Search Results (463)

Initial attitude calibration is a critical yet challenging phase in hardware-in-the-loop (HIL) testing for space docking, often hindered by cumbersome procedures, safety concerns, and reliance on external equipment. This paper introduces a human–robot collaborative calibration method based on H∞ robust control. The core objective is to achieve symmetric pose alignment between docking mechanisms by allowing the operator to manually guide the test device, thereby rapidly obtaining initial attitude calibration results. An interactive model incorporating a time delay is established. Using H∞ synthesis, a stabilizing controller is designed to accurately track low-frequency operator commands while strongly suppressing high-frequency disturbances. Notably, the H∞ framework reconstructs an ideal interactive symmetry in human–robot collaboration by compensating for delays and disturbances. The solution to the Riccati equation within a game-theoretic framework effectively achieves symmetric optimization that balances tracking accuracy with safety constraints. Experimental results demonstrate that the method successfully compensates for system delays, enabling symmetric pose alignment while maintaining smooth and continuous motion of the docking mechanism. It also faithfully translates the operator’s low-frequency traction intent into motion. By retaining contact forces/torques within safe thresholds, the method balances interaction safety with operational precision, ultimately providing a reliable solution for initial attitude calibration in space docking HIL tests. Full article

This paper introduces a novel and efficient approach for Gaussian Splatting in dynamic scenes that leverages symmetry principles for enhanced computational efficiency and visual fidelity. First, we diverge from conventional methods that process static and dynamic regions uniformly by implementing an adaptive separation mechanism. This approach exploits the inherent symmetry-breaking properties between static and dynamic Gaussian points, utilizing motion differentials to identify and isolate dynamic elements. This symmetry-aware partitioning allows for the application of specialized processing techniques to each region type, with static regions benefiting from their temporal symmetry while dynamic regions receive targeted deformation modeling. Second, through this fine-grained partitioning of static and dynamic components guided by symmetry analysis, we achieve more judicious allocation of computational resources. The symmetric treatment of spatially coherent static regions and the focused processing of symmetry-breaking dynamic elements substantially reduce memory requirements and training time while preserving reconstruction quality. This optimization effectively conserves valuable computational resources without compromising visual fidelity. Third, we introduce a sophisticated deformation modeling framework that learns the transformational characteristics of grids composed of multiple Gaussian points. By incorporating radial basis function principles, which inherently preserve local rotational and translational symmetries, our method efficiently encodes complex motion information of dynamic Gaussian points. This symmetry-preserving deformation approach not only enables high-fidelity reconstruction of dynamic regions but also significantly improves the rendering of continuously evolving shadow interactions by maintaining physical consistency. The result is a marked reduction in visual distortion and rendering outputs that demonstrate exceptional correspondence to ground truth imagery across diverse dynamic scenes. Full article

This study investigates the steady-state behavior of a four-way opposed diaphragm pump. Simulations and experimental results confirm that peak stress locations align with observed damage sites. During the return stroke, diaphragm flipping induces tension at the flow-fixed interface edges, creating stress concentrations that contribute to fatigue and failure. Particle image velocimetry (PIV) shows that, under constant flow, increased voltage enhances umbrella valve opening, accelerates movement, broadens flow distribution, and disrupts symmetry. At 90°, valve-edge velocity exhibits sharp, high-amplitude oscillations and a narrow, elongated return region. Vortices near the valve port interfere with fluid motion, causing pressure fluctuations and potential sealing issues or increased opening resistance. Higher flow rates intensify vortex strength and shift their position, generating diaphragm pressure differentials that alter flow direction and velocity, reducing stability and inducing secondary vortices. Compared to a modified diaphragm, the standard type shows more complex vortex structures, greater flow instability, and dynamic response degradation under identical pressure and varying flow. These fragmented vortices further disrupt flow, affecting pump performance. The findings provide design insights for diaphragm pump optimization. Full article

Gait analysis is a valuable tool for a wide range of clinical applications. Until now, the standard for gait analysis has been marker-based 3D optical systems. Recently, markerless gait analysis systems that utilize pose estimation models based on Convolutional Neural Networks (CNNs) and computer vision have gained importance. In this pilot study, we validated the performance of a CNN-based, markerless pose estimation algorithm (Orthelligent^® VISION; OV) compared to a standard marker-based 3D motion capture system in 16 healthy adults. Standard gait metrics were analyzed by calculating concordance correlation coefficients (CCCs) and coefficients of variation. With regard to gait event detection, we found good overlaps for both systems. Compared to the marker-based motion analysis, OV achieved a strong to almost complete concordance regarding the sagittal measurement of cadence, gait variability, step time, stance time, step length, and double support (CCC ≥ 0.624), as well as regarding the frontal plane parameters of cadence, step time, stance time, and step width (CCC ≥ 0.805). For gait symmetry only, we found a moderate to weak correlation. These results support the CNN-based, markerless gait analysis system OV as an alternative to marker-based 3D motion capture systems for a broad variety of clinical applications. Full article

Conventional hip disarticulation prostheses often require amputees to produce limited leg-lifting torque through exaggerated pelvic motion, resulting in complex control and pronounced gait abnormalities. To overcome the limitations, we present a mapping control strategy for a powered hip disarticulation prosthesis aimed at improving gait symmetry. A quaternion-based method was implemented to capture hip joint kinematics, while a gated recurrent unit (GRU) neural network was trained to model the kinematic relationship between the intact and prosthetic limbs, enabling biomimetic trajectory control. Validation experiments showed that trajectory similarity between predicted and actual motions increased with walking speed, reaching 98.12% at 3.0 km/h. Comparative walking tests revealed an 84.00% improvement in hip flexion angle with the powered prosthesis over conventional designs. Notable improvements in gait symmetry were observed: stride symmetry (measured by SI and RII) improved by 23.21% and 19.28%, respectively, while hip trajectory symmetry increased by 68.07% (SI) and 47.59% (RII). These results confirm that the GRU-based kinematic mapping model offers robust trajectory prediction and that the powered prosthesis significantly enhances gait symmetry, delivering more natural and biomimetic motion. Full article

This review article explores the theory of control sets for linear control systems defined on two-dimensional Lie groups, with a focus on the plane ${\mathbb{R}}^2$ and the affine group $Af{f}_{+}\left(2\right)$. We systematically summarize recent advances, emphasizing how the geometric and algebraic structures inherent in low-dimensional Lie groups influence the formation, shape, and properties of control sets—maximal regions where controllability is maintained. Control sets with non-empty interiors are of particular interest as they characterize regions where the system can be steered between states via bounded inputs. The review highlights key results concerning the existence, uniqueness, and boundedness of these sets, including criteria based on the Ad-rank condition and orbit analysis. We also underscore the central role of the symmetry properties of Lie groups, which facilitate the systematic classification and description of control sets, linking the abstract mathematical framework to concrete, physically motivated applications. To illustrate the practical relevance of the theory, we present examples from mechanics, motion planning, and neuroscience, demonstrating how control sets naturally emerge in diverse domains. Overall, this work aims to deepen the understanding of controllability regions in low-dimensional Lie group systems and to foster future research that bridges geometric control theory with applied problems. Full article

This work investigates the stability analysis of linear control systems defined on Lie groups, with a particular focus on low-dimensional cases. Unlike their Euclidean counterparts, such systems evolve on manifolds with non-Euclidean geometry, where trajectories respect the group’s intrinsic symmetries. Stability notions, such as inner asymptotic, inner, and input–output (BIBO) stability, are studied. The qualitative behavior of solutions is shown to depend critically on the spectral decomposition of derivations associated with the drift, and on the algebraic structure of the underlying Lie algebra. We study two classes of examples in detail: Abelian and solvable two-dimensional Lie groups, and the three-dimensional nilpotent Heisenberg group. These settings, while mathematically tractable, retain essential features of non-commutativity, geometric non-linearity, and sub-Riemannian geometry, making them canonical models in control theory. The results highlight the interplay between algebraic properties, invariant submanifolds, and trajectory behavior, offering insights applicable to robotic motion planning, quantum control, and signal processing. Full article

Training-free video summarization tackles the challenge of selecting the most informative keyframes from a video without relying on costly training or complex deep models. This work introduces C2FVS-DPP (Contextual Feature Fusion Video Summarization with Determinantal Point Process), a lightweight framework that generates concise video summaries by jointly modeling semantic importance, visual diversity, temporal structure, and symmetry. The design centers on a symmetry-aware fusion strategy, where appearance, motion, and semantic cues are aligned in a unified embedding space, and on a reward-guided optimization logic that balances representativeness and diversity. Specifically, appearance features from ResNet-50, motion cues from optical flow, and semantic representations from BERT-encoded BLIP captions are fused into a contextual embedding. A Transformer encoder assigns importance scores, followed by shot boundary detection and K-Medoids clustering to identify candidate keyframes. These candidates are refined through a reward-based re-ranking mechanism that integrates semantic relevance, representativeness, and visual uniqueness, while a Determinantal Point Process (DPP) enforces globally diverse selection under a keyframe budget. To enable reliable evaluation, enhanced versions of the SumMe and TVSum50 datasets were curated to reduce redundancy and increase semantic density. On these curated benchmarks, C2FVS-DPP achieves F1-scores of 0.22 and 0.43 and fidelity scores of 0.16 and 0.40 on SumMe and TVSum50, respectively, surpassing existing models on both metrics. In terms of compression ratio, the framework records 0.9959 on SumMe and 0.9940 on TVSum50, remaining highly competitive with the best-reported values of 0.9981 and 0.9983. These results highlight the strength of C2FVS-DPP as an inference-driven, symmetry-aware, and resource-efficient solution for video summarization. Full article

An important goal in cardiology and other fields is to identify and control dynamic spiral wave patterns in reaction–diffusion partial differential equations. This research focuses on the Barkley model. The spiral wave motion is controlled and suppressed within the Euclidean group rather than through Euclidean symmetry by applying a controller equation. The eigenfunctions associated with the left eigenspace of the adjoint linear equation can be used to characterize the drift or movement of the spiral wave tip trajectory when the system is perturbed. These eigenfunctions provide details regarding how the spiral wave reacts to disruptions. Perturbations to the Barkley system are examined by applying control functions and calculating the principle eigenvalue numerically. The left eigenfunctions of the Barkley equation are determined by solving the left problem associated with the $2\mathrm{D}$ Barkley equation and a $1\mathrm{D}$ dynamical controller. In addition, the control function can be used to suppress the periodic and meandering regimes of the system. In this work, the focus is on the periodic regime. Full article

The long-distance high-voltage transmission tower-line system, frequently traversing active fault zones, is vulnerable to severe symmetry-breaking damage during earthquakes due to asymmetric permanent ground displacements. However, the seismic performance of such systems, particularly concerning symmetry-breaking effects caused by asymmetric fault displacements, remains inadequately studied. This study investigates the symmetry degradation mechanisms in a 1:40 scaled 500 kV tower-line system subjected to cross-fault ground motions via shaking table tests. The testing protocol incorporates representative fault mechanisms—strike-slip and normal/reverse faults—to systematically evaluate their differential impacts on symmetry response. Measurements of acceleration, strain, and displacement reveal that while acceleration responses are spectrally controlled, structural damage is highly fault-type dependent and markedly asymmetric. The acceleration of towers without permanent displacement was 35–50% lower than that of towers with permanent displacement. Under identical permanent displacement conditions, peak displacements caused by normal/reverse motions exceeded those from strike-slip motions by 50–100%. Accordingly, a fault-type-specific amplification factor of 1.5 is proposed for the design of towers in dip-slip fault zones. These results offer novel experimental insights into symmetry violation under fault ruptures, including fault-specific correction factors and asymmetry-resistant design strategies. However, the conclusions are subject to limitations such as scale effects and the exclusion of vertical ground motion components. Full article

Natural and unconstrained locomotion remains a fundamental challenge in creating truly immersive virtual reality (VR) experiences. This paper presents the design and control of a novel robotic omnidirectional treadmill (ODT) based on the bilateral symmetry of two cooperative five-bar planar mechanisms designed to replicate realistic walking mechanics. The central contribution is a human in the loop control strategy designed to achieve stable walking in place. This framework employs a specific control strategy that actively repositions the footplates along a dynamically defined ‘Line of Movement’ (LoM), compensating for the user’s motion to ensure the midpoint between the feet remains stabilized and symmetrical at the platform’s geometric center. A comprehensive dynamic model of both the ODT and a coupled humanoid robot was developed to validate the system. Numerical simulations demonstrate robust performance across various gaits, including turning and catwalks, maintaining the user’s locomotion center with a maximum resultant drift error of 11.65 cm, a peak value that occurred momentarily during a turning motion and remained well within the ODT’s safe operational boundaries, with peak errors along any single axis remaining below 9 cm. The system operated with notable efficiency, requiring RMS torques below 22 Nm for the primary actuators. This work establishes a viable dynamic and control architecture for foot-tracking ODTs, paving the way for future enhancements such as haptic terrain feedback and elevation simulation. Full article

This cross-sectional study analyzed the lower limb (LL) behavior in terms of gait asymmetry and joints’ kinematic parameters, comparing people with multiple sclerosis (pwMS) and unaffected individuals. Methods: Data from 15 patients, EDSS ≤ 4.5, and 15 healthy control volunteers were gathered. The VICON Motion Capture System (14 infrared cameras), NEXUS software, Plug-in–Gait skeleton model and reflective markers were used to collect data for each subject during five gait cycles on a plane surface. Biomechanical analysis included evaluation of LL joints’ range of motion (ROM) bilaterally, as well as movement symmetry. Results: Comparative biomechanical analysis revealed a hierarchy of vulnerability between the groups: the ankle is the most affected joint in pwMS (p = 0.008–0.014), the knee is moderately affected (p = 0.015 in swing phase), and the hip is the least affected (p > 0.05 in all phases). The swing phase showed the most significant left–right asymmetry impairment, as reflected by root mean square error (RMSE) values: swing-phase RMSE = 9.306 ± 4.635 (higher and more variable) versus stance-phase RMSE = 6.363 ± 2.306 (lower and more consistent). Conclusions: MS does not affect the joints structurally; rather, it eliminates the ability to differentiate the fine-tuning control between them. The absence of significant left–right joint asymmetry differences during complete gait cycle indicates dysfunction in the global motor control. Full article

Electromyography (EMG) signals reflect hand motion intention and exhibit a certain degree of amplitude symmetry. Nowadays, recognition of hand motion intention based on EMG has enriched its burgeoning promotion in various applications, such as rehabilitation, prostheses, and intelligent supply chains. For instance, the motion intentions of humans can be conveyed to logistics equipment, thereby improving the level of intelligence in a supply chain. To enhance the recognition accuracy of multiple hand motion intentions, this paper proposes a hand motion intention recognition method that decodes EMG signals based on improved long short-term memory (LSTM). Firstly, we performed preprocessing and utilized overlapping sliding windows on EMG segments. Secondly, we chose LSTM and improved it so as to capture features and enable prediction of hand motion intention. Specifically, we introduced the optimal key hyperparameter combination in the LSTM model using a genetic algorithm (GA). We found that our proposed method achieved relatively high accuracy in detecting hand motion intention, with average accuracies of 92.0% (five gestures) and 89.7% (seven gestures), while the highest accuracy reached 100.0% (seven gestures). Our paper may provide a way to predict the motion intention of the human hand for intention communication. Full article

The classification of exact solutions of Maxwell vacuum equations for pseudo-Riemannian spaces with spatial symmetry (homogeneous non-null spaces in Petrov) in the presence of electromagnetic fields invariant with respect to the action of the group of space motions is summarized. A new classification method is used, common to all homogeneous zero spaces of Petrov. The method is based on the use of canonical reper vectors and on the use of a new approach to the systematization of solutions. The classification results are presented in a form more convenient for further use. Using the previously made refinement of the classification of Petrov spaces, the classification of exact solutions of Maxwell vacuum equations for spaces with the group of motions $G_3\left(VIII\right)$ is completed. Full article

Crawling is an almost universal stage of locomotor development in infants; however, it is difficult to quantify using typical motion analysis techniques. The crawling stage therefore has underutilized potential to assess development and detect deviations or abnormalities. This study measured longitudinal weightbearing asymmetries in typically developing (TD) crawling children and compared this population to children with limb loss or limb differences (LLD) using a pressure-sensing mat. The LLD group bore significantly more weight using their arms vs. their legs than the TD group (p < 0.001), but even in cases of unilateral limb loss, bilateral weightbearing symmetry was similar to TD, controlling for body mass and age (p = 0.570). As children in the TD group developed and gained body mass, their weight shifted significantly to their left side (η² = 0.050) and away from their arms and toward their legs (η² = 0.255). The results provide insight into the biomechanical development of TD infant crawling, and the ways in which an atypically developing population manages weightbearing during crawling. The establishment of symmetry data will be useful, as crawling can serve as an opportunity for earlier detection of neuromotor conditions such as cerebral palsy. Furthermore, insight into the crawling patterns of children with limb loss and limb difference can inform prosthetic prescription and the need to consider a missing weight shift toward the legs as children develop. Full article