraft safe proximity environment model with dynamic obstacles is constructed, and the GAT-SACL algorithm proposed in this paper is validated by the Monte Carlo shooting method. The results show that the GAT-SACL algorithm possess excellent exploratory characteristics and delivers significant advantages in balancing optimality and safety. Full article
(This article belongs to the Section Astronautics & Space Science)
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