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Search Results (3,065)

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Keywords = trajectory optimization

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29 pages, 3567 KiB  
Article
Kinematic Fuzzy Logic-Based Controller for Trajectory Tracking of Wheeled Mobile Robots in Virtual Environments
by José G. Pérez-Juárez, José R. García-Martínez, Alejandro Medina Santiago, Edson E. Cruz-Miguel, Luis F. Olmedo-García, Omar A. Barra-Vázquez and Miguel A. Rojas-Hernández
Symmetry 2025, 17(2), 301; https://doi.org/10.3390/sym17020301 - 17 Feb 2025
Viewed by 24
Abstract
Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller [...] Read more.
Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller with a symmetric distribution of fuzzy numbers is proposed and designed for implementation in the kinematic model of a non-holonomic mobile robot. The symmetry in the distribution of triangular fuzzy numbers contributes to a balanced response to disturbances and minimizes systematic errors in direction estimation. Additionally, it improves the system’s adaptability to various reference paths, ensuring accurate tracking and optimized performance in robot navigation. Furthermore, this fuzzy logic-based controller emulates the behavior of a classic PID controller by offering a robust and flexible alternative to traditional methods. A virtual environment was also developed using the UNITY platform to evaluate the performance of the fuzzy controller. The results were evaluated by considering the average tracking error, maximum error, steady-state error, settling time, and total distance traveled, emphasizing the trajectory error. The circular trajectory showed high accuracy with an average error of 0.0089 m, while the cross trajectory presented 0.01814 m, reflecting slight deviations in the turns. The point-to-point trajectory registered a more significant error of 0.9531 m due to abrupt transitions, although with effective corrections in a steady state. The simulation results validate the robustness of the proposed fuzzy controller, providing quantitative insights into its precision and efficiency in a virtual environment, and demonstrating the effectiveness of the proposal. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)
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<p>Bibliometric map of related works.</p>
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<p>Kinematic model of the Ackerman-type robot.</p>
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<p>Control structure proposed.</p>
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<p>Error linguistic variable distribution.</p>
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<p>Error derivative linguistic variable distribution.</p>
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<p>Integral of error linguistic variable distribution.</p>
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<p>Virtual environment block diagram.</p>
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<p>Determination of the yaw angle.</p>
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<p>Flowchart of the first stage.</p>
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<p>Flowchart of the second stage.</p>
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<p>Virtual environment scene.</p>
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<p>A 3D model of the robot in Fusion 360.</p>
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<p>First test: simulate circular path in Python.</p>
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<p>Angular error for circular path.</p>
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<p>Circular path control signal.</p>
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<p>Simulation of the circular trajectory made in Unity. (<b>a</b>) View of the robot orientation for the path. (<b>b</b>) Front view of the circular path simulation. (<b>c</b>) Aerial view of the circular path simulation.</p>
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<p>Second trajectory test: point-to-point case.</p>
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<p>Angular error for point tracking path.</p>
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<p>Control signal for point-to-point trajectory.</p>
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<p>Point tracking path simulation done in Unity. (<b>a</b>) Partial path of the simulated robot in Unity. (<b>b</b>) Complete robot path in Unity.</p>
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<p>Third case of trajectories: movement always in change.</p>
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<p>Angular error of rotation <math display="inline"><semantics> <mi>δ</mi> </semantics></math> for the crossed trajectory.</p>
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<p>Control signal for the cross path.</p>
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<p>Simulation of the crossing trajectory implemented in Unity. (<b>a</b>) Partial robot path of the crossed trajectory. (<b>b</b>) Full robot path of the cross trajectory.</p>
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35 pages, 2984 KiB  
Article
Target Ship Recognition and Tracking with Data Fusion Based on Bi-YOLO and OC-SORT Algorithms for Enhancing Ship Navigation Assistance
by Shuai Chen, Miao Gao, Peiru Shi, Xi Zeng and Anmin Zhang
J. Mar. Sci. Eng. 2025, 13(2), 366; https://doi.org/10.3390/jmse13020366 - 16 Feb 2025
Viewed by 261
Abstract
With the ever-increasing volume of maritime traffic, the risks of ship navigation are becoming more significant, making the use of advanced multi-source perception strategies and AI technologies indispensable for obtaining information about ship navigation status. In this paper, first, the ship tracking system [...] Read more.
With the ever-increasing volume of maritime traffic, the risks of ship navigation are becoming more significant, making the use of advanced multi-source perception strategies and AI technologies indispensable for obtaining information about ship navigation status. In this paper, first, the ship tracking system was optimized using the Bi-YOLO network based on the C2f_BiFormer module and the OC-SORT algorithms. Second, to extract the visual trajectory of the target ship without a reference object, an absolute position estimation method based on binocular stereo vision attitude information was proposed. Then, a perception data fusion framework based on ship spatio-temporal trajectory features (ST-TF) was proposed to match GPS-based ship information with corresponding visual target information. Finally, AR technology was integrated to fuse multi-source perceptual information into the real-world navigation view. Experimental results demonstrate that the proposed method achieves a mAP0.5:0.95 of 79.6% under challenging scenarios such as low resolution, noise interference, and low-light conditions. Moreover, in the presence of the nonlinear motion of the own ship, the average relative position error of target ship visual measurements is maintained below 8%, achieving accurate absolute position estimation without reference objects. Compared to existing navigation assistance, the AR-based navigation assistance system, which utilizes ship ST-TF-based perception data fusion mechanism, enhances ship traffic situational awareness and provides reliable decision-making support to further ensure the safety of ship navigation. Full article
31 pages, 1751 KiB  
Article
A Study on Path Planning for Curved Surface UV Printing Robots Based on Reinforcement Learning
by Jie Liu, Xianxin Lin, Chengqiang Huang, Zelong Cai, Zhenyong Liu, Minsheng Chen and Zhicong Li
Mathematics 2025, 13(4), 648; https://doi.org/10.3390/math13040648 - 16 Feb 2025
Viewed by 212
Abstract
In robotic surface UV printing, the irregular shape of the workpiece and frequent curvature changes require the printing robot to maintain the nozzle’s perpendicular orientation to the surface during path planning, which imposes high demands on trajectory accuracy and path smoothness. To address [...] Read more.
In robotic surface UV printing, the irregular shape of the workpiece and frequent curvature changes require the printing robot to maintain the nozzle’s perpendicular orientation to the surface during path planning, which imposes high demands on trajectory accuracy and path smoothness. To address this challenge, this paper proposes a reinforcement-learning-based path planning method. First, an ideal main path is defined based on the nozzle characteristics, and then a robot motion accuracy model is established and transformed into a Markov Decision Process (MDP) to improve path accuracy and smoothness. Next, a framework combining Generative Adversarial Imitation Learning (GAIL) and Soft Actor–Critic (SAC) methods is proposed to solve the MDP problem and accelerate the convergence of SAC training. Experimental results show that the proposed method outperforms traditional path planning methods, as well as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Specifically, the maximum Cartesian space error in path accuracy is reduced from 1.89 mm with PSO and 2.29 mm with GA to 0.63 mm. In terms of joint space smoothness, the reinforcement learning method achieves the smallest standard deviation, especially with a standard deviation of 0.00795 for joint 2, significantly lower than 0.58 with PSO and 0.729 with GA. Moreover, the proposed method also demonstrates superior training speed compared to the baseline SAC algorithm. The experimental results validate the application potential of this method in intelligent manufacturing, particularly in industries such as automotive manufacturing, aerospace, and medical devices, with significant practical value. Full article
37 pages, 9511 KiB  
Review
Trends in Flexible Sensing Technology in Smart Wearable Mechanisms–Materials–Applications
by Sen Wang, Haorui Zhai, Qiang Zhang, Xueling Hu, Yujiao Li, Xin Xiong, Ruhong Ma, Jianlei Wang, Ying Chang and Lixin Wu
Nanomaterials 2025, 15(4), 298; https://doi.org/10.3390/nano15040298 - 15 Feb 2025
Viewed by 267
Abstract
Flexible sensors are revolutionizing our lives as a key component of intelligent wearables. Their pliability, stretchability, and diverse designs enable foldable and portable devices while enhancing comfort and convenience. Advances in materials science have provided numerous options for creating flexible sensors. The core [...] Read more.
Flexible sensors are revolutionizing our lives as a key component of intelligent wearables. Their pliability, stretchability, and diverse designs enable foldable and portable devices while enhancing comfort and convenience. Advances in materials science have provided numerous options for creating flexible sensors. The core of their application in areas like electronic skin, health medical monitoring, motion monitoring, and human–computer interaction is selecting materials that optimize sensor performance in weight, elasticity, comfort, and flexibility. This article focuses on flexible sensors, analyzing their “sensing mechanisms–materials–applications” framework. It explores their development trajectory, material characteristics, and contributions in various domains such as electronic skin, health medical monitoring, and human–computer interaction. The article concludes by summarizing current research achievements and discussing future challenges and opportunities. Flexible sensors are expected to continue expanding into new fields, driving the evolution of smart wearables and contributing to the intelligent development of society. Full article
(This article belongs to the Special Issue Polymeric 3D Printing: Applications in Nanoscience and Nanotechnology)
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<p>Flexible sensing technology in smart wearable devices from sensing mechanism to materials to applications.</p>
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<p>The main development process of flexible sensors in the field of intelligent wearables.</p>
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<p>Signal conversion mechanism diagram of four flexible sensor mechanisms [<a href="#B65-nanomaterials-15-00298" class="html-bibr">65</a>]. (<b>a</b>) Schematic diagram of flexible resistive sensor. (<b>b</b>) Schematic diagram of flexible piezoelectric sensor. (<b>c</b>) Schematic diagram of flexible capacitive sensor. (<b>d</b>) Schematic diagram of flexible triboelectric sensor.</p>
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<p>(<b>a</b>) Resistance measurement results of AMSS three modes and forward and reverse bending resistance tests [<a href="#B59-nanomaterials-15-00298" class="html-bibr">59</a>]. (<b>b</b>) Concept design of –rigid-in-soft piezoelectric tactile sensor array [<a href="#B68-nanomaterials-15-00298" class="html-bibr">68</a>]. (<b>c</b>) High SNR capacitive sensor based on corer–shell structure [<a href="#B71-nanomaterials-15-00298" class="html-bibr">71</a>]. (<b>d</b>) Overview of smart insole for gait detection [<a href="#B74-nanomaterials-15-00298" class="html-bibr">74</a>].</p>
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<p>(<b>a</b>) Schematic of flexible CNF porous material preparation and illustration of LbL self-assembly with PEI and PEDOT: PSS [<a href="#B75-nanomaterials-15-00298" class="html-bibr">75</a>]. (<b>b</b>) Fabrication and structure schematic of flexible resistive gas sensors [<a href="#B76-nanomaterials-15-00298" class="html-bibr">76</a>]. (<b>c</b>) Four-dimensional printing methods and schematic diagram of the sensor-reversible actuator [<a href="#B56-nanomaterials-15-00298" class="html-bibr">56</a>]. (<b>d</b>) Schematic diagram of the sensor with the MWCNT/PDMS sensitive film [<a href="#B58-nanomaterials-15-00298" class="html-bibr">58</a>].</p>
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<p>(<b>a</b>) Schematic illustration of the fabrication process for MXene/CNF/GI composite film and supercapacitor [<a href="#B78-nanomaterials-15-00298" class="html-bibr">78</a>]. (<b>b</b>) Schematic illustration of the interface interaction of the CNT@LM droplets [<a href="#B79-nanomaterials-15-00298" class="html-bibr">79</a>]. (<b>c</b>) Schematic illustration of the fabrication process and the structure of CT-LM droplets with its surface non-wettability, recycling ability, and easy magnetointeractive locomotion [<a href="#B80-nanomaterials-15-00298" class="html-bibr">80</a>]. (<b>d</b>) Schematic diagram of fracture and instant healing of α-thioctic acid–butyl acrylate copolymer by hydrogen bond and dynamic disulfide bond [<a href="#B84-nanomaterials-15-00298" class="html-bibr">84</a>].</p>
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<p>(<b>a</b>) Printing and tensile failure process of printed negative Poisson’s ratio CFRSMCs [<a href="#B85-nanomaterials-15-00298" class="html-bibr">85</a>]. (<b>b</b>) The preparation process of CF/PEEK powder composites [<a href="#B86-nanomaterials-15-00298" class="html-bibr">86</a>]. (<b>c</b>) Fabrication process of the sensor and the solubility of MWCNTs-COOH and g-MWCNTs in screen-printing ink with ethanol and DMF solvents in different time periods: initial state; 7 days; 30 days [<a href="#B88-nanomaterials-15-00298" class="html-bibr">88</a>]. (<b>d</b>) Schematic illustration of the fabrication of MWCNT functionalized PEDOT nanowires and its applications in K<sup>+</sup> sensors based on fiber organic electrochemical transistors [<a href="#B90-nanomaterials-15-00298" class="html-bibr">90</a>].</p>
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<p>(<b>a</b>) Fabrication process and structure of the 1T MoS<sub>2</sub>-PDMS foam pressure sensor [<a href="#B92-nanomaterials-15-00298" class="html-bibr">92</a>]. (<b>b</b>) The procedure diagram of preparation procedure of the piezoresistive sensor based on MXene composite with wrinkle structure [<a href="#B95-nanomaterials-15-00298" class="html-bibr">95</a>]. (<b>c</b>) Schematic illustration of fabrication process of 3D MXene/rGO/CuO aerogel [<a href="#B96-nanomaterials-15-00298" class="html-bibr">96</a>]. (<b>d</b>) Schematic of the chemical reactions during the preparation of SnO-SnO<sub>2</sub>/Ti<sub>3</sub>C<sub>2</sub>T<sub>x</sub> nanocomposites [<a href="#B97-nanomaterials-15-00298" class="html-bibr">97</a>].</p>
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<p>(<b>a</b>) Simple strategy diagram of cancer cell mechanical and electronic regulation hydrogel based on MXene immobilized hyaluronic acid polymer dots (M-PD) [<a href="#B98-nanomaterials-15-00298" class="html-bibr">98</a>]. (<b>b</b>) The multifunctionality of elastomers and their application in flexible sensing [<a href="#B99-nanomaterials-15-00298" class="html-bibr">99</a>]. (<b>c</b>) Schematic structure of MWCNTs/CNMs/PAM/SA hydrogels [<a href="#B101-nanomaterials-15-00298" class="html-bibr">101</a>]. (<b>d</b>) Schematic diagram of the manufacturing process and advantages of PTSL hydrogel [<a href="#B102-nanomaterials-15-00298" class="html-bibr">102</a>].</p>
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<p>(<b>a</b>) Pulse waveform measured on the left wrist; periodic signal transmission of index finger bending motion; signal transmission for controlling thumb movement [<a href="#B114-nanomaterials-15-00298" class="html-bibr">114</a>]. (<b>b</b>) Photos comparing the adhesion of PDMS and P32-PDMS elastomers on the arm skin in their original and stretched states [<a href="#B115-nanomaterials-15-00298" class="html-bibr">115</a>]. (<b>c</b>) The manufactured electronic skin patch is attached to the skin. Electronic skin patches adhere closely to the skin under different conditions of twisting and stretching [<a href="#B116-nanomaterials-15-00298" class="html-bibr">116</a>].</p>
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<p>(<b>a</b>) Composition of CMXW<sub>2</sub> humidity sensor, infrared thermal images of temperature changes in the area before and after exercise (such as the back of the hand, palm, forehead, and neck), and comparison of capacitance changes based on sweating in the area [<a href="#B117-nanomaterials-15-00298" class="html-bibr">117</a>]. (<b>b</b>) The capacitance changes of CMXW2 humidity sensor under slow, normal, and fast oral and nasal breathing [<a href="#B117-nanomaterials-15-00298" class="html-bibr">117</a>]. (<b>c</b>) Schematic diagram of PAAm oxCNTs hydrogel and images under stretching, used to monitor subtle human movement [<a href="#B118-nanomaterials-15-00298" class="html-bibr">118</a>]. (<b>d</b>) Data collection of swallowing movements while drinking water [<a href="#B59-nanomaterials-15-00298" class="html-bibr">59</a>]. (<b>e</b>) CP@GM on the throat of volunteers to monitor the movement of the head, neck, and throat [<a href="#B119-nanomaterials-15-00298" class="html-bibr">119</a>].</p>
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<p>(<b>a</b>) Waveforms obtained when volunteers wear the mask correctly to detect nasal, deep, and mouth breathing [<a href="#B119-nanomaterials-15-00298" class="html-bibr">119</a>]. (<b>b</b>) Structural design and working principle of the TENG-based SANES [<a href="#B120-nanomaterials-15-00298" class="html-bibr">120</a>]. (<b>c</b>) Schematic diagram of intelligent pillow monitoring head movement [<a href="#B121-nanomaterials-15-00298" class="html-bibr">121</a>]. (<b>d</b>) Schematic diagram of wearable system monitoring blood pressure [<a href="#B122-nanomaterials-15-00298" class="html-bibr">122</a>].</p>
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<p>(<b>a</b>) Wearable applications for human motion monitoring [<a href="#B123-nanomaterials-15-00298" class="html-bibr">123</a>]. (<b>b</b>) Application of FCPS device in human basketball motion monitoring [<a href="#B124-nanomaterials-15-00298" class="html-bibr">124</a>]. (<b>c</b>) Application of AMSS in wearable smart devices for detecting various physiological movements [<a href="#B59-nanomaterials-15-00298" class="html-bibr">59</a>]. (<b>d</b>) Hydrogel sensors for motion detection in different parts of the human body [<a href="#B3-nanomaterials-15-00298" class="html-bibr">3</a>].</p>
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<p>(<b>a</b>) Interpretation of sign language images used by deaf and mute individuals [<a href="#B126-nanomaterials-15-00298" class="html-bibr">126</a>]. (<b>b</b>) Human joint motion manipulation robot arm diagram [<a href="#B127-nanomaterials-15-00298" class="html-bibr">127</a>]. (<b>c</b>) ATH-Ring based applications, sensing and feedback functions [<a href="#B132-nanomaterials-15-00298" class="html-bibr">132</a>]. (<b>d</b>) Structural diagram of soft gripper and its digital twin application [<a href="#B133-nanomaterials-15-00298" class="html-bibr">133</a>].</p>
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<p>Flexible sensor materials and their applications and challenges in wearable devices.</p>
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18 pages, 1668 KiB  
Article
Transition Control of a Rotary Double Inverted Pendulum Using Direct Collocation
by Doyoon Ju, Taegun Lee and Young Sam Lee
Mathematics 2025, 13(4), 640; https://doi.org/10.3390/math13040640 - 15 Feb 2025
Viewed by 264
Abstract
The rotary double inverted pendulum system is characterized by one stable equilibrium point and three unstable equilibrium points due to its kinematic properties. This paper defines the transition control problem between these equilibrium points to extend the conventional swing-up control problem and proposes [...] Read more.
The rotary double inverted pendulum system is characterized by one stable equilibrium point and three unstable equilibrium points due to its kinematic properties. This paper defines the transition control problem between these equilibrium points to extend the conventional swing-up control problem and proposes an implementation method using a laboratory-developed rotary double inverted pendulum. To minimize energy consumption during the transition process while satisfying the boundary conditions of different equilibrium points, a two-point boundary value optimal control problem is formulated. The feedforward trajectory required for feedforward control is computed offline by solving this problem. The direct collocation method is employed to convert the constrained continuous optimal control problem into a nonlinear optimization problem. Furthermore, a time-varying linear–quadratic (LQ) controller is utilized as a feedback controller to accurately track the generated feedforward trajectory during real-time control, compensating for uncertainties in the feedforward control process. The proposed transition control strategy is experimentally implemented, and its effectiveness and practicality are validated through the successful tracking of 12 transition trajectories. Full article
(This article belongs to the Section C2: Dynamical Systems)
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<p>A rotary double inverted pendulum constructed in the laboratory.</p>
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<p>Conceptual diagram of a rotary double inverted pendulum.</p>
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<p>Inertia tensors of the first and second pendulums.</p>
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<p>Double reduction structure of the rotary double inverted pendulum.</p>
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<p>The 2-DOF control structure for the double inverted pendulum.</p>
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<p>Four equilibrium points of a rotary double inverted pendulum.</p>
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<p>Twelve-step transition diagram of a double inverted pendulum.</p>
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<p>Feedforward transition trajectory from EP0 to EP3.</p>
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<p>Feedforward transition trajectories for control input.</p>
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<p>Time-varying LQ gain of feedforward transition trajectory from EP0 to EP3.</p>
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<p>Twelve-step transition trajectories of a rotary double inverted pendulum: model trajectory (solid line) and actual trajectory (dotted line).</p>
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<p>A YouTube video capture of the 12 transition controls of a rotary double inverted pendulum.</p>
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26 pages, 5032 KiB  
Article
Study on Life-Cycle Carbon Emission of Urban Residential Buildings: A Case Study of Xi’an
by Lina Shen, Zilong Ma and Chang Liu
Sustainability 2025, 17(4), 1602; https://doi.org/10.3390/su17041602 - 14 Feb 2025
Viewed by 275
Abstract
According to statistics from the United Nations Environment Program (UNEP), the construction industry accounts for approximately 30% to 40% of global energy consumption and greenhouse gas emissions, making it a major source of carbon emissions. As a critical component of urban construction, residential [...] Read more.
According to statistics from the United Nations Environment Program (UNEP), the construction industry accounts for approximately 30% to 40% of global energy consumption and greenhouse gas emissions, making it a major source of carbon emissions. As a critical component of urban construction, residential buildings are characterized by their large scale and significant potential for carbon reduction. Building on this context, this study utilizes diversified geospatial data and applies the life-cycle stage framework for residential buildings alongside the emission factor method to calculate total carbon emissions during the material production, construction, and operation phases. It systematically analyzes the distribution characteristics and spatial evolution trends of life-cycle carbon emissions for urban residential buildings. The findings reveal that 63.06% of the cumulative carbon emissions from residential buildings in Xi’an originate from the operation phase, underscoring the importance of optimizing carbon emissions in this phase as a critical priority for future reductions. Additionally, the spatial distribution of residential building carbon emissions exhibits significant clustering, with an increasingly pronounced expansion pattern. Over time, the direction of expansion has shifted from a northeast–southwest orientation to a northwest–southeast trajectory and continues to extend toward peripheral areas. Economic growth, increased urbanization, and the intensive consumption of specific building materials are identified as significant drivers of residential carbon emissions, while population growth and improvements in material utilization efficiency help mitigate emissions to some extent. This study offers valuable insights to support the green development of China’s construction industry and to advance energy-saving and carbon-reduction strategies. Full article
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<p>Map of study area.</p>
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<p>Analysis of the annual consumption of building materials at each stage.</p>
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<p>Total life-cycle carbon emissions of residential buildings in Xi’an.</p>
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<p>Kernel Density Analysis of Residential Buildings in Xi’an Across Different Time Periods. (<b>a</b>) 1989–1993; (<b>b</b>) 1994–1998; (<b>c</b>) 1999–2003; (<b>d</b>) 2004–2008; (<b>e</b>) 2009–2013; (<b>f</b>) 2014–2018; (<b>g</b>) 2019–2022.</p>
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<p>Kernel Density Analysis of Residential Buildings in Xi’an Across Different Time Periods. (<b>a</b>) 1989–1993; (<b>b</b>) 1994–1998; (<b>c</b>) 1999–2003; (<b>d</b>) 2004–2008; (<b>e</b>) 2009–2013; (<b>f</b>) 2014–2018; (<b>g</b>) 2019–2022.</p>
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<p>Hotspot Maps of Residential Building Carbon Emissions in Xi’an Across Different Time Periods. (<b>a</b>) 1989–1993; (<b>b</b>) 1994–1998; (<b>c</b>) 1999–2003; (<b>d</b>) 2004–2008; (<b>e</b>) 2009–2013; (<b>f</b>) 2014–2018; (<b>g</b>) 2019–2022.</p>
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<p>Hotspot Maps of Residential Building Carbon Emissions in Xi’an Across Different Time Periods. (<b>a</b>) 1989–1993; (<b>b</b>) 1994–1998; (<b>c</b>) 1999–2003; (<b>d</b>) 2004–2008; (<b>e</b>) 2009–2013; (<b>f</b>) 2014–2018; (<b>g</b>) 2019–2022.</p>
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<p>Xi’an Residential Building Carbon Emissions SDE. (<b>a</b>) overall time; (<b>b</b>) different time period.</p>
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<p>Characteristics of Carbon Emission Agglomeration of Urban Roads and Residential Buildings in Xi’an City.</p>
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<p>The Distribution of Xi’an Metro and the Agglomeration Characteristics of Carbon Emissions from Residential Buildings.</p>
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27 pages, 662 KiB  
Article
GRU-Based Deep Learning Framework for Real-Time, Accurate, and Scalable UAV Trajectory Prediction
by Seungwon Yoon, Dahyun Jang, Hyewon Yoon, Taewon Park and Kyuchul Lee
Drones 2025, 9(2), 142; https://doi.org/10.3390/drones9020142 - 14 Feb 2025
Viewed by 304
Abstract
Trajectory prediction is critical for ensuring the safety, reliability, and scalability of Unmanned Aerial Vehicle (UAV) in urban environments. Despite advances in deep learning, existing methods often struggle with dynamic UAV conditions, such as rapid directional changes and limited forecasting horizons, while lacking [...] Read more.
Trajectory prediction is critical for ensuring the safety, reliability, and scalability of Unmanned Aerial Vehicle (UAV) in urban environments. Despite advances in deep learning, existing methods often struggle with dynamic UAV conditions, such as rapid directional changes and limited forecasting horizons, while lacking comprehensive real-time validation and generalization capabilities. This study addresses these challenges by proposing a gated recurrent unit (GRU)-based deep learning framework optimized through Look_Back and Forward_Length labeling to capture complex temporal patterns. The model demonstrated state-of-the-art performance, surpassing existing unmanned aerial vehicles (UAV) and aircraft trajectory prediction approaches, including FlightBERT++, in terms of both accuracy and robustness. It achieved reliable long-range predictions up to 4 s, and its real-time feasibility was validated due to its efficient resource utilization. The model’s generalization capability was confirmed through evaluations on two independent UAV datasets, where it consistently predicted unseen trajectories with high accuracy. These findings highlight the model’s ability to handle rapid maneuvers, extend prediction horizons, and generalize across platforms. This work establishes a robust trajectory prediction framework with practical applications in collision avoidance, mission planning, and anti-drone systems, paving the way for safer and more scalable UAV operations. Full article
26 pages, 27528 KiB  
Article
A Stereo Visual-Inertial SLAM Algorithm with Point-Line Fusion and Semantic Optimization for Forest Environments
by Bo Liu, Hongwei Liu, Yanqiu Xing, Weishu Gong, Shuhang Yang, Hong Yang, Kai Pan, Yuanxin Li, Yifei Hou and Shiqing Jia
Forests 2025, 16(2), 335; https://doi.org/10.3390/f16020335 - 13 Feb 2025
Viewed by 209
Abstract
Accurately localizing individual trees and identifying species distribution are critical tasks in forestry remote sensing. Visual Simultaneous Localization and Mapping (visual SLAM) algorithms serve as important tools for outdoor spatial positioning and mapping, mitigating signal loss caused by tree canopy obstructions. To address [...] Read more.
Accurately localizing individual trees and identifying species distribution are critical tasks in forestry remote sensing. Visual Simultaneous Localization and Mapping (visual SLAM) algorithms serve as important tools for outdoor spatial positioning and mapping, mitigating signal loss caused by tree canopy obstructions. To address these challenges, a semantic SLAM algorithm called LPD-SLAM (Line-Point-Distance Semantic SLAM) is proposed, which integrates stereo cameras with an inertial measurement unit (IMU), with contributions including dynamic feature removal, an individual tree data structure, and semantic point distance constraints. LPD-SLAM is capable of performing individual tree localization and tree species discrimination tasks in forest environments. In mapping, LPD-SLAM reduces false species detection and filters dynamic objects by leveraging a deep learning model and a novel individual tree data structure. In optimization, LPD-SLAM incorporates point and line feature reprojection error constraints along with semantic point distance constraints, which improve robustness and accuracy by introducing additional geometric constraints. Due to the lack of publicly available forest datasets, we choose to validate the proposed algorithm on eight experimental plots, which are selected to cover different seasons, various tree species, and different data collection paths, ensuring the dataset’s diversity and representativeness. The experimental results indicate that the average root mean square error (RMSE) of the trajectories of LPD-SLAM is reduced by up to 81.2% compared with leading algorithms. Meanwhile, the mean absolute error (MAE) of LPD-SLAM in tree localization is 0.24 m, which verifies its excellent performance in forest environments. Full article
(This article belongs to the Section Forest Inventory, Modeling and Remote Sensing)
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<p>System framework.</p>
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<p>Example of real-time system operation.</p>
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<p>Data collection equipment.</p>
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<p>Generation of the semantic segmentation mask.</p>
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<p>Semantic feature extraction.</p>
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<p>Stereo vision geometry.</p>
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<p>Extraction of stereo point and line features.</p>
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<p>Establishment of global individual tree database.</p>
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<p>Postex multi-functional tree measurement system.</p>
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<p>TSI acquisition of ground truth trajectory data.</p>
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<p>Experimental data.</p>
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<p>Individual tree localization coordinate comparison on 8 experimental plots.</p>
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<p>Individual tree localization coordinate comparison on 8 experimental plots.</p>
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<p>Trajectory comparison of different algorithms on 8 experimental plots.</p>
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<p>Trajectory comparison of different algorithms on 8 experimental plots.</p>
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<p>Trajectory comparison of different algorithms on 8 experimental plots.</p>
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24 pages, 1238 KiB  
Article
Ascent Trajectory Optimization Using Second-Order Birkhoff Pseudospectral Methods
by Xiaopeng Xue, Yujia Xie, Hui Zhou, Qinghai Gong and Dangjun Zhao
Aerospace 2025, 12(2), 141; https://doi.org/10.3390/aerospace12020141 - 13 Feb 2025
Viewed by 254
Abstract
This paper proposes a novel convex optimization framework for two-stage launch vehicle (TSLV) ascent trajectory planning from liftoff to orbit insertion, featuring two groundbreaking advancements over existing convex optimization methodologies: (1) an innovative second-order Birkhoff pseudospectral (BPS) method is developed that reduces the [...] Read more.
This paper proposes a novel convex optimization framework for two-stage launch vehicle (TSLV) ascent trajectory planning from liftoff to orbit insertion, featuring two groundbreaking advancements over existing convex optimization methodologies: (1) an innovative second-order Birkhoff pseudospectral (BPS) method is developed that reduces the number of dynamic equality constraints by 50% compared to traditional PS methods, meanwhile, an augmented variable transcription technique is used to formulate inequality constraints; therefore, the sparsity ratio of the inequality matrix is reduced to less than 1%; (2) a new iterative solution strategy initialized by a few guesses is proposed to efficiently obtain the optimal solution. The framework is rigorously supported by theoretical convergence guarantees and validated through comprehensive numerical experiments. The numerical results demonstrate around a 50% reduction in computational time compared to the differential PS baseline method. With the significantly reduced computational cost, the proposed method exhibits strong potential for real-time onboard implementation in the future. Full article
(This article belongs to the Section Astronautics & Space Science)
20 pages, 590 KiB  
Article
Reconstruction of Highway Vehicle Paths Using a Two-Stage Model
by Weifeng Yin, Junyong Zhai and Yongbo Yu
Mathematics 2025, 13(4), 618; https://doi.org/10.3390/math13040618 - 13 Feb 2025
Viewed by 186
Abstract
The accurate reconstruction of vehicle paths is essential for effective highway toll management. To address the challenge of multiple possible paths due to missing trajectory data, this study proposes a novel two-stage model for vehicle path reconstruction. In the first stage, a Gaussian [...] Read more.
The accurate reconstruction of vehicle paths is essential for effective highway toll management. To address the challenge of multiple possible paths due to missing trajectory data, this study proposes a novel two-stage model for vehicle path reconstruction. In the first stage, a Gaussian Mixture Model (GMM) is integrated into a path choice model to estimate the mean and standard deviation of travel times for each road segment, utilizing an improved Expectation Maximization (EM) algorithm. In the second stage, based on the estimated time parameters, path choice prior probabilities and observed data are combined using maximum likelihood estimation to infer the most probable paths among candidate routes. The results indicate that the improved EM algorithm achieved convergence in 17 iterations compared to 41 iterations for the traditional EM algorithm. The two-stage model outperforms the Shortest Path and Bidirectional Long Short-Term Memory models in path reconstruction, particularly with a high number of missing trajectory points. Additionally, when the number of candidate paths K=4, the path reconstruction performance is optimal. These results demonstrate the effectiveness of the proposed method in handling sparse and incomplete trajectory data, offering robust and accurate vehicle path estimations that enhance traffic management and toll calculation precision. Full article
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<p>Spatial scope of the case study.</p>
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<p>Distribution of the number of complete trajectories.</p>
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<p>Distribution of missing trajectory points between trajectory point pairs.</p>
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<p>Comparison of EM algorithm performance.</p>
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<p>Path travel time deviation characteristics under different numbers of missing trajectory points.</p>
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<p>Comparison of <math display="inline"><semantics> <mrow> <mi>W</mi> <mi>O</mi> <mi>L</mi> <mi>R</mi> </mrow> </semantics></math>.</p>
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<p><math display="inline"><semantics> <mrow> <mi>W</mi> <mi>O</mi> <mi>L</mi> <mi>R</mi> </mrow> </semantics></math> varies with <span class="html-italic">K</span>.</p>
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15 pages, 4396 KiB  
Article
Speed Optimization Control of a Permanent Magnet Synchronous Motor Based on TD3
by Zuolei Hu, Yingjie Zhang, Ming Li and Yuhua Liao
Energies 2025, 18(4), 901; https://doi.org/10.3390/en18040901 - 13 Feb 2025
Viewed by 282
Abstract
Permanent magnet synchronous motors (PMSMs) are widely used in industrial automation and electric vehicles due to their high efficiency and excellent dynamic performance. However, controlling PMSMs presents challenges such as parameter variations and system nonlinearities. This paper proposes a twin delayed deep deterministic [...] Read more.
Permanent magnet synchronous motors (PMSMs) are widely used in industrial automation and electric vehicles due to their high efficiency and excellent dynamic performance. However, controlling PMSMs presents challenges such as parameter variations and system nonlinearities. This paper proposes a twin delayed deep deterministic policy gradient (TD3)-based energy-saving optimization control method for PMSM drive systems. The TD3 algorithm uses double networks, target policy smoothing regularization, and delayed actor network updates to improve training stability and accuracy. Simulation experiments under two operating conditions show that the TD3 algorithm outperforms traditional proportional–integral (PI) controllers and linear active disturbance rejection control (LADRC) controllers in terms of reference trajectory tracking, q-axis current regulation, and speed tracking error minimization. The results demonstrate the TD3 algorithm’s effectiveness in enhancing motor efficiency and system robustness, offering a novel approach to PMSM drive system control through deep reinforcement learning. Full article
(This article belongs to the Section F1: Electrical Power System)
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<p>Three-phase PMSM vector control block diagram.</p>
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<p>Structure of the TD3 algorithm.</p>
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<p>The dual closed-loop control structure of PMSM speed and current based on TD3.</p>
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<p>Snapshot of the implemented software.</p>
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<p>Training results for working condition 1.</p>
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<p>Experimental results of a PMSM operating in working condition 1. (<b>a</b>) Rotor speed; (<b>b</b>) Q-axis current; (<b>c</b>) speed tracking error.</p>
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<p>Training results for working condition 2.</p>
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<p>Experimental results of PMSM operating in working condition 2. (<b>a</b>) Rotor speed; (<b>b</b>) Q-axis current; (<b>c</b>) speed tracking error.</p>
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<p>Experimental results of a PMSM operating in working condition 2 with torque disturbances. (<b>a</b>) Working condition 1; (<b>b</b>) working condition 2.</p>
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27 pages, 17362 KiB  
Article
A Unified Control System with Autonomous Collision-Free and Trajectory-Tracking Abilities for Unmanned Surface Vessels Under Effects of Modeling Certainties and Ocean Environmental Disturbances
by Chun-Yen Lee, Cheng-Yen Sun, I-Ching Hung and Yung-Yue Chen
Mathematics 2025, 13(4), 609; https://doi.org/10.3390/math13040609 - 13 Feb 2025
Viewed by 316
Abstract
A unified control system that possesses the abilities to arrange collision-free trajectories, precise trajectory tracking, and control allocation for unmanned surface vessels is investigated in this paper by integrating methods, including an image-based trajectory generator, a nonlinear robust controller, and a control allocation [...] Read more.
A unified control system that possesses the abilities to arrange collision-free trajectories, precise trajectory tracking, and control allocation for unmanned surface vessels is investigated in this paper by integrating methods, including an image-based trajectory generator, a nonlinear robust controller, and a control allocation maker. For the purpose of rapidly generating an optimal collision-free trajectory, a rapid image-searching method, named double-sided Finite Angle A* (FAA*), is developed to cooperate with a continuous trajectory generator. This proposed control system provides an effective means for letting controlled unmanned surface vessels be able to execute given tasks by following collision-free trajectories under the influences of modeling uncertainties and ocean environmental disturbances. To eliminate the effects of modeling uncertainties and ocean environmental disturbances, a robust compensator is developed to co-work with a nonlinear control law. Furthermore, the required robust control commands are perfectly performed by a pair of rotatable actuators with an analytical control allocation design. Finally, two demonstrations are examined to validate the control performance of this proposed unified control system. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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<p>The block diagram of the proposed unified control system.</p>
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<p>Satellite image of the interested region where the controlled USV executes tasks.</p>
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<p>Binarization result of <a href="#mathematics-13-00609-f002" class="html-fig">Figure 2</a> after applying Otsu’s method.</p>
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<p>An original binary image (<b>left</b>) and the structuring element (<b>right</b>).</p>
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<p>Output image and the geofencing (pink color) by using a dilation operation.</p>
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<p>Dilation result of <a href="#mathematics-13-00609-f002" class="html-fig">Figure 2</a> by using Equation (2).</p>
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<p>Path-searching result of the FAA* algorithm.</p>
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<p>Path-searching result of the double-sided FAA* algorithm.</p>
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<p>The illustration of the searched collision-free waypoints (blue points).</p>
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<p>The smooth trajectory with several sharp turning angles.</p>
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<p>Illustration of path planning using collision-free waypoints.</p>
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<p>The desired smooth trajectory (red color) via using the proposed interpolation algorithm.</p>
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<p>The appearance of controlled USV.</p>
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<p>The sailing trajectory of the controlled USV in Scenario 1.</p>
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<p>Trajectory-tracking history on <span class="html-italic">X</span> axis of Scenario 1.</p>
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<p>Trajectory-tracking history on <span class="html-italic">Y</span> axis of Scenario 1.</p>
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<p>Trajectory-tracking history in <span class="html-italic">ψ</span> of Scenario 1.</p>
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<p>Tracking error on <span class="html-italic">X</span> axis of Scenario 1.</p>
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<p>Tracking error on <span class="html-italic">Y</span> axis of Scenario 1.</p>
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<p>Tracking error in <span class="html-italic">ψ</span> axis of Scenario 1.</p>
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<p>History of the control torque <span class="html-italic">τ<sub>x</sub></span> of Scenario 1.</p>
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<p>History of the control torque <span class="html-italic">τ<sub>y</sub></span> of Scenario 1.</p>
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<p>History of the control moment <span class="html-italic">τ<sub>ψ</sub></span> of Scenario 1.</p>
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<p>History of right thruster force for Scenario 1.</p>
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<p>History of turning angle of right waterjet for Scenario 1.</p>
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<p>History of left thruster force for Scenario 1.</p>
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<p>History of turning angle of left waterjet for Scenario 1.</p>
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<p>Trajectory-tracking history of the controlled USV in Scenario 2.</p>
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<p>Velocity history of the guided USV in Scenario 2.</p>
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<p>Trajectory-tracking history on <span class="html-italic">X</span> axis of Scenario 2.</p>
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<p>Trajectory-tracking history on <span class="html-italic">Y</span> axis of Scenario 2.</p>
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<p>Trajectory-tracking history in <span class="html-italic">ψ</span> of Scenario 2.</p>
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<p>Tracking error on <span class="html-italic">X</span> axis of Scenario 2.</p>
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<p>Tracking error on <span class="html-italic">Y</span> axis of Scenario 2.</p>
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<p>Tracking error in <span class="html-italic">ψ</span> axis of Scenario 2.</p>
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<p>History of the control torque <span class="html-italic">τ<sub>x</sub></span> of Scenario 2.</p>
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<p>History of the control torque <span class="html-italic">τ<sub>y</sub></span> of Scenario 2.</p>
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<p>History of the control moment <span class="html-italic">τ<sub>ψ</sub></span> of Scenario 2.</p>
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<p>History of right thruster force for Scenario 2.</p>
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<p>History of turning angle of right waterjet for Scenario 2.</p>
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<p>History of left thruster force for Scenario 2.</p>
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<p>History of turning angle of left waterjet for Scenario 2.</p>
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19 pages, 1222 KiB  
Article
Unmanned-Aerial-Vehicle Trajectory Planning for Reliable Edge Data Collection in Complex Environments
by Zhengzhe Xiang, Fuli Ying, Xizi Xue, Xiaorui Peng and Yufei Zhang
Biomimetics 2025, 10(2), 109; https://doi.org/10.3390/biomimetics10020109 - 12 Feb 2025
Viewed by 315
Abstract
With the rapid advancement of edge-computing technology, more computing tasks are moving from traditional cloud platforms to edge nodes. This shift imposes challenges on efficiently handling the substantial data generated at the edge, especially in extreme scenarios, where conventional data collection methods face [...] Read more.
With the rapid advancement of edge-computing technology, more computing tasks are moving from traditional cloud platforms to edge nodes. This shift imposes challenges on efficiently handling the substantial data generated at the edge, especially in extreme scenarios, where conventional data collection methods face limitations. UAVs have emerged as a promising solution for overcoming these challenges by facilitating data collection and transmission in various environments. However, existing UAV trajectory optimization algorithms often overlook the critical factor of the battery capacity, leading to potential mission failures or safety risks. In this paper, we propose a trajectory planning approach Hyperion that incorporates charging considerations and employs a greedy strategy for decision-making to optimize the trajectory length and energy consumption. By ensuring the UAV’s ability to return to the charging station after data collection, our method enhances task reliability and UAV adaptability in complex environments. Full article
(This article belongs to the Special Issue Bio-Inspired Robotics and Applications)
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<p>An illustration of the simulation environment.The blue line represents the possible flight path of the UAV.</p>
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<p>The trajectory paths of the <tt>Hyperion</tt> and baseline algorithms for the same parameters. The coordinates are not measured in meters (m) but are instead based on energy consumption, with the unit being milliampere-hours (mAh).The dotted lines in the figure represent the trajectory paths generated by the algorithm, and the numbers indicate the nodes.</p>
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<p>The energy consumption gaps among various algorithms with only the battery’s capacity being varied: (<b>a</b>) The battery capacity <math display="inline"><semantics> <msup> <mi>B</mi> <mo>*</mo> </msup> </semantics></math> = 1000 mAh; (<b>b</b>) The battery capacity <math display="inline"><semantics> <msup> <mi>B</mi> <mo>*</mo> </msup> </semantics></math> = 1500 mAh; (<b>c</b>) The battery capacity <math display="inline"><semantics> <msup> <mi>B</mi> <mo>*</mo> </msup> </semantics></math> = 2000 mAh; (<b>d</b>) The battery capacity <math display="inline"><semantics> <msup> <mi>B</mi> <mo>*</mo> </msup> </semantics></math> = 2500 mAh.</p>
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<p>The performance of other algorithms compared to the <tt>BEST</tt> algorithm at different clustering degrees of edge nodes: (<b>a</b>) cluster_min = 0.2, cluster_max = 0.5; (<b>b</b>) cluster_min = 0.1, cluster_max = 0.4; (<b>c</b>) cluster_min = 0.05, cluster_max = 0.3.</p>
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<p>Comparison of the completion rates of the different approaches.</p>
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<p>The time costs for different end-device numbers.</p>
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<p>The time costs of different spatial ranges.</p>
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<p>Comparison of Hyperion and Learning-Based Methods across different aspects: (<b>a</b>) Execution time; (<b>b</b>) Path lengths; (<b>c</b>) Energy consumption.</p>
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19 pages, 10296 KiB  
Article
Extended Maximum Actor–Critic Framework Based on Policy Gradient Reinforcement for System Optimization
by Jung-Hyun Kim, Yong-Hoon Choi, You-Rak Choi, Jae-Hyeok Jeong and Min-Suk Kim
Appl. Sci. 2025, 15(4), 1828; https://doi.org/10.3390/app15041828 - 11 Feb 2025
Viewed by 296
Abstract
Recently, significant research efforts have been directed toward leveraging Artificial Intelligence for sensor data processing and system control. In particular, it is essential to determine the optimal path and trajectory by calculating sensor data for effective control systems. For instance, model-predictive control based [...] Read more.
Recently, significant research efforts have been directed toward leveraging Artificial Intelligence for sensor data processing and system control. In particular, it is essential to determine the optimal path and trajectory by calculating sensor data for effective control systems. For instance, model-predictive control based on Proportional-Integral-Derivative models is intuitive, efficient, and provides outstanding control performance. However, challenges in tracking persist, which requires active research and development to integrate and optimize the control system in terms of Machine Learning. Specifically, Reinforcement Learning, a branch of Machine Learning, has been used in several research fields to solve optimal control problems. In this paper, we propose an Extended Maximum Actor–Critic using a Reinforcement Learning-based method to combine the advantages of both value and policy to enhance the learning stability of actor–critic for optimization of system control. The proposed method integrates the actor and the maximized actor in the learning process to evaluate and identify actions with the highest value, facilitating effective learning exploration. Additionally, to enhance the efficiency and robustness of the agent learning process, we propose Prioritized Hindsight Experience Replay, combining the advantages of Prioritized Experience Replay and Hindsight Experience Replay. To verify this, we performed evaluations and experiments to examine the improved training stability in the MuJoCo environment, which is a simulator based on Reinforcement Learning. The proposed Prioritized Hindsight Experience Replay method significantly enhances the experience to be compared with the standard replay buffer and PER in experimental simulators, such as the simple HalfCheetah-v4 and the complex Ant-v4. Thus, Prioritized Hindsight Experience Replay achieves a higher success rate than PER in FetchReach-v2, demonstrating the significant effectiveness of our proposed method in more complex reward environments. Full article
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<p>Markov decision process workflow overview.</p>
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<p>Advancements in Reinforcement Learning algorithms.</p>
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<p>RL-based device sensor control process.</p>
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<p>RL-based learning process for device sensor control.</p>
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<p>Architecture of Prioritized Hindsight Experience Replay.</p>
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<p>Mujoco Environments of (<b>a</b>) HalfCheetah-v4, (<b>b</b>) Hopper-v4, (<b>c</b>) Ant-v4, and (<b>d</b>) Humanoid-v4.</p>
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<p>Maximum vs. minimum average results after 5 experimental iterations of (<b>a</b>) HalfCheetah-v4 and (<b>b</b>) Ant-v4.</p>
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<p>Maximum vs. minimum average results after 5 experimental iterations of (<b>a</b>) Hopper-v4 and (<b>b</b>) Humanoid-v4.</p>
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<p>Buffer learning performance in the Humanoid-v4 environment.</p>
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<p>Simulation environments for multi-goal tasks of (<b>a</b>) FetchReach-v2, (<b>b</b>) FetchPush-v2, (<b>c</b>) FetchPickAndPlace-v2, and (<b>d</b>) FetchSlide-v2.</p>
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<p>Experimental results in FetchReach-v2 for average success rate.</p>
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<p>Experimental results in FetchPickAndPlace-v2 for average success rate.</p>
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<p>Experimental results in FetchPush-v2 for average success rate.</p>
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<p>Experimental results in FetchSlide-v2 for average success rate.</p>
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23 pages, 10476 KiB  
Article
Balance Control Method for Bipedal Wheel-Legged Robots Based on Friction Feedforward Linear Quadratic Regulator
by Aimin Zhang, Renyi Zhou, Tie Zhang, Jingfu Zheng and Shouyan Chen
Sensors 2025, 25(4), 1056; https://doi.org/10.3390/s25041056 - 10 Feb 2025
Viewed by 366
Abstract
With advancements in mobile robot technology, wheel-legged robots have emerged as promising next-generation mobile solutions, reducing design costs and enhancing adaptability in unstructured environments. As underactuated systems, their balance control has become a prominent research focus. Despite there being numerous control approaches, challenges [...] Read more.
With advancements in mobile robot technology, wheel-legged robots have emerged as promising next-generation mobile solutions, reducing design costs and enhancing adaptability in unstructured environments. As underactuated systems, their balance control has become a prominent research focus. Despite there being numerous control approaches, challenges remain. Balance control methods for wheel-legged robots are influenced by hardware characteristics, such as motor friction, which can induce oscillations and hinder dynamic convergence. This paper presents a friction feedforward Linear Quadratic Regulator (LQR) balance control method. Specifically, a basic LQR controller is developed based on the dynamics model of the wheel-legged robot, and a Stribeck friction model is established to characterize motor friction. A constant-speed excitation trajectory is designed to gather data for friction identification, and the Particle Swarm Optimization (PSO) algorithm is applied to determine the optimal friction parameters. The identified friction model is subsequently incorporated as feedforward compensation for the LQR controller’s torque output, resulting in the proposed friction feedforward LQR balance control algorithm. The minimum standard deviation for friction identification is approximately 0.30, and the computed friction model values closely match the actual values, indicating effective and accurate identification results. Balance experiments demonstrate that under diverse conditions—such as flat ground, single-sided bridges, and disturbance scenarios—the convergence performance of the friction feedforward LQR algorithm markedly surpasses that of the baseline LQR, effectively reducing oscillations, accelerating convergence, and improving the robot’s stability and robustness. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>A structural diagram of the friction feedforward LQR Robot balance controller.</p>
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<p>The equivalent model of the robot and a force analysis of each component: (<b>a</b>) the equivalent model; (<b>b</b>) the force analysis of the left drive wheel; (<b>c</b>) the force analysis of the chassis.</p>
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<p>Experimental platform for balance control of bipedal wheel-legged robot.</p>
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<p>Iterative process of friction identification error: (<b>a</b>) left in-wheel motor; (<b>b</b>) right in-wheel motor.</p>
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<p>Fitting results of joint friction torque: (<b>a</b>) left in-wheel motor; (<b>b</b>) right in-wheel motor.</p>
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<p>Results of left in-wheel motor speed tracking experiment: (<b>a</b>) kp = 0.5, ki = 0.05; (<b>b</b>) kp = 0.05, ki = 0.05; (<b>c</b>) kp = 0.05, ki = 0.01.</p>
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<p>Results of right in-wheel motor speed tracking experiment: (<b>a</b>) kp = 0.5, ki = 0.05; (<b>b</b>) kp = 0.05, ki = 0.05; (<b>c</b>) kp = 0.05, ki = 0.01.</p>
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<p>Experimental results of flat ground steady point balance experiment: (<b>a</b>) displacement; (<b>b</b>) velocity; (<b>c</b>) pitch angle.</p>
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<p>Process of flat ground steady point balance experiment.</p>
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<p>Experimental results of single-sided bridge steady point balance experiment: (<b>a</b>) displacement; (<b>b</b>) velocity; (<b>c</b>) pitch angle.</p>
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<p>Process of single-sided bridge steady point balance experiment.</p>
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<p>Experimental results of disturbance rejection experiment: (<b>a</b>) displacement; (<b>b</b>) velocity; (<b>c</b>) pitch angle.</p>
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<p>Process of disturbance rejection steady point balance experiment.</p>
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