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Keywords = kinematic trajectory data

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26 pages, 2128 KB  
Article
A Rigid-Body Pendulum Model for Plyometric Push-Up Biomechanics: Analytical Derivation and Numerical Quantification of Flight Time, Arc Displacement, Maximum Height, and Mechanical Power Output
by Wissem Dhahbi
Bioengineering 2026, 13(4), 445; https://doi.org/10.3390/bioengineering13040445 (registering DOI) - 11 Apr 2026
Abstract
Aim: Conventional free-fall kinematic models applied to plyometric push-up assessment treat the upper body as a vertically translating point mass, ignoring the curvilinear trajectory imposed by the ankle pivot and systematically biasing flight-time and height estimates. Methods: A planar rigid-body pendulum pivoting about [...] Read more.
Aim: Conventional free-fall kinematic models applied to plyometric push-up assessment treat the upper body as a vertically translating point mass, ignoring the curvilinear trajectory imposed by the ankle pivot and systematically biasing flight-time and height estimates. Methods: A planar rigid-body pendulum pivoting about the ankle axis was formulated via two independent derivation pathways (static moment equilibrium and a gravitational-torque coordinate approach), yielding effective pendulum length L = (MW/M) × LOS. Closed-form expressions for flight time, arc displacement, maximum height, and mean mechanical power were derived analytically from energy conservation and compared against free-fall predictions across seven pendulum arm lengths (LOW = 0.50–2.00 m) and 500 initial hand velocities per length, using adaptive Gauss–Kronrod quadrature (relative tolerance 10−10) with ODE cross-validation (maximum discrepancy < 2.5 × 10−7 s). Results: Flight time equivalence (tH = tG) was formally established. The free-fall model overestimated flight time by up to 18.82% (Δt = 0.096 s; LOW = 0.50 m, VH,0 = 2.50 m/s) and maximum height by up to 28.43% (Δh = 0.087 m; LOW = 0.50 m, tflight = 0.50 s), with both errors growing nonlinearly with initial velocity. Overestimation in height was proportionally larger at shorter pendulum arm lengths (18.18% at tflight = 0.30 s for LOW = 0.50 m vs. 10.91% for LOW = 1.00 m). Conclusions: The pendulum model provides a physically consistent, analytically tractable framework for geometry-adjusted upper-body power assessment from four field-obtainable anthropometric inputs. These results reflect computational self-consistency; prospective experimental validation against force-plate kinematics is required before applied deployment. Prospective empirical validation against dual force-plate and motion-capture reference data is required to establish the model’s accuracy boundaries under real push-up kinematics. Full article
(This article belongs to the Special Issue Biomechanics of Physical Exercise)
24 pages, 1735 KB  
Article
Can Non-Translational Simplified Tasks Mimic Knee Kinematics During Gait? A Comparative Study of Tibiofemoral ICR Trajectories
by Fernando Valencia, Fernando Nadal and María Prado-Novoa
Biomimetics 2026, 11(4), 260; https://doi.org/10.3390/biomimetics11040260 - 9 Apr 2026
Viewed by 84
Abstract
Understanding knee kinematics during gait is essential for the design of prostheses, orthoses, and biomimetic mechanisms. In many biomechanical analyses, tibiofemoral motion is simplified to the sagittal plane, allowing the locus of the instantaneous center of rotation (ICR) to describe joint kinematics derived [...] Read more.
Understanding knee kinematics during gait is essential for the design of prostheses, orthoses, and biomimetic mechanisms. In many biomechanical analyses, tibiofemoral motion is simplified to the sagittal plane, allowing the locus of the instantaneous center of rotation (ICR) to describe joint kinematics derived from the instantaneous axis of rotation (IAR). However, it remains unclear whether ICR trajectories obtained from simplified flexion–extension tasks can represent those observed during gait. This study analyzes the sagittal-plane trajectory of the tibiofemoral ICR during gait swing, standing swing, seated swing, and squat. Motion data from 21 healthy participants were captured using videogrammetry, and the instantaneous axis of rotation (IAR) was computed from homogeneous transformation matrices using the Mozzi–Chasles theorem. Sagittal-plane ICR trajectories were derived and compared within subjects across tasks. Significant differences were found between gait and all other movements in both trajectory shape and spatial position. The shape metric (S), which quantifies differences in trajectory geometry, showed mean values ranging from 0.82 to 1.04 with very large effect sizes (Cohen’s d = 2.90 to 4.47, p < 0.0001). The centroid distance metric (M), which measures the overall spatial displacement between trajectories, indicated positional differences ranging from 8.15 mm to 12.37 mm between trajectories also showing very large effect sizes (Cohen’s = 1.72–3.40, p < 0.0001). Additionally, the mean deviation of the IAR from the sagittal plane ranged from 14° to 18° during gait, whereas smaller deviations were observed in non–weight-bearing swing movements. These results demonstrate that tibiofemoral ICR trajectories are task-dependent and that simplified flexion–extension tasks do not fully reproduce the knee kinematics observed during gait. Consequently, the use of gait-derived ICR trajectories, together with their variability, provides a more suitable basis for the design and optimization of polycentric mechanisms, enabling the development of devices that more closely replicate real biomechanics and are potentially better adapted to the user. Full article
(This article belongs to the Section Biomimetic Design, Constructions and Devices)
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20 pages, 5717 KB  
Article
An Improved YOLOv10 and DeepSORT Algorithm for Pedestrian Detection and Tracking in Crowd Navigation
by Shihang Hu and Changyong Li
Algorithms 2026, 19(4), 274; https://doi.org/10.3390/a19040274 - 1 Apr 2026
Viewed by 216
Abstract
In indoor crowd navigation, quickly and accurately acquiring the kinematic data of pedestrians within a robot’s field of view is a crucial factor determining success. Existing indoor pedestrian tracking methods have limitations in accuracy and real-time performance. To address these issues, a lightweight [...] Read more.
In indoor crowd navigation, quickly and accurately acquiring the kinematic data of pedestrians within a robot’s field of view is a crucial factor determining success. Existing indoor pedestrian tracking methods have limitations in accuracy and real-time performance. To address these issues, a lightweight pedestrian tracking method based on an improved YOLOv10s and DeepSORT is proposed. In the detection stage, a CPNGhostNetV2 module incorporating Ghost Convolution and attention mechanisms is first designed to replace the original C2f module in YOLOv10s. This achieves lightweight while effectively preserving global feature information. Secondly, the GSConv module is introduced to further reduce computational load and model parameters. Finally, the Focal Loss function is introduced to enhance the detection capability of the YOLOv10s model in dense scenes. In the tracking stage, a novel trajectory management mechanism is proposed to reduce the ID-switching problem under occlusion conditions. The experimental results show that the improved YOLOv10s reduces computational complexity by 33.9% and parameters by 17.4% compared to the original model. It also improves mAP@50 by 0.6%. The improved DeepSORT algorithm achieves a 7.0% increase in MOTA, a 1.4% increase in MOTP, and a 24.8% reduction in ID-switch counts compared to the original YOLOv10-DeepSORT. It outperforms traditional algorithms in terms of accuracy, real-time performance, and computational efficiency, demonstrating promising application prospects. Full article
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23 pages, 2866 KB  
Article
A Cloud–Robot–Wearable System for Bilateral Reaching Rehabilitation: Affected-Side Identification and Quality Quantification
by Chia-Hau Chen, Li-Hsien Tang, Chang-Hsin Yeh, Eric Hsiao-Kuang Wu and Shih-Ching Yeh
Electronics 2026, 15(7), 1459; https://doi.org/10.3390/electronics15071459 - 1 Apr 2026
Viewed by 323
Abstract
Therapist shortages make home-based rehabilitation an essential component of post-stroke care, yet patients often exhibit reduced adherence when functional gains are difficult to quantify and interpret. This study presents a cloud-enabled assessment framework centered on a dynamic reaching task for upper-limb rehabilitation in [...] Read more.
Therapist shortages make home-based rehabilitation an essential component of post-stroke care, yet patients often exhibit reduced adherence when functional gains are difficult to quantify and interpret. This study presents a cloud-enabled assessment framework centered on a dynamic reaching task for upper-limb rehabilitation in individuals with mild stroke. The proposed system combines wearable sensing and Internet of Things (IoT) connectivity to stream kinematic data to the cloud for near real-time analysis, and integrates a force-feedback rehabilitation robot to deliver motion guidance during training. The pipeline proceeds in three stages. First, smoothness-related kinematic descriptors are extracted and fed into a deep multi-class classifier to discriminate the affected side (left, right, or healthy). Second, movement quality is modeled using a Gaussian Mixture Model (GMM) trained on IoT-acquired trajectories to quantify performance via probabilistic similarity. Third, a calibrated scoring function transforms GMM log-likelihood into a normalized 0–1 quality index, producing visual reports that support interpretable feedback for patients and therapists. The framework is validated using motion data collected from stroke patients at Taipei Veterans General Hospital. Experimental results demonstrate that the neural network multi-classifier achieved an F1-score of 0.95. Incorporating robot-derived interaction signals further improved classification performance by approximately 5%. For movement quality assessment, the derived scores showed a significant positive correlation (Pearson correlation = 0.632, p = 0.02) with therapist-defined gold reference standards for right-affected patients. Additionally, integrating robot force-feedback signals and AIoT-enabled dynamic streams improved score accuracy by 8% and score responsiveness by 10%. These quantitative outcomes substantiate the efficacy of combining IoT-driven sensing and robot-assisted training for objective, interpretable, and remotely deployable motor assessment. Full article
(This article belongs to the Section Computer Science & Engineering)
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24 pages, 8557 KB  
Article
Dynamic Modelling and Control Strategy Analysis of a Lower-Limb Exoskeleton
by Huanrong Xiao, Teng Ran and Afang Jin
Sensors 2026, 26(7), 2124; https://doi.org/10.3390/s26072124 - 29 Mar 2026
Viewed by 347
Abstract
Lower-limb exoskeleton robots play a pivotal role in rehabilitation medicine and assistive augmentation, where precise dynamic modelling and trajectory tracking control are fundamental to effective assistance. Existing models predominantly focus on hip and knee rotational degrees of freedom, with insufficient attention to ankle [...] Read more.
Lower-limb exoskeleton robots play a pivotal role in rehabilitation medicine and assistive augmentation, where precise dynamic modelling and trajectory tracking control are fundamental to effective assistance. Existing models predominantly focus on hip and knee rotational degrees of freedom, with insufficient attention to ankle dynamics and pelvic translation. To address these limitations, this paper establishes a sagittal-plane dynamic model comprising nine generalised coordinates, treating the human lower limb and exoskeleton as an integrated coupled system. A seven-segment kinematic model encompassing the trunk, bilateral thighs, shanks, and feet is constructed via a modified Denavit–Hartenberg parameter method, and dynamic equations are derived using Lagrangian formulation. Three control strategies—PD control, PD with gravity compensation, and the computed torque method—are designed and evaluated through simulations using gait data from five subjects (two self-collected, three from a public dataset) acquired via Vicon motion capture. Results demonstrate that the computed torque method achieves a joint angle tracking root mean square error (RMSE) of 0.59°, representing an 86.3% improvement over conventional PD control, while maintaining a low control torque RMS of 4.44 N·m. The controller exhibits stable tracking performance across walking speeds of 0.4–1.45 m/s, validating the effectiveness of the proposed model and control strategies. Full article
(This article belongs to the Section Sensors and Robotics)
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16 pages, 3089 KB  
Article
A Sound Power Measurement Method for Radiated Noise of the Collaborative Robot with Multi-Joint Arms
by Wenshuo Zhu and Yu Huang
Appl. Sci. 2026, 16(6), 3063; https://doi.org/10.3390/app16063063 - 22 Mar 2026
Viewed by 211
Abstract
The growing demand for noise reduction in multi-joint long-reach robotic arms necessitates the development of precise noise measurement methodologies. However, accurate characterization remains challenging due to the robot’s complex kinematics. Specifically, dynamic joint positions and motion trajectories can lead to acoustic occlusion, while [...] Read more.
The growing demand for noise reduction in multi-joint long-reach robotic arms necessitates the development of precise noise measurement methodologies. However, accurate characterization remains challenging due to the robot’s complex kinematics. Specifically, dynamic joint positions and motion trajectories can lead to acoustic occlusion, while the inherent directivity of sound sources further compromises measurement reliability. To address these issues, this study proposes a component-based hybrid measurement approach. First, the noise generated by a single joint was characterized using a simplified 4-point method, with Green’s function applied to correct for variable propagation distances. Subsequently, the total sound power level of the entire robotic arm was synthesized in a virtual environment by integrating the single-joint acoustic data with the arm’s operational kinematic program. Validation results demonstrate that the proposed method achieves a measurement error of only 0.8 dB relative to the reverberation chamber benchmark—an accuracy superior to that of direct measurements of the full robotic arm cycle (2.6 dB). Furthermore, a comparison with the ISO 3744:2025 9-point standard method reveals that while the proposed 4-point approach yields a slightly larger error (0.8 dB vs. 0.2 dB), it significantly reduces experimental complexity. Consequently, this method offers a sufficiently accurate and operationally efficient solution for practical engineering applications. Full article
(This article belongs to the Special Issue Sound and Vibration: Measurement, Perception, and Control)
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18 pages, 8749 KB  
Article
Biomechanical and Signal-Based Characterization of Karate Lateral Kicks Using Videogrammetry Analysis
by Luis Antonio Aguilar-Pérez, Jorge Luis Rojas-Arce, Luis Jímenez-Ángeles, Carlos Alberto Espinoza-Garces, Adolfo Ángel Casarez-Duran and Christopher René Torres-SanMiguel
Machines 2026, 14(3), 339; https://doi.org/10.3390/machines14030339 - 17 Mar 2026
Viewed by 393
Abstract
Martial arts have evolved from self-defense practices into structured competitive sports that demand high levels of neuromotor control, where improper execution remains a major source of injury. This study evaluates lower-limb control during the execution of the karate lateral kick using videogrammetry biomechanical [...] Read more.
Martial arts have evolved from self-defense practices into structured competitive sports that demand high levels of neuromotor control, where improper execution remains a major source of injury. This study evaluates lower-limb control during the execution of the karate lateral kick using videogrammetry biomechanical analysis. Three participants were recorded during regular training sessions and selected according to their level of expertise. Each participant performed lateral kicks at three predefined distances (close, comfortable, and long), selected based on common training practice and individual biomechanical considerations. Videogrammetry data were generated using Kinovea version 0.9.5 software to extract sagittal ankle trajectories. Statistical analyses were carried out in MATLAB version 2025b using spatial coordinates to obtain kinematic data on the practitioner’s performance. The results revealed skill-dependent differences in movement control, characterized by temporal evolution of kinematic variables and their corresponding time–frequency representations. Novice practitioners exhibited limited control during the raising and recovery phases, despite reaching the target. In contrast, expert practitioners demonstrated consistent posture, controlled acceleration during impact, and stable limb trajectories during descent. These observations provide a foundation for data-driven classification of kick execution quality and outline potential applications in supervised learning, real-time feedback systems, and injury risk reduction during karate training. Full article
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14 pages, 50163 KB  
Article
Stroke Asymmetry in Bird Wing Dynamics During Flight from Video Data
by Valentina Leontiuk, Innokentiy Kastalskiy, Waleed Khalid and Victor B. Kazantsev
Biomimetics 2026, 11(3), 212; https://doi.org/10.3390/biomimetics11030212 - 16 Mar 2026
Viewed by 883
Abstract
The aerodynamics of avian flight provides critical inspiration for the design of bioinspired aerial vehicles, yet the quantitative characterization of free-flight wing kinematics remains challenging. This study employs a neural-network-based motion tracking approach (DeepLabCut) to analyze wingbeat kinematics in free-flying birds from video [...] Read more.
The aerodynamics of avian flight provides critical inspiration for the design of bioinspired aerial vehicles, yet the quantitative characterization of free-flight wing kinematics remains challenging. This study employs a neural-network-based motion tracking approach (DeepLabCut) to analyze wingbeat kinematics in free-flying birds from video data. We automatically digitize key wing points and reconstruct three-dimensional trajectories to quantify asymmetric flapping patterns. Our analysis reveals that while wing oscillations approximate sinusoidal motion, they exhibit statistically significant velocity differences between upstroke and downstroke phases, confirming the stroke asymmetry of avian flapping. Furthermore, using video of a flying frigatebird (Fregata ariel), we quantify the changes in the effective wing area throughout the wingbeat cycle, showing a ~19% variation that significantly impacts lift generation efficiency. These findings provide quantitative benchmarks for avian-inspired wing design and offer insights for optimizing flapping kinematics in bioinspired aerial systems, particularly for enhancing takeoff and landing capabilities in micro air vehicles. Full article
(This article belongs to the Section Development of Biomimetic Methodology)
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20 pages, 2758 KB  
Article
A Dynamic Risk Assessment System for Expressway Lane-Changing: Integrating Bayesian Networks and Markov Chains Under High-Density Traffic
by Quantao Yang and Peikun Li
Systems 2026, 14(3), 306; https://doi.org/10.3390/systems14030306 - 15 Mar 2026
Viewed by 290
Abstract
In high-density expressway environments, lane-changing (LC) maneuvers act as stochastic perturbations that compromise the hydrodynamic stability of traffic flow, leading to safety hazards and operational delays. While existing literature has extensively modeled crash severity in static complex environments (e.g., tunnels and mountainous terrains), [...] Read more.
In high-density expressway environments, lane-changing (LC) maneuvers act as stochastic perturbations that compromise the hydrodynamic stability of traffic flow, leading to safety hazards and operational delays. While existing literature has extensively modeled crash severity in static complex environments (e.g., tunnels and mountainous terrains), there remains a critical deficiency in quantifying the dynamic, systemic risks induced by LC maneuvers under saturation conditions. To address this gap, this study proposes a novel Systemic Risk Assessment Framework. First, a Hidden Markov Model (HMM) is employed to decode the latent state transitions of following vehicles, quantifying the systemic consequence of LC maneuvers as “operational delay” based on traffic wave theory. Second, a Bayesian Network (BN) is constructed to infer the causal probability of risk, integrating geometric proxies such as insertion angle with kinematic variables. Validated with real-world trajectory data, the model achieves high accuracy in identifying risk accumulation precursors. This research contributes to the field of transportation systems by shifting the risk paradigm from static collision prediction to dynamic system reliability analysis, offering theoretical support for Connected and Autonomous Vehicle (CAV) decision logic. Full article
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81 pages, 28674 KB  
Article
Representation Learning for Maritime Vessel Behaviour: A Three-Stage Pipeline for Robust Trajectory Embeddings
by Ghassan Al-Falouji, Shang Gao, Zhixin Huang, Ben Biesenbach, Peer Kröger, Bernhard Sick and Sven Tomforde
J. Mar. Sci. Eng. 2026, 14(5), 507; https://doi.org/10.3390/jmse14050507 - 8 Mar 2026
Viewed by 297
Abstract
The growing complexity of maritime navigation creates safety challenges that drive the shift toward autonomous systems. Maritime vessel behaviour modelling is critical for safe and efficient autonomous operations. Representation learning offers a systematic approach to learn feature embeddings encoding vessel behaviour for improved [...] Read more.
The growing complexity of maritime navigation creates safety challenges that drive the shift toward autonomous systems. Maritime vessel behaviour modelling is critical for safe and efficient autonomous operations. Representation learning offers a systematic approach to learn feature embeddings encoding vessel behaviour for improved situational awareness and decision-making. We introduce a three-stage representation learning pipeline evaluating six architectures on real-world AIS trajectories. Grouped Masked Autoencoder (GMAE)-Risk Extrapolation (REx) combines group-wise masked autoencoding at the semantic feature level with risk extrapolation regularisation, forcing encoders to learn cross-group dependencies between temporal, kinematic, spatial, and interaction features. DAE and EAE provide robust and uncertainty-aware baselines. Evaluation uses a dual-pipeline framework on two years of Kiel Fjord AIS data (176,787 trajectories, 527,225 segments). Pipeline 1 applies three-stage representation learning using vessel-type classification as encoder selection probe. GMAE-REx achieves 86.03% validation accuracy, outperforming DAE (85.63%), EAE (85.56%), and baselines Transformer (84.93%), TCN (76.27%), LiST (85.12%). Pipeline 2 applies unsupervised clustering to discover intrinsic behavioural structure. Learnt representations consistently outperform expert features on DBCV, conductance, and modularity metrics, organising trajectories by operational context rather than vessel type. This behaviour-oriented organisation enables cross-vessel knowledge transfer for autonomous navigation, VTS monitoring, and safety analysis. Full article
(This article belongs to the Special Issue Intelligent Solutions for Marine Operations)
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18 pages, 2558 KB  
Article
Evaluating a Multi-Camera Markerless System for Capturing Basketball-Specific Movements: An Exploration Using 25 Hz Video Streams
by Zhaoyu Li, Zhenbin Tan, Wen Zheng, Ganling Yang, Junye Tao, Mingxin Zhang and Xiao Xu
Sensors 2026, 26(5), 1689; https://doi.org/10.3390/s26051689 - 7 Mar 2026
Viewed by 512
Abstract
Markerless motion capture (MMC) provides a non-invasive alternative for motion analysis; however, its validity at the standard frame rate of 25 Hz commonly used in broadcast and surveillance applications remains to be established. This study evaluated the performance of a 25 Hz multi-camera [...] Read more.
Markerless motion capture (MMC) provides a non-invasive alternative for motion analysis; however, its validity at the standard frame rate of 25 Hz commonly used in broadcast and surveillance applications remains to be established. This study evaluated the performance of a 25 Hz multi-camera MMC workflow using consumer-grade cameras for capturing basketball-specific movements. Three highly trained male athletes completed seven tasks, including sprinting and simulated sport-specific skills, while being synchronously recorded by six MMC cameras (DJI Action 5 Pro, 25 fps) and a 10-camera Vicon system (25 Hz). Kinematic data were processed using an RTMDet–RTMPose pipeline and low-pass filtered at 6 Hz. Waveform validity was assessed using Pearson’s correlation coefficient (r) and the root mean square error (RMSE). The displacement magnitudes of 12 joints showed excellent agreement (r = 0.916–0.994; median nRMSE = 0.54–1.32%), indicating robust trajectory reconstruction. In contrast, agreement decreased for derivative variables: velocity (r = 0.583–0.867) and acceleration (r = 0.232–0.677) were highly sensitive to the low sampling rate and numerical differentiation. Although a 25 Hz configuration is insufficient for high-precision impact analysis, it provides acceptable accuracy for macroscopic displacement tracking and external-load quantification in resource-constrained training environments. Future optimization should prioritize temporal synchronization to improve the reliability of derivative variables. Full article
(This article belongs to the Special Issue Multi-Sensor Systems for Object Tracking—2nd Edition)
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22 pages, 3339 KB  
Article
Particle Velocity Measurement in Battery Thermal Runaway Jets Using an Enhanced Deep Learning and Adaptive Matching Framework
by Xinhua Mao, Zhimin Chen, Mengqi Zhang, Jinwei Sun and Chengshan Xu
Batteries 2026, 12(3), 90; https://doi.org/10.3390/batteries12030090 - 6 Mar 2026
Viewed by 389
Abstract
High-speed solid particles ejected during battery thermal runaway pose severe safety threats, yet their velocity measurement is hindered by high density, microscopic size, and intense glare. This study proposes a non-intrusive velocimetry framework that integrates an enhanced single-stage object detector with a structural [...] Read more.
High-speed solid particles ejected during battery thermal runaway pose severe safety threats, yet their velocity measurement is hindered by high density, microscopic size, and intense glare. This study proposes a non-intrusive velocimetry framework that integrates an enhanced single-stage object detector with a structural similarity matching algorithm. The detector incorporates specialized feature extraction modules and a high-resolution layer to identify microscopic targets in extreme environments, while the matching algorithm employs adaptive direction constraints to ensure precise trajectory tracking. Experimental validation demonstrates that the framework achieves a mean average precision of 92.7% and supports real-time processing. The method successfully quantifies a three-stage velocity evolution in battery failure events, identifying a peak particle speed exceeding 120 m/s. These findings provide critical kinematic data for optimizing battery safety structures and modeling fire propagation mechanisms. Full article
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21 pages, 3931 KB  
Article
Vehicle Speed Estimation Using Infrastructure-Mounted LiDAR via Rectangle Edge Matching
by Injun Hong and Manbok Park
Appl. Sci. 2026, 16(5), 2513; https://doi.org/10.3390/app16052513 - 5 Mar 2026
Viewed by 290
Abstract
Smart transportation infrastructure is increasingly deployed, and cooperative perception using stationary Light Detection and Ranging (LiDAR) sensors installed at intersections and along roadsides is becoming more important. However, infrastructure LiDAR often suffers from sparse point-cloud data (PCD) at long ranges and frequent occlusions, [...] Read more.
Smart transportation infrastructure is increasingly deployed, and cooperative perception using stationary Light Detection and Ranging (LiDAR) sensors installed at intersections and along roadsides is becoming more important. However, infrastructure LiDAR often suffers from sparse point-cloud data (PCD) at long ranges and frequent occlusions, which can degrade the stability of inter-frame displacement and speed estimation. This paper proposes a real-time vehicle speed estimation method that operates robustly under sparse and partially observed conditions. The proposed approach extracts boundary points from clustered vehicle PCD and removes outliers, and then fits a 2D rectangle to the vehicle contour via Gauss–Newton optimization by minimizing distance-based residuals between boundary points and rectangle edges. To further improve robustness, we incorporate Hessian augmentation terms that account for boundary states and size variations, thereby alleviating excessive boundary violations and abnormal deformation of the width and height parameters during iterations. Next, from the fitted rectangles in consecutive frames, we construct a nearest corner with respect to the LiDAR origin and an auxiliary point, and perform 2D SVD-based alignment using only these two representative points. This enables efficient computation of inter-frame displacement and speed without full point-cloud registration (e.g., iterative closest point (ICP)). Experiments conducted at an intersection in K-City (Hwaseong, Republic of Korea) using a 40-channel LiDAR, a test vehicle (Genesis G70), and a real-time kinematic (RTK) system (MRP-2000) show that the proposed method stably preserves representative points and fits rectangles, even in sparse regions where only about two LiDAR rings are observed. Using CAN-based vehicle speed as the reference, the proposed method achieves an MAE of 0.76–1.37 kph and an RMSE of 0.90–1.58 kph over the tested speed settings (30, 50, and 70 kph, as well as high speed (~90 kph)) and trajectory scenarios. Furthermore, per-object processing-time measurements confirm the real-time feasibility of the proposed algorithm. Full article
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32 pages, 5003 KB  
Article
A Novel Hybrid IK Architecture for Robotic Arms: Iterative Refinement of Soft-Computing Approximations with Validation on ABB IRB-1200 Robotic Arm
by Meenalochani Jayabalan, Karunamoorthy Loganathan and Palanikumar Kayaroganam
Machines 2026, 14(3), 292; https://doi.org/10.3390/machines14030292 - 4 Mar 2026
Viewed by 413
Abstract
Adaptive Neuro-Fuzzy Inference System (ANFIS)-based inverse kinematics (IK) is highly accurate for trained poses but often yields approximations for unseen inputs due to non-standardized training data. This research addresses these limitations through two novel contributions designed for any generic Degrees of Freedom (DoF) [...] Read more.
Adaptive Neuro-Fuzzy Inference System (ANFIS)-based inverse kinematics (IK) is highly accurate for trained poses but often yields approximations for unseen inputs due to non-standardized training data. This research addresses these limitations through two novel contributions designed for any generic Degrees of Freedom (DoF) serial revolute robotic arm. First, A structured training methodology is introduced using workspace decomposition and cubic path planning. Instead of random sampling, the workspace is partitioned into cubic regions where 28 unique trajectories (12 edges, 12 face diagonals, four space diagonals) connect the eight vertices using cubic polynomial interpolation. This ensures physically consistent data mirroring real world point to point (PTP) movements. Even though validated on an ABB IRB-1200 robotic arm, this modular design is inherently scalable, allowing the local cubic expertise to be extended to cover the entire reachable workspace. Second, a two-stage hybrid IK framework is proposed, where an initial ANFIS approximation is refined via Jacobian-based iterative methods. Three Hybrid Frame works were evaluated, Framework-1 (ANFIS + Jacobian Gradient), Framework-2 (ANFIS + Jacobian Pseudoinverse/Newton–Raphson), and Framework-3 (ANFIS + Damped Least Squares). The results show that all three hybrid IK frameworks achieve reliable convergence, while the DLS-based hybrid provides the best trade-off between accuracy, convergence speed, and numerical stability. This generic, analytical free architecture provides a computationally efficient solution even in a hybrid scenario, bridging the gap between offline structured training and online, real-time refinement for digital twin synchronization and industrial automation. Full article
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12 pages, 1261 KB  
Article
Age-Related Changes in Virtual Pivot Point Position and Variability During Pediatric Gait Development
by Lucas Schreff, Katharina Nirmaier, Christian Blank, Rainer Abel and Roy Müller
Children 2026, 13(3), 363; https://doi.org/10.3390/children13030363 - 3 Mar 2026
Viewed by 375
Abstract
Background/Objectives: During adult walking, ground reaction forces (GRFs) consistently intersect near a point above the center of mass (CoM), termed the virtual pivot point (VPP). The VPP is hypothesized to contribute to upper body stabilization. However, little is known about its presence [...] Read more.
Background/Objectives: During adult walking, ground reaction forces (GRFs) consistently intersect near a point above the center of mass (CoM), termed the virtual pivot point (VPP). The VPP is hypothesized to contribute to upper body stabilization. However, little is known about its presence and developmental trajectory during early childhood. This study investigated age-related differences in VPP position, variability, and GRF focusing during walking in typically developing children. Methods: Kinematic and kinetic data were collected from 29 children across three age groups: Group I (aged 1 year), Group II (aged 2–3 years), and Group III (aged 10–15 years) using markerless motion capture and force plates. VPP position relative to the CoM, its variability and GRF focusing (R2) were analyzed in sagittal plane during single support phases. Results: Across all age groups, GRFs were strongly focused toward a VPP (R2 > 0.95), with no significant age-related differences in GRF focusing. In contrast, significant age-related differences emerged in VPP position and variability. The normalized vertical VPP position increased progressively from Group I (7.58 cm) to Group III (14.79 cm). Notably, in several toddlers, the VPP was located at or below the CoM, contrasting with the consistent above-CoM position observed in adolescents. Conclusions: These findings demonstrate that while GRF focusing behavior is present in toddlers who can walk independently, VPP characteristics undergo substantial developmental changes. The shifting VPP position and the decrease in variability in toddlers likely reflect progressive changes in gait mechanics and trunk stabilization strategies during childhood. Full article
(This article belongs to the Section Pediatric Orthopedics & Sports Medicine)
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