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25 pages, 7682 KB  
Article
A General Path Planning Algorithm with Soft Constraints for UAVs in High-Density and Large-Sized Obstacle Scenarios
by Jinjie Chen, Xixiang Liu, Guangrun Sheng, Qiantong Shao and Bingquan Zhao
Drones 2025, 9(11), 793; https://doi.org/10.3390/drones9110793 - 14 Nov 2025
Cited by 1 | Viewed by 982
Abstract
Autonomous navigation of unmanned aerial vehicles (UAVs) in unknown complex environments requires safe, fast and efficient path planning algorithms. Currently, the two-stage framework of “front-end search and back-end optimization” is widely adopted. However, existing research primarily focuses on path planning performance in high-density [...] Read more.
Autonomous navigation of unmanned aerial vehicles (UAVs) in unknown complex environments requires safe, fast and efficient path planning algorithms. Currently, the two-stage framework of “front-end search and back-end optimization” is widely adopted. However, existing research primarily focuses on path planning performance in high-density obstacle scenarios, lacking effective strategies for large-sized obstacles. Furthermore, the current two-stage framework suffers from issues such as path divergence and reduced flight speed. To address these limitations, this paper proposes a general path planning algorithm with soft constraints for UAVs in high-density obstacle scenarios and large-sized obstacle scenarios. The core of the algorithm involves guiding the UAV trajectory through the establishment of well-defined local target points. The front-end employs an expanded space observer for two observations, constructing a real-time safety region, and integrates flight state information to generate local target points using reinforcement learning. The back-end generates trajectories that allows UAVs to fly towards the local target points at higher speeds through an improved Soft Differential Constrained Minimum Snap (SDC-Minimum Snap) algorithm. For large-sized obstacles, a cost-function-based backtracking and circumvention mechanism is introduced to ensure reliable obstacle avoidance. Simulations and real-world experiments validate the generality and feasibility of the proposed algorithm in both scenarios. Full article
(This article belongs to the Section Artificial Intelligence in Drones (AID))
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16 pages, 758 KB  
Article
Real-Time Robust Path Following of a Biomimetic Robotic Dolphin in Disturbance-Rich Underwater Environments
by Yukai Feng, Sijie Li, Zhengxing Wu, Junzhi Yu and Min Tan
Biomimetics 2025, 10(10), 687; https://doi.org/10.3390/biomimetics10100687 - 13 Oct 2025
Cited by 1 | Viewed by 873
Abstract
In ocean engineering, path following serves as a fundamental capability for autonomous underwater vehicles (AUVs), enabling essential operations such as environmental exploration and inspection. However, for robotic dolphins employing dorsoventral undulatory propulsion, the periodic pitching induces strong coupling between propulsion and attitude, posing [...] Read more.
In ocean engineering, path following serves as a fundamental capability for autonomous underwater vehicles (AUVs), enabling essential operations such as environmental exploration and inspection. However, for robotic dolphins employing dorsoventral undulatory propulsion, the periodic pitching induces strong coupling between propulsion and attitude, posing significant challenges for precise path following in disturbed environments. In this paper, a real-time robust path-following control framework is proposed for robotic dolphins to address these challenges. First, a novel robotic dolphin platform is presented by integrating a dorsoventral propulsion mechanism with a passive peduncle joint, followed by the systematic formulation of a full-state dynamic model. Then, a minimum-snap-based path optimizer is constructed to generate smooth and dynamically feasible trajectories, improving path quality and motion safety. Subsequently, a robust model predictive controller is developed, which incorporates control surface dynamics, a nonlinear disturbance observer, and a Sigmoid-based disturbance-grading mechanism to ensure fast attitude response and precise tracking performance. Finally, extensive simulations under various environmental disturbances validate the effectiveness of the proposed approach in both trajectory optimization and robust path following. The proposed framework not only demonstrates strong robustness in path following and disturbance rejection, but also provides practical guidance for future underwater missions such as long-term environmental monitoring, inspection, and rescue. Full article
(This article belongs to the Special Issue Bionic Robotic Fish: 2nd Edition)
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35 pages, 111295 KB  
Article
A Visual Guidance and Control Method for Autonomous Landing of a Quadrotor UAV on a Small USV
by Ziqing Guo, Jianhua Wang, Xiang Zheng, Yuhang Zhou and Jiaqing Zhang
Drones 2025, 9(5), 364; https://doi.org/10.3390/drones9050364 - 12 May 2025
Cited by 3 | Viewed by 4440
Abstract
Unmanned Surface Vehicles (USVs) are commonly used as mobile docking stations for Unmanned Aerial Vehicles (UAVs) to ensure sustained operational capabilities. Conventional vision-based techniques based on horizontally-placed fiducial markers for autonomous landing are not only susceptible to interference from lighting and shadows but [...] Read more.
Unmanned Surface Vehicles (USVs) are commonly used as mobile docking stations for Unmanned Aerial Vehicles (UAVs) to ensure sustained operational capabilities. Conventional vision-based techniques based on horizontally-placed fiducial markers for autonomous landing are not only susceptible to interference from lighting and shadows but are also restricted by the limited Field of View (FOV) of the visual system. This study proposes a method that integrates an improved minimum snap trajectory planning algorithm with an event-triggered vision-based technique to achieve autonomous landing on a small USV. The trajectory planning algorithm ensures trajectory smoothness and controls deviations from the target flight path, enabling the UAV to approach the USV despite the visual system’s limited FOV. To avoid direct contact between the UAV and the fiducial marker while mitigating the interference from lighting and shadows on the marker, a landing platform with a vertically placed fiducial marker is designed to separate the UAV landing area from the fiducial marker detection region. Additionally, an event-triggered mechanism is used to limit excessive yaw angle adjustment of the UAV to improve its autonomous landing efficiency and stability. Experiments conducted in both terrestrial and river environments demonstrate that the UAV can successfully perform autonomous landing on a small USV in both stationary and moving scenarios. Full article
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19 pages, 10941 KB  
Article
Research on the Bearing Characteristics of Folding Steel Arch Frames with Different Snap-Fit Types Based on the Compensation Excavation Concept
by Shaohua Li, Changfu Huang, Xiaojie Yang, Zhigang Tao, Jiaqi Guo, Humin Li, Tiejun Yao and Jie Hu
Buildings 2025, 15(9), 1423; https://doi.org/10.3390/buildings15091423 - 23 Apr 2025
Viewed by 913
Abstract
As the core technology for mechanized installation of tunnel folding steel arch frames, snap-fit connection optimization proves critical in enhancing the load-bearing efficiency of support systems and addressing surrounding rock deformation and instability caused by excavation-induced stress redistribution. Addressing the theoretical gaps in [...] Read more.
As the core technology for mechanized installation of tunnel folding steel arch frames, snap-fit connection optimization proves critical in enhancing the load-bearing efficiency of support systems and addressing surrounding rock deformation and instability caused by excavation-induced stress redistribution. Addressing the theoretical gaps in existing research regarding snap-fit selection mechanisms and quantitative evaluation criteria, this study adopts a combined approach of numerical simulation and field monitoring verification based on the excavation compensation concept to systematically investigate the load-bearing characteristics of folding steel arch frames with different snap-fit configurations. Key findings include (1) identification of 20 mm as the optimal joint diameter, where the vertical displacements of Type A and B snap-fit connections reached their minimum values of 43.1 mm and 39.2 mm, respectively; (2) demonstration of significant geometric configuration effects on principal stress distribution, with Type B connections exhibiting 4.5% lower maximum principal stress compared to Type A, effectively mitigating stress concentration; and (3) field monitoring data verification, revealing that Type B connections achieved 15.8% lower stress values than Type A at critical crown sections, satisfying yield strength requirements while demonstrating enhanced resistance to surrounding rock deformation induced by excavation-induced geostress redistribution. These results confirm Type B snap-fit connections as superior structural solutions for folding steel arch frames, thereby facilitating the advancement of mechanized installation technology for tunnel steel arch frames. Full article
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19 pages, 9382 KB  
Article
Minimum Snap Trajectory Planning and Augmented MPC for Morphing Quadrotor Navigation in Confined Spaces
by Chaojun Qin, Na Zhao, Qiuyu Wang, Yudong Luo and Yantao Shen
Drones 2025, 9(4), 304; https://doi.org/10.3390/drones9040304 - 12 Apr 2025
Cited by 2 | Viewed by 2708
Abstract
Existing studies rarely investigate the dynamic morphology factor on motion planning and control, which is crucial for morphing quadrotors to achieve autonomous flight. Therefore, this paper studies the collaborative optimization of trajectory generation and flight control for the morphing quadrotor with real-time adjustable [...] Read more.
Existing studies rarely investigate the dynamic morphology factor on motion planning and control, which is crucial for morphing quadrotors to achieve autonomous flight. Therefore, this paper studies the collaborative optimization of trajectory generation and flight control for the morphing quadrotor with real-time adjustable arms. In the motion planning layer, an objective function that combines position and morphology is constructed by embedding variable arm length as a decision variable into the conventional minimum snap trajectory generation framework. The generated trajectory not only satisfies the speed and acceleration constraints, but also smoothly passes through the narrow spaces that are difficult for traditional quadrotors to traverse. In the control layer, a constrained augmented model predictive control based on the dynamics of the morphing quadrotors is proposed to follow the generated trajectory with an embedded integrator, which is added by exploiting the differential flat variables to improve the tracking performance. In the numerical studies, a scenario with a corridor was considered to demonstrate the effectiveness of the proposed control strategy to achieve optimal trajectory under multiple constraints. Full article
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15 pages, 2333 KB  
Article
Insights into the Genetics Underlying the Resistance to Root-Knot Nematode Reproduction in the Common Bean Ouro Negro
by Ana M. Pesqueira, Ana M. González, Teresa Barragán-Lozano, María S. Arnedo, Rafael Lozano and Marta Santalla
Plants 2025, 14(7), 1073; https://doi.org/10.3390/plants14071073 - 1 Apr 2025
Cited by 2 | Viewed by 1156
Abstract
Root-knot nematodes (RKNs, Meloidogyne spp.) have become the major yield-limiting biological factor in common bean production in many warmer-climate regions such as the south of Europe. Broadening the genetic base of resistance in elite common bean cultivars is the most effective and environmentally [...] Read more.
Root-knot nematodes (RKNs, Meloidogyne spp.) have become the major yield-limiting biological factor in common bean production in many warmer-climate regions such as the south of Europe. Broadening the genetic base of resistance in elite common bean cultivars is the most effective and environmentally friendly method for managing this disease. Toward this goal, F1, F2, and F3 populations from crosses between susceptible snap beans (Helda and Perona) and the resistant Ouro Negro cultivar were phenotyped for M. incognita and M. javanica-induced root-galling (GI) and egg mass production (EM) in controlled growth chamber infection assays. F1 progenies showed a susceptible response to both RKN isolates, with high GI and EM values, indicating a recessive inheritance of nematode resistance. The estimates for broad-sense heritability for GI and EM in the F2 Helda × Ouro Negro population infected with M. incognita were 0.62 and 0.54, respectively. RKN resistance in Ouro Negro is largely controlled by partial to overdominant genetic effects and that susceptibility factor leads recessive resistance. The minimum number of genes involved in nematode resistance was estimated to be about two or three. In agreement, genetic analysis of F2 segregating populations supported duplicate recessive epistasis as the inheritance pattern involved in the resistance provided by the Ouro Negro cultivar. Ouro Negro is an important resource for broadening RKN resistance in elite common bean cultivars. Full article
(This article belongs to the Special Issue The Mechanisms of Plant Resistance and Pathogenesis)
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15 pages, 3691 KB  
Article
Adaptive Steered Frequency–Wavenumber Analysis for High-Frequency Source Localization in Shallow Water
by Y. H. Choi, Gihoon Byun, Donghyeon Kim and J. S. Kim
Sensors 2025, 25(7), 2036; https://doi.org/10.3390/s25072036 - 25 Mar 2025
Cited by 1 | Viewed by 1040
Abstract
In shallow-water environments, source localization often suffers from reduced performance in conventional array signal processing techniques for frequency bands above 1 kHz due to environmental mismatch. A recently proposed technique, called the steered frequency–wavenumber (SFK) analysis method, overcomes this limitation. By incorporating beam-steering [...] Read more.
In shallow-water environments, source localization often suffers from reduced performance in conventional array signal processing techniques for frequency bands above 1 kHz due to environmental mismatch. A recently proposed technique, called the steered frequency–wavenumber (SFK) analysis method, overcomes this limitation. By incorporating beam-steering techniques into frequency–wavenumber analysis, this method enables target localization even in sparse conditions where high-frequency signals are received. This study extends the SFK method by applying various adaptive signal processing techniques, with a particular focus on the minimum-variance distortionless response and white noise gain constraint methods. Using snapping shrimp sounds from the SAVEX15 experiment, we analyzed localization performance and compared it with the Bartlett SFK approach. The snapping shrimp signals have frequency components ranging from 5 to 24 kHz and exhibit impulsive characteristics with a duration of 0.2 ms. Signals recorded by a sparse vertical array of 16 sensors, with a 60-m aperture in 100-m shallow water, enabled the localization of a source at a range of 38 m and a depth of 99.8 m. Full article
(This article belongs to the Section Environmental Sensing)
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10 pages, 3707 KB  
Article
Unveiling Software Limitations in the Assessment of the Minimum Sectional Area and Volume in Cleft LIP and Palate Patients
by Beethoven Estevao Costa, Renato Yassutaka Faria Yaedú, Maísa Pereira-Silva, André Luis da Silva Fabris, Michele Garcia-Usó, Osvaldo Magro Filho and Simone Soares
Life 2025, 15(2), 226; https://doi.org/10.3390/life15020226 - 4 Feb 2025
Cited by 1 | Viewed by 1143
Abstract
The increasing use of cone beam computed tomography (CBCT) has led to a growing demand for DICOM software that enables the assessment and measurement of craniofacial structures. This study aimed to compare the airway volume and the minimum axial area in patients with [...] Read more.
The increasing use of cone beam computed tomography (CBCT) has led to a growing demand for DICOM software that enables the assessment and measurement of craniofacial structures. This study aimed to compare the airway volume and the minimum axial area in patients with cleft lip and palate using five different imaging software programs: Dolphin3D, InVivo Dental, ITK Snap, InVesalius, and NemoFAB. Initially, 100 CBCT scans were selected by an examiner, and their corresponding DICOM files were collected. The oropharyngeal segments were delineated following the manufacturer’s guidelines, using two different segmentation techniques: interactive and fixed threshold. The results were analyzed using the Friedman test and Wilcoxon post hoc test, with a 5% significance level for all statistical tests. The findings for both the minimum axial area and total volume revealed that the median values across the software groups were higher than expected, and significant differences were observed when comparing the groups (p < 0.001). All five software programs showed notable differences in their outputs. Specifically, a statistically significant difference in volume was found across all groups, except between InVivo and ITK-Snap. It is recommended that pre- and post-treatment comparisons be performed using the same software for consistency. Full article
(This article belongs to the Section Medical Research)
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39 pages, 10058 KB  
Article
Utilizing the Finite Fourier Series to Generate Quadrotor Trajectories Through Multiple Waypoints
by Yevhenii Kovryzhenko and Ehsan Taheri
Drones 2025, 9(1), 77; https://doi.org/10.3390/drones9010077 - 20 Jan 2025
Cited by 1 | Viewed by 2263
Abstract
Motion planning is critical for ensuring precise and efficient operations of unmanned aerial vehicles (UAVs). While polynomial parameterization has been the prevailing approach, its limitations in handling complex trajectory requirements have motivated the exploration of alternative methods. This paper introduces a finite Fourier [...] Read more.
Motion planning is critical for ensuring precise and efficient operations of unmanned aerial vehicles (UAVs). While polynomial parameterization has been the prevailing approach, its limitations in handling complex trajectory requirements have motivated the exploration of alternative methods. This paper introduces a finite Fourier series (FFS)-based trajectory parameterization for UAV motion planning, highlighting its unique capability to produce piecewise infinitely differentiable trajectories. The proposed approach addresses the challenges of fixed-time minimum-snap trajectory optimization by formulating the problem as a quadratic programming (QP) problem, with an analytical solution derived for unconstrained cases. Additionally, we compare the FFS-based parameterization with the polynomial-based minimum-snap algorithm, demonstrating comparable performance across several representative trajectories while uncovering key differences in higher-order derivatives. Experimental validation of the FFS-based parameterization using an in-house quadrotor confirms the practical applicability of the FFS-based minimum-snap trajectories. The results indicate that the proposed FFS-based parameterization offers new possibilities for motion planning, especially for scenarios requiring smooth and higher-order derivative continuity at the expense of minor increase in computational cost. Full article
(This article belongs to the Special Issue Path Planning, Trajectory Tracking and Guidance for UAVs: 2nd Edition)
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27 pages, 9595 KB  
Article
A Control System Design and Implementation for Autonomous Quadrotors with Real-Time Re-Planning Capability
by Yevhenii Kovryzhenko, Nan Li and Ehsan Taheri
Robotics 2024, 13(9), 136; https://doi.org/10.3390/robotics13090136 - 9 Sep 2024
Cited by 7 | Viewed by 3313
Abstract
Real-time (re-)planning is crucial for autonomous quadrotors to navigate in uncertain environments where obstacles may be detected and trajectory plans must be adjusted on-the-fly to avoid collision. In this paper, we present a control system design for autonomous quadrotors that has real-time re-planning [...] Read more.
Real-time (re-)planning is crucial for autonomous quadrotors to navigate in uncertain environments where obstacles may be detected and trajectory plans must be adjusted on-the-fly to avoid collision. In this paper, we present a control system design for autonomous quadrotors that has real-time re-planning capability, including the hardware pipeline for the hardware–software integration to realize the proposed real-time re-planning algorithm. The framework is based on a modified version of the PX4 Autopilot and a Raspberry Pi 5 companion computer. The planning algorithm utilizes minimum-snap trajectory generation, taking advantage of the differential flatness property of quadrotors, to realize computationally light, real-time re-planning using an onboard computer. We first verify the control system and the planning algorithm through simulation experiments, followed by implementing and demonstrating the system on hardware using a quadcopter. Full article
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29 pages, 3153 KB  
Article
Towards Autonomous Operation of UAVs Using Data-Driven Target Tracking and Dynamic, Distributed Path Planning Methods
by Jae-Young Choi, Rachit Prasad and Seongim Choi
Aerospace 2024, 11(9), 720; https://doi.org/10.3390/aerospace11090720 - 3 Sep 2024
Cited by 1 | Viewed by 2692
Abstract
A hybrid real-time path planning method has been developed that employs data-driven target UAV trajectory tracking methods. It aims to autonomously manage the distributed operation of multiple UAVs in dynamically changing environments. The target tracking methods include a Gaussian mixture model, a long [...] Read more.
A hybrid real-time path planning method has been developed that employs data-driven target UAV trajectory tracking methods. It aims to autonomously manage the distributed operation of multiple UAVs in dynamically changing environments. The target tracking methods include a Gaussian mixture model, a long short-term memory network, and extended Kalman filters with pre-specified motion models. Real-time vehicle-to-vehicle communication is assumed through a cloud-based system, enabling virtual, dynamic local networks to facilitate the high demand of vehicles in airspace. The method generates optimal paths by adaptively employing the dynamic A* algorithm and the artificial potential field method, with minimum snap trajectory smoothing to enhance path trackability during real flights. For validation, software-in-the-loop testing is performed in a dynamic environment composed of multiple quadrotors. The results demonstrate the framework’s ability to generate real-time, collision-free flight paths at low computational costs. Full article
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15 pages, 627 KB  
Article
Extreme Body Condition Index Values in Small Mammals
by Linas Balčiauskas and Laima Balčiauskienė
Life 2024, 14(8), 1028; https://doi.org/10.3390/life14081028 - 19 Aug 2024
Viewed by 1891
Abstract
The body condition index (BCI) values in small mammals are important in understanding their survival and reproduction. The upper values could be related to the Chitty effect (presence of very heavy individuals), while the minimum ones are little known. In this study, we [...] Read more.
The body condition index (BCI) values in small mammals are important in understanding their survival and reproduction. The upper values could be related to the Chitty effect (presence of very heavy individuals), while the minimum ones are little known. In this study, we analyzed extremes of BCI in 12 small mammal species, snap-trapped in Lithuania between 1980 and 2023, with respect to species, animal age, sex, and participation in reproduction. The proportion of small mammals with extreme body condition indices was negligible (1.33% with a BCI < 2 and 0.52% with a BCI > 5) when considering the total number of individuals processed (n = 27,073). When compared to the expected proportions, insectivores and herbivores were overrepresented, while granivores and omnivores were underrepresented among underfit animals. The proportions of granivores and insectivores were higher, while those of omnivores and herbivores were lower than expected in overfit animals. In several species, the proportions of age groups in underfit and overfit individuals differed from that expected. The male–female ratio was not expressed, with the exception of Sorex araneus. The highest proportion of overfit and absence of underfit individuals was found in Micromys minutus. The observation that individuals with the highest body mass are not among those with the highest BCI contributes to the interpretation of the Chitty effect. For the first time in mid-latitudes, we report individuals of very high body mass in three shrew species. Full article
(This article belongs to the Section Animal Science)
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23 pages, 6934 KB  
Article
UAV Path Planning for Container Terminal Yard Inspection in a Port Environment
by Gang Tang, Chenyuan Wang, Zhao Zhang and Shaoyang Men
J. Mar. Sci. Eng. 2024, 12(1), 128; https://doi.org/10.3390/jmse12010128 - 9 Jan 2024
Cited by 4 | Viewed by 3011
Abstract
Container terminal yards are automated terminal yards. The rail-mounted gantry crane (RMGC) and rail-mounted gantry crane tracks (RMGCTs) that frequently operate in terminal yards need to be inspected regularly to ensure the safe operation of container transportation in the yard. This paper proposes [...] Read more.
Container terminal yards are automated terminal yards. The rail-mounted gantry crane (RMGC) and rail-mounted gantry crane tracks (RMGCTs) that frequently operate in terminal yards need to be inspected regularly to ensure the safe operation of container transportation in the yard. This paper proposes a framework for the path planning of RMGCT visual inspection using a UAV in container terminal yards in a port environment. The framework consisted of two main aspects. First, a global path to all inspection viewpoints was planned according to the inspection requirements using the A* algorithm and the improved minimum snap method. Second, the intelligent bidirectional rapidly exploring random trees star (IB-RRT*) algorithm was introduced to plan the local path during the flight of the UAV. Finally, the feasibility of the path-planning framework was demonstrated using simulation experiments. Full article
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37 pages, 2479 KB  
Review
Survey on Motion Planning for Multirotor Aerial Vehicles in Plan-Based Control Paradigm
by Geesara Kulathunga and Alexandr Klimchik
Remote Sens. 2023, 15(21), 5237; https://doi.org/10.3390/rs15215237 - 3 Nov 2023
Cited by 6 | Viewed by 3390
Abstract
In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favor of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice [...] Read more.
In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favor of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning, both local and global, the key metrics to bear in mind are execution time, asymptotic optimality, and quick reaction to dynamic obstacles. Such planning approaches can address the aforementioned target metrics more efficiently compared to other approaches, such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyze related literature in order to understand how the motion planning problem, especially the trajectory planning problem, is formulated when being applied for generating optimal trajectories in real-time for multirotor aerial vehicles, as well as how it impacts the listed metrics. As a result of this research, the trajectory planning problem was broken down into a set of subproblems, and the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline. Full article
(This article belongs to the Special Issue UAV Positioning: From Ground to Sky)
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22 pages, 7012 KB  
Article
Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates
by Saeid Saberi, Hamid Nasiri, Omid Ghorbani, Michael I. Friswell and Saullo G. P. Castro
Materials 2023, 16(15), 5381; https://doi.org/10.3390/ma16155381 - 31 Jul 2023
Cited by 12 | Viewed by 2897
Abstract
Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to [...] Read more.
Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh–Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model’s output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively. Full article
(This article belongs to the Special Issue Variable Stiffness Composite Materials and Structures)
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