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Search Results (2,069)

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16 pages, 4963 KiB  
Article
Simultaneous Localization and Mapping Methods for Snake-like Robots Based on Gait Adjustment
by Chaoquan Tang, Zhipeng Zhang, Meng Sun, Menggang Li, Hongwei Tang and Deen Bai
Biomimetics 2024, 9(11), 710; https://doi.org/10.3390/biomimetics9110710 (registering DOI) - 19 Nov 2024
Abstract
Snake robots require autonomous localization and mapping capabilities for field applications. However, the characteristics of their motion, such as large turning angles and fast rotation speeds, can lead to issues like drift or even failure in positioning and map building. In response to [...] Read more.
Snake robots require autonomous localization and mapping capabilities for field applications. However, the characteristics of their motion, such as large turning angles and fast rotation speeds, can lead to issues like drift or even failure in positioning and map building. In response to this situation, this paper starts from the gait motion characteristics of the snake robot itself, proposing an improved gait motion method and a tightly coupled method based on IMU and visual information to solve the problem of poor algorithm convergence caused by head-shaking in snake robot SLAM. Firstly, the adaptability of several typical gaits of the snake robot to SLAM methods was evaluated. Secondly, the serpentine gait was selected as the object of gait improvement, and a head stability control method for the snake robot was proposed, thereby reducing the interference of the snake robot’s motion on the sensors. Thirdly, a visual–inertial tightly coupled SLAM method for the snake robot’s serpentine gait and Arc-Rolling gait was proposed, and the method was verified to enhance the robustness of the visual SLAM algorithm and improve the positioning and mapping accuracy of the snake robot. Finally, experiments proved that the methods proposed in this paper can effectively improve the accuracy of positioning and map building for snake robots. Full article
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<p>Principle of head stability control.</p>
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<p>Angular differential variation.</p>
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<p>Comparison of SLAM simulation under the serpentine gait.</p>
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<p>Comparison of SLAM simulation under the arc-rolling gait.</p>
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<p>The experimental system of the snake robot.</p>
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<p>Comparison of localization and mapping under the serpentine gait.</p>
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<p>Comparison of localization and mapping under the two methods.</p>
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<p>Comparison of localization and mapping under the arc-rolling gait.</p>
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<p>Localization and mapping results under the arc-rolling gait.</p>
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21 pages, 2496 KiB  
Review
Transportation Mode Detection Using Learning Methods and Self-Contained Sensors: Review
by Ilhem Gharbi, Fadoua Taia-Alaoui, Hassen Fourati, Nicolas Vuillerme and Zebo Zhou
Sensors 2024, 24(22), 7369; https://doi.org/10.3390/s24227369 (registering DOI) - 19 Nov 2024
Viewed by 70
Abstract
Due to increasing traffic congestion, travel modeling has gained importance in the development of transportion mode detection (TMD) strategies over the past decade. Nowadays, recent smartphones, equipped with integrated inertial measurement units (IMUs) and embedded algorithms, can play a crucial role in such [...] Read more.
Due to increasing traffic congestion, travel modeling has gained importance in the development of transportion mode detection (TMD) strategies over the past decade. Nowadays, recent smartphones, equipped with integrated inertial measurement units (IMUs) and embedded algorithms, can play a crucial role in such development. In particular, obtaining much more information on the transportation modes used by users through smartphones is very challenging due to the variety of the data (accelerometers, magnetometers, gyroscopes, proximity sensors, etc.), the standardization issue of datasets and the pertinence of learning methods for that purpose. Reviewing the latest progress on TMD systems is important to inform readers about recent datasets used in detection, best practices for classification issues and the remaining challenges that still impact the detection performances. Existing TMD review papers until now offer overviews of applications and algorithms without tackling the specific issues faced with real-world data collection and classification. Compared to these works, the proposed review provides some novelties such as an in-depth analysis of the current state-of-the-art techniques in TMD systems, relying on recent references and focusing particularly on the major existing problems, and an evaluation of existing methodologies for detecting travel modes using smartphone IMUs (including dataset structures, sensor data types, feature extraction, etc.). This review paper can help researchers to focus their efforts on the main problems and challenges identified. Full article
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<p>Processing pipeline for predicting the transportation modes.</p>
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<p>Transforming time series (raw sensor data) into feature space through the segmentation (window partitioning in red) and computation of features (feature extraction (FE)) [<a href="#B35-sensors-24-07369" class="html-bibr">35</a>].</p>
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<p>Resultant acceleration in Tram [<a href="#B31-sensors-24-07369" class="html-bibr">31</a>].</p>
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<p>Resultant acceleration in Walk [<a href="#B31-sensors-24-07369" class="html-bibr">31</a>].</p>
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<p>Resultant acceleration in Car [<a href="#B31-sensors-24-07369" class="html-bibr">31</a>].</p>
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<p>Resultant acceleration in Motorcycle [<a href="#B31-sensors-24-07369" class="html-bibr">31</a>].</p>
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<p>Sensor placement for the perscido dataset [<a href="#B23-sensors-24-07369" class="html-bibr">23</a>].</p>
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<p>Sensor placement for the SHL dataset [<a href="#B27-sensors-24-07369" class="html-bibr">27</a>].</p>
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<p>Android applications: (<b>a</b>) Phyphox, (<b>b</b>) Physics toolbox suite and (<b>c</b>) Sensorlogger.</p>
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13 pages, 2889 KiB  
Article
Assessing Changes in Motor Function and Mobility in Individuals with Parkinson’s Disease After 12 Sessions of Patient-Specific Adaptive Dynamic Cycling
by Younguk Kim, Brittany E. Smith, Lara Shigo, Aasef G. Shaikh, Kenneth A. Loparo and Angela L. Ridgel
Sensors 2024, 24(22), 7364; https://doi.org/10.3390/s24227364 (registering DOI) - 19 Nov 2024
Viewed by 122
Abstract
Background and Purpose: This pilot randomized controlled trial evaluated the effects of 12 sessions of patient-specific adaptive dynamic cycling (PSADC) versus non-adaptive cycling (NA) on motor function and mobility in individuals with Parkinson’s disease (PD), using inertial measurement unit (IMU) sensors for objective [...] Read more.
Background and Purpose: This pilot randomized controlled trial evaluated the effects of 12 sessions of patient-specific adaptive dynamic cycling (PSADC) versus non-adaptive cycling (NA) on motor function and mobility in individuals with Parkinson’s disease (PD), using inertial measurement unit (IMU) sensors for objective assessment. Methods: Twenty-three participants with PD (13 in the PSADC group and 10 in the NA group) completed the study over a 4-week period. Motor function was measured using the Kinesia™ sensors and the MDS-UPDRS Motor III, while mobility was assessed with the TUG test using OPAL IMU sensors. Results: The PSADC group showed significant improvements in MDS-UPDRS Motor III scores (t = 5.165, p < 0.001) and dopamine-sensitive symptoms (t = 4.629, p = 0.001), whereas the NA group did not improve. Both groups showed non-significant improvements in TUG time. IMU sensors provided continuous, quantitative, and unbiased measurements of motor function and mobility, offering a more precise and objective tracking of improvements over time. Conclusions: PSADC demonstrated enhanced treatment effects on PD motor function compared to NA while also reducing variability in individual responses. The integration of IMU sensors was essential for precise monitoring, supporting the potential of a data-driven, individualized exercise approach to optimize treatment outcomes for individuals with PD. Full article
(This article belongs to the Special Issue Advanced Wearable Sensor for Human Movement Monitoring)
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<p>CONSORT flowchart illustrating the progression of participants through the phases of the clinical trial. Twenty-four participants were randomized into two groups: the PSADC group (<span class="html-italic">n</span> = 14) and the NA group (<span class="html-italic">n</span> = 10). All participants in the NA group completed the NA dynamic cycling intervention and the follow-up visit. In the PSADC group, 13 participants completed both the PSADC and the follow-up visit, while one participant discontinued the study.</p>
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<p>(<b>A</b>) MDS-UPDRS Motor III score changes for the PSADC (black circles) and NA (white squares) groups. (<b>B</b>) Changes between groups. The PSADC group showed improvement, as indicated by a decrease in scores, and the NA group showed a slight increase. Error bars = standard deviation. ***, <span class="html-italic">p</span> &lt; 0.001. (<b>C</b>) MDS-UPDRS Motor III Score change histogram. Improvements are shown as negative values, and worsening is illustrated as positive. PSADC = black bars, NA = gray bars.</p>
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<p>(<b>A</b>) MDS-UPDRS Motor III Dopamine Sensitive Symptom Scores. The PSADC group (black circles) exhibited a decrease in symptoms post-intervention, while the NA group (white squares) exhibited a slight increase. Error bars represent the standard deviation, highlighting the variability within each group. The decrease in the PSADC group was statistically significant (*** <span class="html-italic">p</span> &lt; 0.001). (<b>B</b>) MDS-UPDRS Motor III Dopamine Less-Sensitive Symptom Scores. Both the PSADC (black circles) and NA (white squares) groups show minimal changes.</p>
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<p>(<b>A</b>) Movement speed score: The PSADC group improved in movement speed after the intervention. Conversely, the NA group shows a worsening of symptoms. Error bars = standard deviation. (<b>B</b>) Movement rhythms score: The total score for movement speed, rhythm, and amplitude is 12 points each. A decrease in score (improvement) is observed in the PSADC group post-intervention. NA group scores were unchanged. (<b>C</b>) Movement amplitude score: Movement amplitude scores show a significant increase in the PSADC group post-intervention compared to the NA group (***, <span class="html-italic">p</span> &lt; 0.001).</p>
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<p>(<b>A</b>) TUG test time: The PSADC group (white squares) and the NA group (black circles) showed a reduction in time at post-intervention. (<b>B</b>) Turn velocity: Turn velocity shows an increase for the PSADC group, while the NA did not change. Error bars = standard deviation.</p>
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22 pages, 12893 KiB  
Article
Research on Visual–Inertial Measurement Unit Fusion Simultaneous Localization and Mapping Algorithm for Complex Terrain in Open-Pit Mines
by Yuanbin Xiao, Wubin Xu, Bing Li, Hanwen Zhang, Bo Xu and Weixin Zhou
Sensors 2024, 24(22), 7360; https://doi.org/10.3390/s24227360 (registering DOI) - 18 Nov 2024
Viewed by 260
Abstract
As mining technology advances, intelligent robots in open-pit mining require precise localization and digital maps. Nonetheless, significant pitch variations, uneven highways, and rocky surfaces with minimal texture present substantial challenges to the precision of feature extraction and positioning in traditional visual SLAM systems, [...] Read more.
As mining technology advances, intelligent robots in open-pit mining require precise localization and digital maps. Nonetheless, significant pitch variations, uneven highways, and rocky surfaces with minimal texture present substantial challenges to the precision of feature extraction and positioning in traditional visual SLAM systems, owing to the intricate terrain features of open-pit mines. This study proposes an improved SLAM technique that integrates visual and Inertial Measurement Unit (IMU) data to address these challenges. The method incorporates a point–line feature fusion matching strategy to enhance the quality and stability of line feature extraction. It integrates an enhanced Line Segment Detection (LSD) algorithm with short segment culling and approximate line merging techniques. The combination of IMU pre-integration and visual feature restrictions is executed inside a tightly coupled visual–inertial framework utilizing a sliding window approach for back-end optimization, enhancing system robustness and precision. Experimental results demonstrate that the suggested method improves RMSE accuracy by 36.62% and 26.88% on the MH and VR sequences of the EuRoC dataset, respectively, compared to ORB-SLAM3. The improved SLAM system significantly reduces trajectory drift in the simulated open-pit mining tests, improving localization accuracy by 40.62% and 61.32%. The results indicate that the proposed method demonstrates significance. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>The system framework diagram. This procedure encompasses data input, front-end visual–inertial odometry, closed-loop detection, back-end optimization, and mapping; The red box in the data input section represents the sparse textured slope.</p>
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<p>An example diagram of the line feature extraction optimization method. The efficacy of line segment identification is enhanced by implementing short line elimination and approximate line segment amalgamation procedures.</p>
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<p>(<b>a</b>) Flowchart of improved LSD line feature detection algorithm; (<b>b</b>) schematic diagram of similar line feature merging.</p>
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<p>Visual observation model and IMU schematic diagram. The IMU data must be integrated and calculated in discrete time due to the fact that its data acquisition frequency is significantly higher than that of the camera. Consequently, a unified data format is necessary to ensure close coupling of the data. This diagram uses hollow circles, hollow triangles, green stars, and black squares to represent image frames, keyframes, IMU data, and the pre-integration process.</p>
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<p>Marginalization model. The relationship model between the camera and the landmark locations during the marginalization process.</p>
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<p>Histogram for the performance comparison of the line feature extraction algorithm: (<b>a</b>) the average time required to derive line features; (<b>b</b>) the average number of line feature extractions.</p>
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<p>Line feature extraction algorithm performance comparison: (<b>a</b>) the LSD algorithm’s effect on line feature extraction; (<b>b</b>) the enhanced LSD method. Utilizing short segment elimination and approximate line merging techniques markedly eliminates redundant short line features while preserving the longer line segments essential for localization precision. The red box highlights the comparison section between the two images, with the green dots and lines representing the extracted point and line features from the images, respectively.</p>
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<p>Histogram of absolute trajectory error. The histogram illustrates that, in the MH sequence, the absolute trajectory error of the enhanced algorithm is less than that of other algorithms, whereas, in the VR sequence, the enhanced algorithm performs comparably to or better than the perfect algorithm.</p>
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<p>Analysis results of trajectory error comparison: (<b>a</b>) comparison of the trajectory for Sequence MH_04_difficult; (<b>b</b>) comparison of difficult trajectories in Sequence V2_03. The black boxes and red arrows in the figure are used to enlarge key areas and mark trajectory deviations, highlighting the accuracy differences among different algorithms in these regions.</p>
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<p>Results of absolute pose inaccuracy for each series: (<b>a</b>) Sequence MH_04_difficult; (<b>b</b>) Sequence MH_05_difficult; (<b>c</b>) Sequence V1_02_medium; (<b>d</b>) Sequence V1_03_difficult. The color-coded line represents varying levels of Absolute Pose Error (APE) along the trajectory, with red indicating higher error and blue indicating lower error, highlighting accuracy differences across segments.</p>
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<p>Three-dimensional point cloud maps: (<b>a</b>) Sequence MH_05_difficult; (<b>b</b>) Sequence V1_03_difficult. The figure shows a 3D mapping visualization where the green lines represent the estimated trajectory, red points indicate mapped features, and black points show additional environmental points.</p>
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<p>Experimental mining intelligent robot platform: (<b>a</b>) left view; (<b>b</b>) front view.</p>
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<p>Scene 1: circular open-pit excavation: (<b>a</b>) real-world scene; (<b>b</b>) diagram of movement trajectory. In (<b>a</b>), the red arrows represent the motion trajectory of the mapping robot. In (<b>b</b>), points A, B, and C represent key checkpoints along the closed-loop path.</p>
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<p>Comparison of trajectory errors in Scenario 1.</p>
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<p>Analysis of experimental outcomes in Scenario 1: (<b>a</b>) comparison of 2D plane trajectories; (<b>b</b>) absolute trajectory error of data series.</p>
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<p>Scene 2: Uneven road conditions in an open-pit mine: (<b>a</b>) real-world scene; (<b>b</b>) diagram of movement trajectory. In (<b>a</b>), the red arrows represent the motion trajectory of the mapping robot. In (<b>b</b>), points A, B, and C represent key checkpoints along the path.</p>
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<p>Comparison of trajectory errors in Scenario 2.</p>
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24 pages, 5276 KiB  
Article
An Improved LKF Integrated Navigation Algorithm Without GNSS Signal for Vehicles with Fixed-Motion Trajectory
by Haosu Zhang, Zihao Wang, Shiyin Zhou, Zhiying Wei, Jianming Miao, Lingji Xu and Tao Liu
Electronics 2024, 13(22), 4498; https://doi.org/10.3390/electronics13224498 - 15 Nov 2024
Viewed by 489
Abstract
Without a GNSS (global navigation satellite system) signal, the integrated navigation system in vehicles with a fixed trajectory (e.g., railcars) is limited to the use of micro-electromechanical system-inertial navigation system (MEMS-INS) and odometer (ODO). Due to the significant measurement error of the MEMS [...] Read more.
Without a GNSS (global navigation satellite system) signal, the integrated navigation system in vehicles with a fixed trajectory (e.g., railcars) is limited to the use of micro-electromechanical system-inertial navigation system (MEMS-INS) and odometer (ODO). Due to the significant measurement error of the MEMS inertial device and the inability of ODO to output attitude, the positioning error is generally large. To address this problem, this paper presents a new integrated navigation algorithm based on a dynamically constrained Kalman model. By analyzing the dynamics of a railcar, several new observations have been investigated, including errors of up and lateral velocity, centripetal acceleration, centripetal D-value (difference value), and an up-gyro bias. The state transition matrix and observation matrix for the error state model are represented. To improve navigation accuracy, virtual noise technology is applied to correct errors of up and lateral velocity. The vehicle-running experiment conducted within 240 s demonstrates that the positioning error rate of the dead-reckoning method based on MEMS-INS is 83.5%, whereas the proposed method exhibits a rate of 4.9%. Therefore, the accuracy of positioning can be significantly enhanced. Full article
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<p>Schematic diagram of the <span class="html-italic">b</span> frame of a railcar.</p>
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<p>(<b>a</b>) A schematic diagram of the railcar running in a straight line. (<b>b</b>) A schematic diagram of the turning movement of the railcar.</p>
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<p>A diagrammatic sketch of the angular speed of rotation around the <span class="html-italic">OZ<sub>b</sub></span> axis of the railcar. The solid arrow represents the previous true direction, the short dashed arrow represents the assumed translation direction at the current moment, and the long dashed line segment arrow represents the current true direction.</p>
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<p>A flow chart of an integrated navigation algorithm applicable to the railcar in SNRE.</p>
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<p>Physical photo of FOG-INS.</p>
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<p>MEMS-INS (<b>a</b>) Schematic diagram. (<b>b</b>) Physical photo. (<b>c</b>) Diagram of structural composition.</p>
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<p>MEMS-INS (<b>a</b>) Schematic diagram. (<b>b</b>) Physical photo. (<b>c</b>) Diagram of structural composition.</p>
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<p>Output of the up-gyroscope in MEMS-IMU.</p>
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<p>Speed curve calculated by FOG-IMU/GNSS integrated navigation.</p>
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<p>(<b>a</b>) Track graph. (<b>b</b>) Enlarged graph near the star. (<b>c</b>) Enlarged view near the curved road segment. (<b>d</b>) Enlarged graph near the end. (<b>e</b>) Track graph.</p>
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<p>(<b>a</b>) Attitude angles calculated by MEMS-INS/GNSS combination navigation. (<b>b</b>) Misalignment angles calculated by MEMS-INS/GNSS combination navigation.</p>
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15 pages, 11432 KiB  
Article
A Triangular Structure Constraint for Pedestrian Positioning with Inertial Sensors Mounted on Foot and Shank
by Jianyu Wang, Jing Liang, Chao Wang, Wanwei Tang, Mingzhe Wei and Yiling Fan
Electronics 2024, 13(22), 4496; https://doi.org/10.3390/electronics13224496 - 15 Nov 2024
Viewed by 264
Abstract
To suppress pedestrian positioning drift, a velocity constraint commonly known as zero-velocity update (ZUPT) is widely used. However, it cannot correct the error in the non-zero velocity interval (non-ZVI) or observe heading errors. In addition, the positioning accuracy will be further affected when [...] Read more.
To suppress pedestrian positioning drift, a velocity constraint commonly known as zero-velocity update (ZUPT) is widely used. However, it cannot correct the error in the non-zero velocity interval (non-ZVI) or observe heading errors. In addition, the positioning accuracy will be further affected when a velocity error occurs in the ZVI (e.g., foot tremble). In this study, the foot, ankle, and shank were regarded as a triangular structure. Consequently, an angle constraint was established by utilizing the sum of the internal angles. Moreover, in contrast to the traditional ZUPT algorithm, a velocity constraint method combined with Coriolis theorem was constructed. Magnetometer measurements were used to correct heading. Three groups of experiments with different trajectories were carried out. The ZUPT method of the single inertial measurement unit (IMU) and the distance constraint method of dual IMUs were employed for comparisons. The experimental results showed that the proposed method had high accuracy in positioning. Furthermore, the constraints built by the lower limb structure were applied to the whole gait cycle (ZVI and non-ZVI). Full article
(This article belongs to the Special Issue Intelligent Perception and Control for Robotics)
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<p>Connecting rod structure of the foot and shank. The circles represent joints.</p>
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<p>Gait characteristics.</p>
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<p>The ZVI judgment method of GLRT. (<b>a</b>) Using a threshold for standing detection; (<b>b</b>) partial enlarged view.</p>
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<p>System flow chart.</p>
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<p>Data acquisition. (<b>a</b>) Hardware circuit; (<b>b</b>) sensor installation mode.</p>
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<p>Total station.</p>
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<p>Estimation results of rectangular trajectory.</p>
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<p>Estimation results of irregular trajectory.</p>
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<p>Estimation results of stairs.</p>
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<p>Positioning error ranges of different methods.</p>
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<p>End-to-end error ranges of different methods.</p>
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<p>Height error ranges of different methods.</p>
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23 pages, 4323 KiB  
Article
LIMUNet: A Lightweight Neural Network for Human Activity Recognition Using Smartwatches
by Liangliang Lin, Junjie Wu, Ran An, Song Ma, Kun Zhao and Han Ding
Appl. Sci. 2024, 14(22), 10515; https://doi.org/10.3390/app142210515 - 15 Nov 2024
Viewed by 452
Abstract
The rise of mobile communication, low-power chips, and the Internet of Things has made smartwatches increasingly popular. Equipped with inertial measurement units (IMUs), these devices can recognize user activities through artificial intelligence (AI) analysis of sensor data. However, most existing AI-based activity recognition [...] Read more.
The rise of mobile communication, low-power chips, and the Internet of Things has made smartwatches increasingly popular. Equipped with inertial measurement units (IMUs), these devices can recognize user activities through artificial intelligence (AI) analysis of sensor data. However, most existing AI-based activity recognition algorithms require significant computational power and storage, making them unsuitable for low-power devices like smartwatches. Additionally, discrepancies between training data and real-world data often hinder model generalization and performance. To address these challenges, we propose LIMUNet and its smaller variant LIMUNet-Tiny—lightweight neural networks designed for human activity recognition on smartwatches. LIMUNet utilizes depthwise separable convolutions and residual blocks to reduce computational complexity and parameter count. It also incorporates a dual attention mechanism specifically tailored to smartwatch sensor data, improving feature extraction without sacrificing efficiency. Experiments on the PAMAP2 and LIMU datasets show that the LIMUNet improves recognition accuracy by 2.9% over leading lightweight models while reducing parameters by 88.3% and computational load by 58.4%. Compared to other state-of-the-art models, LIMUNet achieves a 9.6% increase in accuracy, with a 60% reduction in parameters and a 57.8% reduction in computational cost. LIMUNet-Tiny further reduces parameters by 75% and computational load by 80%, making it even more suitable for resource-constrained devices. Full article
(This article belongs to the Special Issue Mobile Computing and Intelligent Sensing)
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<p>Random signal frames before and after filtering.</p>
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<p>LIMUNet network architecture.</p>
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<p>Residual bottleneck layer.</p>
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<p>Channel attention mechanism.</p>
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<p>Dual attention mechanism.</p>
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<p>Correspondence between activities and waveforms in the LIMU dataset.</p>
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<p>Distribution of data in LIMU across different types of behaviors and users.</p>
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<p>Training curves for different datasets.</p>
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<p>Confusion matrices for different datasets.</p>
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<p>The impact of window size. (<b>a</b>) The impact of window size on accuracy in the PAMAPL2 and LIMU datasets. (<b>b</b>) The impact of window size <span class="html-italic">L</span> on FLOPS for the LIMU datasets.</p>
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<p>LIMUNet (N = 2), LIMUNet-Tiny (N = 1), and LIMUNet-More (N = 3) the accuracy and degree of lightweight design.</p>
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16 pages, 4667 KiB  
Article
State Estimation for Quadruped Robots on Non-Stationary Terrain via Invariant Extended Kalman Filter and Disturbance Observer
by Mingfei Wan, Daoguang Liu, Jun Wu, Li Li, Zhangjun Peng and Zhigui Liu
Sensors 2024, 24(22), 7290; https://doi.org/10.3390/s24227290 - 14 Nov 2024
Viewed by 414
Abstract
Quadruped robots possess significant mobility in complex and uneven terrains due to their outstanding stability and flexibility, making them highly suitable in rescue missions, environmental monitoring, and smart agriculture. With the increasing use of quadruped robots in more demanding scenarios, ensuring accurate and [...] Read more.
Quadruped robots possess significant mobility in complex and uneven terrains due to their outstanding stability and flexibility, making them highly suitable in rescue missions, environmental monitoring, and smart agriculture. With the increasing use of quadruped robots in more demanding scenarios, ensuring accurate and stable state estimation in complex environments has become particularly important. Existing state estimation algorithms relying on multi-sensor fusion, such as those using IMU, LiDAR, and visual data, often face challenges on non-stationary terrains due to issues like foot-end slippage or unstable contact, leading to significant state drift. To tackle this problem, this paper introduces a state estimation algorithm that integrates an invariant extended Kalman filter (InEKF) with a disturbance observer, aiming to estimate the motion state of quadruped robots on non-stationary terrains. Firstly, foot-end slippage is modeled as a deviation in body velocity and explicitly included in the state equations, allowing for a more precise representation of how slippage affects the state. Secondly, the state update process integrates both foot-end velocity and position observations to improve the overall accuracy and comprehensiveness of the estimation. Lastly, a foot-end contact probability model, coupled with an adaptive covariance adjustment strategy, is employed to dynamically modulate the influence of the observations. These enhancements significantly improve the filter’s robustness and the accuracy of state estimation in non-stationary terrain scenarios. Experiments conducted with the Jueying Mini quadruped robot on various non-stationary terrains show that the enhanced InEKF method offers notable advantages over traditional filters in compensating for foot-end slippage and adapting to different terrains. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>Test environments.</p>
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<p>Foot slipping scenarios of a quadruped robot during ground contact.</p>
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<p>Estimation of foot contact probability during unstable contact events, with (<b>a</b>) representing right front leg and (<b>b</b>) left rear leg.</p>
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<p>The position estimates of the quadruped robot in the X, Y, and Z directions on different terrains, with (<b>a</b>–<b>c</b>) depicting the position estimate for rugged slope terrain, (<b>d</b>–<b>f</b>) for shallow grass terrain, and (<b>g</b>–<b>i</b>) for deep grass terrain.</p>
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<p>The position estimates of the quadruped robot in the X, Y, and Z directions on different terrains, with (<b>a</b>–<b>c</b>) depicting the position estimate for rugged slope terrain, (<b>d</b>–<b>f</b>) for shallow grass terrain, and (<b>g</b>–<b>i</b>) for deep grass terrain.</p>
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<p>Pitch and roll angle estimation of the quadruped robot on different terrains, with (<b>a</b>,<b>d</b>) depicting the estimate for rugged slope terrain, (<b>b</b>,<b>e</b>) for shallow grass terrain, and (<b>c</b>,<b>f</b>) for deep grass terrain.</p>
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<p>Pitch and roll angle estimation of the quadruped robot on different terrains, with (<b>a</b>,<b>d</b>) depicting the estimate for rugged slope terrain, (<b>b</b>,<b>e</b>) for shallow grass terrain, and (<b>c</b>,<b>f</b>) for deep grass terrain.</p>
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24 pages, 1146 KiB  
Article
Walk Longer! Using Wearable Inertial Sensors to Uncover Which Gait Aspects Should Be Treated to Increase Walking Endurance in People with Multiple Sclerosis
by Ilaria Carpinella, Rita Bertoni, Denise Anastasi, Rebecca Cardini, Tiziana Lencioni, Maurizio Ferrarin, Davide Cattaneo and Elisa Gervasoni
Sensors 2024, 24(22), 7284; https://doi.org/10.3390/s24227284 - 14 Nov 2024
Viewed by 239
Abstract
Reduced walking endurance is common in people with multiple sclerosis (PwMS), leading to reduced social participation and increased fall risk. This highlights the importance of identifying which gait aspects should be mostly targeted by rehabilitation to maintain/increase walking endurance in this population. A [...] Read more.
Reduced walking endurance is common in people with multiple sclerosis (PwMS), leading to reduced social participation and increased fall risk. This highlights the importance of identifying which gait aspects should be mostly targeted by rehabilitation to maintain/increase walking endurance in this population. A total of 56 PwMS and 24 healthy subjects (HSs) executed the 6 min walk test (6 MWT), a clinical measure of walking endurance, wearing three inertial sensors (IMUs) on their shanks and lower back. Five IMU-based digital metrics descriptive of different gait domains, i.e., double support duration, trunk sway, gait regularity, symmetry, and local dynamic instability, were computed. All metrics demonstrated moderate–high ability to discriminate between HSs and PwMS (AUC: 0.79–0.91) and were able to detect differences between PwMS at minimal (PwMSmFR) and moderate–high fall risk (PwMSFR). Compared to PwMSmFR, PwMSFR walked with a prolonged double support phase (+100%), larger trunk sway (+23%), lower stride regularity (−32%) and gait symmetry (−18%), and higher local dynamic instability (+24%). Normative cut-off values were provided for all metrics to help clinicians in detecting abnormal scores at an individual level. The five metrics, entered into a multiple linear regression model with 6 MWT distance as the dependent variable, showed that gait regularity and the three metrics most related to dynamic balance (i.e., double support duration, trunk sway, and local dynamic instability) were significant independent contributors to 6 MWT distance, while gait symmetry was not. While double support duration and local dynamic instability were independently associated with walking endurance in both PwMSmFR and PwMSFR, gait regularity and trunk sway significantly contributed to 6 MWT distance only in PwMSmFR and PwMSFR, respectively. Taken together, the present results allowed us to provide hints for tailored rehabilitation exercises aimed at specifically improving walking endurance in PwMS. Full article
(This article belongs to the Collection Sensors for Gait, Human Movement Analysis, and Health Monitoring)
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<p>Pearson’s correlation coefficient <span class="html-italic">r</span> between six-minute walk test distance and IMU-based digital metrics descriptive of the gait domains reported on the left. The metric showing the highest correlation for each domain is reported in dark violet. * <span class="html-italic">p</span> &lt; 0.05. Reg.: regularity; CV: coefficient of variation; iHR: improved Harmonic Ratio; ∆: absolute difference between right and left side; T<sub>step</sub>: step duration; T<sub>stride</sub>: stride duration; T<sub>stance</sub>: stance duration; T<sub>swing</sub>: swing duration; T<sub>dsupp</sub>: double support duration; nRMS: normalized root mean square of trunk acceleration; sLyE<sub>stride/step</sub>: short-term Lyapunov exponent computed over one stride/step; Mod.: trunk acceleration modulus; AP: antero-posterior; ML: medio-lateral; VT: vertical.</p>
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<p>Digital metrics descriptive of gait in healthy subjects (HSs) and people with MS (PwMS). Bold line: median; Box: interquartile range; Whisker: range. *** <span class="html-italic">p</span>&lt; 0.001 (HSs vs. PwMS, Mann–Whitney U Test). iHR: improved Harmonic Ratio; nRMS: normalized root mean square of trunk acceleration; sLyE<sub>step</sub>: short-term Lyapunov exponent computed over one step; Mod.: trunk acceleration modulus; AP: antero-posterior; ML: medio-lateral; AUC: Area Under the Receiver Operating Characteristic (ROC) Curve, mean (95% confidence interval).</p>
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18 pages, 2688 KiB  
Article
Deep Learning and IoT-Based Ankle–Foot Orthosis for Enhanced Gait Optimization
by Ferdous Rahman Shefa, Fahim Hossain Sifat, Jia Uddin, Zahoor Ahmad, Jong-Myon Kim and Muhammad Golam Kibria
Healthcare 2024, 12(22), 2273; https://doi.org/10.3390/healthcare12222273 - 14 Nov 2024
Viewed by 385
Abstract
Background/Objectives: This paper proposes a method for managing gait imbalances by integrating the Internet of Things (IoT) and machine learning technologies. Ankle–foot orthosis (AFO) devices are crucial medical braces that align the lower leg, ankle, and foot, offering essential support for individuals with [...] Read more.
Background/Objectives: This paper proposes a method for managing gait imbalances by integrating the Internet of Things (IoT) and machine learning technologies. Ankle–foot orthosis (AFO) devices are crucial medical braces that align the lower leg, ankle, and foot, offering essential support for individuals with gait imbalances by assisting weak or paralyzed muscles. This research aims to revolutionize medical orthotics through IoT and machine learning, providing a sophisticated solution for managing gait issues and enhancing patient care with personalized, data-driven insights. Methods: The smart ankle–foot orthosis (AFO) is equipped with a surface electromyography (sEMG) sensor to measure muscle activity and an Inertial Measurement Unit (IMU) sensor to monitor gait movements. Data from these sensors are transmitted to the cloud via fog computing for analysis, aiming to identify distinct walking phases, whether normal or aberrant. This involves preprocessing the data and analyzing it using various machine learning methods, such as Random Forest, Decision Tree, Support Vector Machine (SVM), Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), and Transformer models. Results: The Transformer model demonstrates exceptional performance in classifying walking phases based on sensor data, achieving an accuracy of 98.97%. With this preprocessed data, the model can accurately predict and measure improvements in patients’ walking patterns, highlighting its effectiveness in distinguishing between normal and aberrant phases during gait analysis. Conclusions: These predictive capabilities enable tailored recommendations regarding the duration and intensity of ankle–foot orthosis (AFO) usage based on individual recovery needs. The analysis results are sent to the physician’s device for validation and regular monitoring. Upon approval, the comprehensive report is made accessible to the patient, ensuring continuous progress tracking and timely adjustments to the treatment plan. Full article
(This article belongs to the Special Issue Smart and Digital Health)
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<p>Working Prototype of a Smart AFO on a patient.</p>
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<p>System Architecture of Machine Learning and IoT-Driven Smart AFO.</p>
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<p>(<b>a</b>) Patient’s gastrocnemius muscle data. (<b>b</b>) Patient’s accelerometer data plotting. (<b>c</b>) Patient’s EMG data plotting.</p>
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<p>Data Denoising Procedure.</p>
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<p>(<b>a</b>) Original signal. (<b>b</b>) Unrectified and absolute rectified signal. (<b>c</b>) Denoised signal.</p>
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<p>Model Accuracies Comparison.</p>
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14 pages, 1507 KiB  
Article
Energetic and Neuromuscular Demands of Unresisted, Parachute- and Sled-Resisted Sprints in Youth Soccer Players: Differences Between Two Novel Determination Methods
by Gabriele Grassadonia, Michele Bruni, Pedro E. Alcaraz and Tomás T. Freitas
Sensors 2024, 24(22), 7248; https://doi.org/10.3390/s24227248 - 13 Nov 2024
Viewed by 414
Abstract
The aim of this study was to analyze the differences in terms of (1) muscle activation patterns; (2) metabolic power (MP) and energy cost (EC) estimated via two determination methods (i.e., the Global Positioning System [GPS] and electromyography-based [EMG]); and (3) the apparent [...] Read more.
The aim of this study was to analyze the differences in terms of (1) muscle activation patterns; (2) metabolic power (MP) and energy cost (EC) estimated via two determination methods (i.e., the Global Positioning System [GPS] and electromyography-based [EMG]); and (3) the apparent efficiency (AE) of 30-m linear sprints in seventeen elite U17 male soccer players performed under different conditions (i.e., unloaded sprint [US], parachute sprint [PS], and four incremental sled loads [SS15, SS30, SS45, SS60, corresponding to 15, 30, 45 and 60 kg of additional mass]). In a single testing session, each participant executed six trials (one attempt per sprint type). The results indicated that increasing the sled loads led to a linear increase in the relative contribution of the quadriceps (R2 = 0.98) and gluteus (R2 = 0.94) and a linear decrease in hamstring recruitment (R2 = 0.99). The MP during the US was significantly different from SS15, SS30, SS45, and SS60, as determined by the GPS and EMG approaches (p-values ranging from 0.01 to 0.001). Regarding EC, significant differences were found among the US and all sled conditions (i.e., SS15, SS30, SS45, and SS60) using the GPS and EMG methods (all p ≤ 0.001). Moreover, MP and EC determined via GPS were significantly lower in all sled conditions when compared to EMG (all p ≤ 0.001). The AE was significantly higher for the US when compared to the loaded sprinting conditions (all p ≤ 0.001). In conclusion, muscle activation patterns, MP and EC, and AE changed as a function of load in sled-resisted sprinting. Furthermore, GPS-derived MP and EC seemed to underestimate the actual neuromuscular and metabolic demands imposed on youth soccer players compared to EMG. Full article
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<p>Comparison of the metabolic power determined through the GPS and EMG approaches in the different loading conditions. * <span class="html-italic">p</span>-value ≤ 0.05, ** <span class="html-italic">p</span> ≤ 0.01, *** <span class="html-italic">p</span> ≤ 0.001; § ES ≥ 0.20, §§ ES ≥ 0.50, §§§ ES ≥ 0.80.</p>
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<p>Comparison of the energy cost determined through the GPS and EMG approaches in the different loading conditions. * <span class="html-italic">p</span>-value ≤ 0.05, ** <span class="html-italic">p</span> ≤ 0.01, *** <span class="html-italic">p</span> ≤ 0.001; § ES ≥ 0.20, §§ ES ≥ 0.50, §§§ ES ≥ 0.80.</p>
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<p>Linear regressions of the relative contribution of the quadriceps, hamstrings, and gluteus muscles as a function of sled load (<b>A</b>). Comparison of the muscle distribution in each loading condition (<b>B</b>). * <span class="html-italic">p</span>-value ≤ 0.05, ** <span class="html-italic">p</span> ≤ 0.01, *** <span class="html-italic">p</span> ≤ 0.001; § ES ≥ 0.20, §§ ES ≥ 0.50, §§§ ES ≥ 0.80.</p>
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<p>Linear regression of the Apparent Efficiency as a function of sled load (<b>A</b>) and qualitative trend states comparison at each 5 m split for a single player (<b>B</b>).</p>
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9 pages, 709 KiB  
Article
Running Gait Complexity During an Overground, Mass-Participation Five-Kilometre Run
by Ben Jones, Ben Heller, Linda van Gelder, Andrew Barnes, Joanna Reeves and Jon Wheat
Sensors 2024, 24(22), 7252; https://doi.org/10.3390/s24227252 - 13 Nov 2024
Viewed by 344
Abstract
Human locomotion contains innate variability which may provide health insights. Detrended fluctuation analysis (DFA) has been used to quantify the temporal structure of variability for treadmill running, although it has been less commonly applied to uncontrolled overground running. This study aimed to determine [...] Read more.
Human locomotion contains innate variability which may provide health insights. Detrended fluctuation analysis (DFA) has been used to quantify the temporal structure of variability for treadmill running, although it has been less commonly applied to uncontrolled overground running. This study aimed to determine how running gait complexity changes in response to gradient and elapsed exercise duration during uncontrolled overground running. Sixty-eight participants completed an overground, mass-participation five-kilometre run (a parkrun). Stride times were recorded using an inertial measurement unit mounted on the distal shank. Data were divided into four consecutive intervals (uphill lap 1, downhill lap 1, uphill lap 2, downhill lap 2). The magnitude (SD) and structure (DFA) of stride time variability were compared across elapsed exercise duration and gradient using a repeated-measures ANOVA. Participants maintained consistent stride times throughout the run. Stride time DFA-α displayed a moderate decrease (d = |0.39| ± 0.13) during downhill running compared to uphill running. DFA-α did not change in response to elapsed exercise duration, although a greater stride time SD was found during the first section of lap 1 (d = |0.30| ± 0.12). These findings suggest that inter- and intra-run changes in gait complexity should be interpreted in the context of course elevation profiles before conclusions on human health are drawn. Full article
(This article belongs to the Special Issue Wearable Sensors for Optimising Rehabilitation and Sport Training)
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<p>Stride times during each section of the run. No significant main effects were observed. The box plots illustrate, from bottom to top, the minimum, first quartile, median, third quartile and maximum value in each course section.</p>
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<p>Stride time standard deviation during each section of the run. Significant main effect for elapsed exercise duration (lap 1 vs. lap 2), <span class="html-italic">p</span> &lt; 0.001. Significant elapsed exercise duration by gradient interaction, <span class="html-italic">p</span> = 0.001. The box plots illustrate, from bottom to top, the minimum, first quartile, median, third quartile and maximum value in each course section.</p>
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<p>Stride time DFA-α during each section of the run. Significant main effect for gradient (uphill vs. downhill), <span class="html-italic">p</span> &lt; 0.001. The box plots illustrate, from bottom to top, the minimum, first quartile, median, third quartile and maximum value in each course section.</p>
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11 pages, 1777 KiB  
Article
Pre-Impact Fall Detection for E-Scooter Riding Using an IMU: Threshold-Based, Supervised, and Unsupervised Approaches
by Seunghee Lee, Bummo Koo and Youngho Kim
Appl. Sci. 2024, 14(22), 10443; https://doi.org/10.3390/app142210443 - 13 Nov 2024
Viewed by 347
Abstract
Pre-impact fall detection during e-scooter riding is essential for rider safety. Both threshold-based and deep learning algorithms (supervised and unsupervised models) were developed in this study. Twenty participants performed normal driving maneuvers such as straight driving, speed bumps, clockwise roundabouts, and counterclockwise roundabouts, [...] Read more.
Pre-impact fall detection during e-scooter riding is essential for rider safety. Both threshold-based and deep learning algorithms (supervised and unsupervised models) were developed in this study. Twenty participants performed normal driving maneuvers such as straight driving, speed bumps, clockwise roundabouts, and counterclockwise roundabouts, along with falls (abnormal driving maneuvers). A 6-axis IMU sensor (Xsens DOT, The Netherlands) was positioned at the T7 location to record data at 60 Hz. The approaches included threshold-based, supervised learning, and unsupervised learning models The threshold-based approach yielded an accuracy of 98.86% with an F1 score of 0.99, while the supervised model had a slightly lower performance, reaching 86.29% accuracy and an F1 score of 0.56. The unsupervised knowledge distillation model achieved 98.86% accuracy, an F1 score of 0.99, and a memory size of only 46 kB. All models demonstrated lead times of more than 250 ms, sufficient for airbag deployment. Full article
(This article belongs to the Special Issue Traffic Emergency: Forecasting, Control and Planning)
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<p>The e-scooter and an IMU sensor (position: T7).</p>
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<p>The real-road e-scooter driving.</p>
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<p>Threshold-based pre-impact fall-detection algorithm flow chart.</p>
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<p>Deep learning autoencoder model.</p>
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<p>Confusion matrices in different models.</p>
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14 pages, 7441 KiB  
Article
Construction of a Wi-Fi System with a Tethered Balloon in a Mountainous Region for the Teleoperation of Vehicular Forestry Machines
by Gyun-Hyung Kim, Hyeon-Seung Lee, Ho-Seong Mun, Jae-Heun Oh and Beom-Soo Shin
Forests 2024, 15(11), 1994; https://doi.org/10.3390/f15111994 - 12 Nov 2024
Viewed by 368
Abstract
In this study, a Wi-Fi system with a tethered balloon is proposed for the teleoperation of vehicular forestry machines. This system was developed to establish a Wi-Fi communication for stable teleoperation in a timber harvesting site. This system consisted of a helium balloon, [...] Read more.
In this study, a Wi-Fi system with a tethered balloon is proposed for the teleoperation of vehicular forestry machines. This system was developed to establish a Wi-Fi communication for stable teleoperation in a timber harvesting site. This system consisted of a helium balloon, Wi-Fi nodes, a measurement system, a global navigation satellite system (GNSS) antenna, and a wind speed sensor. The measurement system included a GNSS module, an inertial measurement unit (IMU), a data logger, and an altitude sensor. While the helium balloon with the Wi-Fi system was 60 m in the air, the received signal strength indicator (RSSI) was measured by moving a Wi-Fi receiver on the ground. Another GNSS set was also utilized to collect the latitude and longitude data from the Wi-Fi receiver as it traveled. The developed Wi-Fi system with a tethered balloon can create a Wi-Fi zone of up to 1.9 ha within an average wind speed range of 2.2 m/s. It is also capable of performing the teleoperation of vehicular forestry machines with a maximum latency of 185.7 ms. Full article
(This article belongs to the Section Forest Operations and Engineering)
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<p>Concept of forest machine teleoperation using Wi-Fi on tethered balloon.</p>
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<p>Overview of helium balloon: (<b>a</b>) front and (<b>b</b>) bottom views.</p>
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<p>Real view of (<b>a</b>) lower jig, (<b>b</b>) Wi-Fi nodes under lower jig, and (<b>c</b>) upper jig.</p>
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<p>Data acquisition logic of the developed data logger.</p>
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<p>Developed mobile mooring and console station.</p>
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<p>Data collection and analysis.</p>
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<p>Study site.</p>
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<p>Wind velocity (<b>left</b>) and coordinates of the helium balloon moved by the wind (<b>right</b>).</p>
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<p>Changes in roll, pitch, and yaw according to altitude of the tethered balloon.</p>
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<p>Installation of the developed system.</p>
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<p>Schematic of the latency occurring in the Wi-Fi system with a tethered balloon (Wi-Fi roaming occurs from Wi-Fi node (1) to Wi-Fi node (2) when Wi-Fi receiver on the machine Wi-Fi goes out of area covered by Wi-Fi node (1)).</p>
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<p>Schematic diagram of LOS distance calculation method.</p>
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<p>Traveled path converted to planar coordinates.</p>
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<p>Creation of the Wi-Fi zone for the developed system.</p>
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<p>Overall latency for RSSI.</p>
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26 pages, 9809 KiB  
Article
Tightly Coupled LIDAR/IMU/UWB Fusion via Resilient Factor Graph for Quadruped Robot Positioning
by Yujin Kuang, Tongfei Hu, Mujiao Ouyang, Yuan Yang and Xiaoguo Zhang
Remote Sens. 2024, 16(22), 4171; https://doi.org/10.3390/rs16224171 - 8 Nov 2024
Viewed by 656
Abstract
Continuous accurate positioning in global navigation satellite system (GNSS)-denied environments is essential for robot navigation. Significant advances have been made with light detection and ranging (LiDAR)-inertial measurement unit (IMU) techniques, especially in challenging environments with varying lighting and other complexities. However, the LiDAR/IMU [...] Read more.
Continuous accurate positioning in global navigation satellite system (GNSS)-denied environments is essential for robot navigation. Significant advances have been made with light detection and ranging (LiDAR)-inertial measurement unit (IMU) techniques, especially in challenging environments with varying lighting and other complexities. However, the LiDAR/IMU method relies on a recursive positioning principle, resulting in the gradual accumulation and dispersion of errors over time. To address these challenges, this study proposes a tightly coupled LiDAR/IMU/UWB fusion approach that integrates an ultra-wideband (UWB) positioning technique. First, a lightweight point cloud segmentation and constraint algorithm is designed to minimize elevation errors and reduce computational demands. Second, a multi-decision non-line-of-sight (NLOS) recognition module using information entropy is employed to mitigate NLOS errors. Finally, a tightly coupled framework via a resilient mechanism is proposed to achieve reliable position estimation for quadruped robots. Experimental results demonstrate that our system provides robust positioning results even in LiDAR-limited and NLOS conditions, maintaining low time costs. Full article
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<p>Overview of the proposed tightly coupled LiDAR/IMU/UWB positioning system.</p>
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<p>Triangular-based ground point cloud exclusion diagram.</p>
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<p>Concentric circle model of ground segmentation. (<b>a</b>) traditional model on the left; (<b>b</b>) improved model on the right.</p>
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<p>Schematic of the proposed LiDAR/IMU/UWB factor graph model of quadruped robot.</p>
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<p>Experimental equipment: (<b>a</b>) Quadruped robot with sensors (Unitree, Hangzhou, China); (<b>b</b>) UWB hardware module (Nooploop, Nanjing, China); (<b>c</b>) Total station (Starfish, Foshan, China).</p>
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<p>UWB anchor deployment and key points of the mobile experiment.</p>
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<p>Experiment layout. The red triangles indicate the locations of the UWB anchor stations. The blue dot represents the location of the robot tag. The black line shows the reference track.</p>
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<p>Comparison of running time for processing a frame of point cloud by different algorithms across various datasets.</p>
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<p>Error comparison of positioning results for different algorithms across various datasets.</p>
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<p>Comparison of point cloud segmentation results. The pink line represents the fitted ground point cloud. (<b>a</b>) Field diagram of a typical complex environment with multiple steps and curbs. (<b>b</b>) Segmentation result using a traditional point cloud processing algorithm (<b>c</b>) Segmentation result using the proposed algorithm.</p>
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<p>IMU Allan variance analysis results. (<b>a</b>) Accelerometer. (<b>b</b>) Gyroscope.</p>
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<p>The result of distance measurement error optimization.</p>
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<p>Changes in the data curve for each decision criterion. (<b>a</b>) Signal strength difference curve for each anchor station; (<b>b</b>) Distance signal difference curve for each anchor station.</p>
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<p>LOS/NLOS discrimination based on information entropy.</p>
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<p>Two-dimensional trajectory comparisons in a parking lot scenario using LS, EKF, LIU, LIUT, and our method.</p>
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<p>Comparison of error results of different positioning algorithms.</p>
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<p>Three-dimensional trajectory coparions in parking lot scenario using LIU, LIUT and our method.</p>
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<p>Comparison of z-axis results of different positioning algorithms.</p>
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<p>Indoor complex environment and corresponding positioning results.</p>
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