Search Results (245)

In recent years, the RRT* algorithm has been widely applied in industrial fields because of its asymptotic optimality. However, the traditional RRT* algorithm exhibits limitations in terms of convergence speed and quality of generated paths, and its path exploration capability in complex environments remains inadequate. To address these issues, this study proposes a self-adaptive bidirectional APF-RRT* (SA-Bi-APF-RRT*) algorithm. Specifically, a hierarchical node expansion mechanism is established, enabling dynamic adjustment of the new node expansion strategy. Furthermore, a bidirectional artificial potential field (APF) guidance strategy is introduced to enhance obstacle avoidance performance. An obstacle range density evaluation module, which autonomously adjusts APF parameters according to the density distribution of surrounding obstacles, is then incorporated. Additionally, the algorithm integrates a segmented greedy approach with Bézier curve fitting techniques to achieve simultaneous optimization of path length and smoothness, while ensuring path safety. Finally, the proposed algorithm is compared against RRT*, GB-RRT*, Bi-RRT*, APF-RRT*, and Bi-APF-RRT*, demonstrating superior adaptability and efficiency in environments characterized by low iteration counts and high obstacle density. Results indicate that the SA-Bi-APF-RRT* algorithm constitutes a promising optimization solution for USVs path planning tasks. Full article

This paper proposes a coordinated planning method for distribution network lines considering geographical constraints and load distribution, aiming to improve the economy and engineering feasibility of distribution network planning. First, a hierarchical system of geographical constraints based on the Interval Analytic Hierarchy Process (IAHP) is established to systematically quantify the influence weights of spatial factors such as terrain undulation, ecological protection zones, and construction obstacles. Second, the density peak clustering algorithm and load complementarity coefficient are introduced to generate equivalent load nodes, and a spatially continuous load density grid model is constructed to accurately characterize the distribution and complementary characteristics of the load. Third, an improved A-star algorithm is adopted, which integrates a heuristic function guided by geographical weights and load density to dynamically avoid high-cost areas and approach high-load areas. Additionally, Bézier curves are used to optimize the path, reducing crossings and obstacle interference, thus enhancing the implementability of line layout. Verification via a real distribution network case study in a certain area of Guangdong Province shows that the proposed method outperforms traditional planning strategies. It significantly improves the economy, safety, and engineering feasibility of the path, providing effective decision support for distribution network line planning in complex environments. Full article

Compared to the traditional non-load-bearing multi-legged robots, the heavy-duty multi-legged robots typically not only have larger body weight, larger volume, and larger load ratio but also require greater energy dissipation. Traditional path planning often focuses on the problem of finding the shortest path. However, the substantial load capacity and multi-jointed structure of heavy-duty multi-legged robots impose stringent requirements on path smoothness. Consequently, the smoothness requirement makes the traditional A* algorithm unsuitable for applications where low-energy operation is critical. An improved low-energy path planning method based on the A* algorithm is presented for an electrically driven heavy-duty six-legged robot. Then, the environment is discretized by using the grid method to facilitate path searching. To address the path zigzagging problem caused by the traditional A* algorithm, the Bézier curve smoothing technique is adopted. The continuous curvature transitions are employed to significantly improve the smoothness of path. The heuristic function in the A* algorithm is enhanced through a dynamic weight adjustment mechanism. The nonlinear suppression strategy is introduced to prevent data changes and improve the robustness of the algorithm. The effectiveness of the proposed method is verified through the MATLAB simulation platform system. The simulation experiments show that, in various environments with different obstacle densities (0.17–0.37%), compared with the traditional A* algorithm, the method proposed in this paper reduces the average path length by 7.2%, the number of turning points by 25.9%, and the energy consumption by 5.75%. The proposed improved A* algorithm can significantly overcome the problem of insufficient smoothness in traditional A* algorithms and reduce the number of nodes generated by the control data stack, which improves the optimization efficiency during path planning. As a result, the heavy-duty six-legged robots can walk farther and operate for longer periods of time while carrying the limited energy sources. Full article

Real-time path planning for autonomous Unmanned Aerial Vehicles (UAVs) under strict hardware limitations remains a central challenge in embedded robotics. This study presents a refined Rapidly-Exploring Random Tree (RRT) algorithm implemented within an onboard embedded system based on a 32-bit STM32 microcontroller, demonstrating that real-time autonomous navigation can be achieved under low-power computation constraints. The proposed framework integrates a three-stage process—path pruning, Bézier curve smoothing, and iterative optimization—designed to minimize computational overhead while maintaining flight stability. By leveraging the STM32’s limited 72 MHz ARM Cortex-M3 core and 20 KB SRAM, the system performs all planning stages directly on the microcontroller without external computation. Experimental flight tests verify that the UAV can autonomously generate and follow smooth, collision-free trajectories across static obstacle fields with high tracking accuracy. The results confirm the feasibility of executing a full RRT-based planner on an STM32-class embedded platform, establishing a practical pathway for resource-efficient, onboard UAV autonomy. Full article

To address the industry pain points of high seed breakage rate and uncontrollable miss-filling rate, multiple-filling rate in traditional rapeseed roller-type precision centralized seed metering devices—while breaking the adaptation limitation of existing empirical hole designs for different small-particle-size crops—this study innovatively proposes a hole optimization scheme based on the Bezier curve and develops a roller-type precision centralized seed metering device suitable for rapeseed and small-particle-size crops. First, combined with the physical properties of rapeseed seeds (particle size 1.5~2.5 mm, high sphericity, strong fluidity) and agronomic requirements for precision seeding, a multi-mechanical coupling model for seed filling and dropping (synergistic effect of gravity–centrifugal force–air blowing force) was established. The regulatory mechanism of hole geometric parameters (wrap angle, width, height) on seeding performance was clarified, and the enhancement mechanism of the Bezier curve’s curvature continuity on seed movement stability was revealed from the theoretical level. On this basis, a three-factor quadratic orthogonal combination experiment of hole wrap angle, width, and height was conducted using EDEM discrete element software. The optimal hole parameter combination was obtained through multi-objective optimization (minimizing miss-filling rate, multiple-filling rate and maximizing seed-filling qualification rate): wrap angle 2.271° (error ± 0.2°), width 3.407 mm (error ± 0.1 mm), and height 2.254 mm (error ± 0.02 mm). Simulation results showed that under this parameter combination, the seed-filling qualification rate reached 99.122%, with the miss-filling rate and multiple-filling rate as low as 0.448% and 0.416%, respectively. Further bench test verification indicated that when the roller speed was in the range of 10~30 r/min, the seed breakage rate was consistently below 0.5%, and the seed-filling qualification rate remained above 94%. Among them, the comprehensive seeding performance was optimal at a speed of 15 r/min, with a miss-seeding rate of 0.65%, a multiple-seeding rate of 2.06%, and a breakage rate of 0.12%, fully meeting the agronomic requirements for rapeseed precision seeding, providing a theoretical basis and engineering reference for the digital and universal design of key components of precision seeders for small-particle-size crops. Full article

Path planning is a critical capability for unmanned aerial vehicles (UAVs) operating in complex 2D environments such as agricultural fields or indoor facilities—scenarios where flight altitude is often constrained and safe, smooth trajectories are essential. While the sampling-based Bidirectional RRT* (BI-RRT*) algorithm offers asymptotic optimality and improved computational efficiency, it frequently generates paths that lack the curvature continuity, obstacle clearance, and low turning angles required for stable drone flight. To address these limitations, this paper proposes a bi-directional rapid exploration random tree algorithm based on cooperative expansion strategy (CE-BI-RRT*) specifically designed for UAVs path planning in cluttered 2D settings. In terms of expansion, for different environments, the algorithm successively tests the direct expansion strategy, the intelligent deflection strategy and the improved artificial potential field method, as these strategies can quickly guide the two trees to the target while avoiding obstacles. In terms of ChooseParent and Rewire, the path length, path smoothness and safety distance are comprehensively considered in the path cost function, and a rotation strategy is applied to make the path away from obstacles after rewiring, so as to realize the gradual optimization of the path. The final path is further refined using a cubic Bezier curve optimization technique to ensure smooth transitions and continuous curvature. Evaluation results confirm its search performance when benchmarked against mainstream randomized motion planning algorithms. Full article

In the context of rapidly growing logistics demand, traditional warehouse management methods are inadequate in meeting contemporary efficiency and accuracy requirements. The present study proposes the development of an intelligent warehouse visualization platform, the objective of which is to address issues such as high labor dependency, opaque inventory, and operational inefficiencies. The construction of a virtual warehouse environment was undertaken using Unity3D, with the aim of simulating real-world zones. These comprised storage areas, automatic guided vehicle (AGV) pathways, and operational spaces. The platform incorporates radio frequency identification devices (RFID) for item tracking and a role-based access system, enabling real-time monitoring and management of inbound, inventory, and outbound processes. In order to optimize AGV path planning, the proposed algorithm incorporates a dynamic weighted heuristic, a five-neighborhood search, a bidirectional search, and Bézier curve-based smoothing. The efficacy of these enhancements has been demonstrated through a reduction in searched nodes, computation time, and path length, while simultaneously enhancing smoothness. As demonstrated by simulations conducted in Unity3D, the optimized algorithm exhibits a reduction in search nodes of 59.19%, in time of 45.41%, and in path length of 18%, in comparison with the conventional A-star algorithm. The platform offers a safe, efficient, and scalable solution for enterprise training and operational simulation, contributing valuable insights for intelligent warehouse upgrading. Full article

Affine invariance is one of the most fundamental properties of free-form curves, ensuring that transformations such as translation, scaling, rotation, and shearing preserve the essential characteristics of the geometric shape. It is exploited by almost every software that uses such curves. However, this property only holds in a theoretical, mathematical sense. The transformation of a curve calculated and displayed on computers using finite precision arithmetic and representation may not be fully identical to the curve calculated from the transformed control points. This deviation, even pixel-level inaccuracy, can cause problems in various applications, such as Computer-Aided Geometric Design, medical image processing, numerical computations, and font design, where this level of error can have serious consequences. In this paper, we study and demonstrate the extent and nature of this deviation using geometric and statistical tools on a cubic Bézier curve. We provide practical methods to mitigate this inaccuracy and decrease the error level using fast and simple alternative computations of the curve, taking advantage of the symmetry of the basis functions, elevating the degree of the curve, and using reparametrization to evaluate the curve on integer values. The effectiveness of these alternatives is evaluated by statistical methods based on 500,000 transformations. Full article

Aiming at the low qualification rate and high damage caused by the lack of identification, localization, and posture estimation of tea buds in the mechanical harvesting process of famous tea, a framework of lightweight detection + PCA-skeleton fusion posture estimation was proposed. Based on the YOLOv8n model, the StarNet backbone network was introduced to enable lightweight detection, and the ASF-YOLO multi-scale attention module was embedded to improve the feature fusion ability. Based on the detection frame, the GrabCut-Watershed fusion segmentation was employed to obtain the bud mask. Combined with PCA and skeleton extraction algorithms, the main direction deviations of bent buds and clasped leaves were solved by Bézier curve fitting, and the morphology–posture dual-factor scoring model was thereby constructed to realize the picking ranking. Compared with the original YOLOv8n model, the results showed that the detection accuracy and mAP50 of the Improved model decreased to 85.6% and 90.5%, respectively, and the recall rate increased to 81.7%. Meanwhile, the calculation load of the improved model was reduced by 23.6%, reaching 6.8 GFLOPs, indicating a significant improvement in lightweight. The morphology–posture dual-factor scoring model achieved a score of 0.88 for a single bud in vertical direction (θ ≈ 90°), a score of approximately 0.66–0.71 for buds with partially unfolded leaves and slightly bent buds, and a score of 0.48–0.53 for severely bent and overlapped buds. The results of this study have the potential to guide the picking robotic arms to preferentially pick tea buds with high adaptability and provide a reliable visual solution for low-loss and high-efficiency mechanized harvesting of famous tea in complex tea gardens. Full article

The pattern of the front contact metallization critically influences solar cell efficiency. This study introduces a novel explicit geometry optimization approach for designing the front contact metallization patterns. In the proposed approach, the front contact patterns are represented by wide Bezier curves with variable widths, where each curve’s geometry is defined by both control points and control circles. The control point coordinates and the control circle radii are taken as design variables. To ensure physical feasibility during the design process, one of the end control points of each curve is fixed at the current extraction point. Unlike geometry optimization techniques employing fixed-width Bezier curves, our approach provides enhanced design flexibility through continuous width modulation along the front contact paths. Simulation experimental validation across the simple solar cell geometries demonstrates the proposed method’s superior performance relative to both the solid isotropic material with penalization (SIMP) approach and geometry optimization method using a fixed-width Bezier. Furthermore, the optimized front contact metallization structures outperform the conventional H-pattern designs. Specifically, for a solar cell with a size of 3.5 cm, compared to a solar cell with conventional H-pattern front contact electrodes, the conversion efficiency, open-circuit voltage, short-circuit current, and fill factor of the solar cell with curve-shaped front contact metallization are relatively increased by 0.415%, 0.0011 V, and 5.091 A·m⁻², and 0.904%, respectively, while the material coverage ratio is reduced by 1.974%. The methodology’s versatility is further evidenced by its successful adaptation to free-form solar cell configurations. Full article

Power line sag monitoring is critical for ensuring transmission system reliability and optimizing grid capacity utilization. Traditional sag detection methods rely on hyperbolic cosine models that assume ideal catenary behavior under uniform loading conditions. However, these models impose restrictive assumptions about weight distribution and suspension conditions that limit accuracy under real-world scenarios involving wind loading, ice accumulation, and non-uniform environmental forces. This study introduces a novel Bézier curve-based mathematical framework for transmission line sag detection and monitoring. Unlike traditional hyperbolic cosine approaches, the proposed methodology eliminates idealized assumptions and provides enhanced flexibility for modeling actual conductor behavior under variable environmental conditions. The Bézier curve approach offers enhanced precision and computational efficiency through intuitive control point manipulation, making it well suited for Dynamic Line Rating (DLR) applications. Experimental validation was performed using a controlled laboratory setup with a 1:100 scaled transmission line model. Results demonstrate improvement in sag measurement accuracy, achieving an average error of 1.1% compared to 6.15% with traditional hyperbolic cosine methods—representing an 82% improvement in measurement precision. Statistical analysis over 30 independent experiments confirms measurement consistency with a 95% confidence interval of [0.93%, 1.27%]. The framework also demonstrates a 1.5 to 2 times increase in computational efficiency improvement over conventional template matching approaches. This mathematical framework establishes a robust foundation for advanced transmission line monitoring systems, with demonstrated advantages for power grid applications where traditional catenary models fail due to non-ideal environmental conditions. The enhanced accuracy and efficiency support improved Dynamic Line Rating implementations and grid modernization efforts. Full article

To address the challenges of inefficient path planning, discontinuous trajectories, and inadequate safety margins in autonomous spraying vehicles for greenhouse environments, this paper proposes a hierarchical motion control architecture. At the global path planning level, the heuristic function of the A* algorithm was redesigned to integrate channel width constraints, thereby optimizing node expansion efficiency. A continuous reference path is subsequently generated using a third-order Bézier curve. For local path planning, a state-space sampling method was adopted, incorporating a multi-objective cost function that accounts for collision distance, curvature change rate, and path deviation, enabling the real-time computation of optimal obstacle-avoidance trajectories. At the control level, an adaptive look-ahead distance pure pursuit algorithm was designed for trajectory tracking. The proposed framework was validated through a Simulink-ROS co-simulation environment and deployed on a Huawei MDC300F computing platform for real-world vehicle tests under various operating conditions. Experimental results demonstrated that compared with the baseline methods, the proposed approach improved the planning efficiency by 38.7%, reduced node expansion by 16.93%, shortened the average path length by 6.3%, and decreased the path curvature variation by 65.3%. The algorithm effectively supports dynamic obstacle avoidance, multi-vehicle coordination, and following behaviors in diverse scenarios, offering a robust solution for automation in facility agriculture. Full article

This article presents aircraft propeller optimal design technology; including an algorithm and OpenVINT 5 code. To achieve greater geometric flexibility, the proposed technique implements Class-Shape Transformation (CST) parameterization combined with Bézier curves, replacing the previous fully Bézier-based system. Performance improvements in the optimization process are accomplished through deep learning models and a genetic algorithm, which substitute XFOIL and Differential Evolution-based approaches, respectively. The scientific novelty of the article lies in the application of a neural network to predict the aerodynamic characteristics of profiles in the form of contour diagrams, rather than scalar values, which execute the neural network repeatedly per ISM algorithm iteration and speed up the design time of propeller blades by 32 times as much. A propeller for an aircraft-type UAV was designed using the proposed methodology and OpenVINT 5. A comparison was made with the results to solve a similar problem using numerical mathematical models and experimental studies in a wind tunnel. Full article

Embedding text on 3D triangular meshes is essential for conveying semantic information and supporting reliable identification and authentication. However, existing methods often fail to incorporate the geometric properties of the underlying mesh, resulting in shape inconsistencies and visual artifacts, particularly in regions with high curvature. To overcome these limitations, we present GeoText, a framework for generating 3D text directly on triangular meshes while faithfully preserving local surface geometry. In our approach, the control points of TrueType Font outlines are mapped onto the mesh along a user-specified placement curve and reconstructed using geodesic Bézier curves. We introduce two mapping strategies—one based on a local tangent frame and another based on straightest geodesics—that ensure natural alignment of font control points. The reconstructed outlines enable the generation of embossed, engraved, or independent 3D text meshes. Unlike Boolean-based methods, which combine text meshes through union or difference and therefore fail to lie exactly on the surface—breaking the symmetry between embossing and engraving—our offset-based approach ensures a symmetric relation: positive offsets yield embossing, whereas negative offsets produce engraving. Furthermore, our method achieves robust text generation without self-intersections or inter-character collisions. These capabilities make GeoTextwell suited for applications such as 3D watermarking, visual authentication, and digital content creation. Full article

Optimal airfoil design remains a critical challenge in aerodynamic engineering, with traditional methods requiring extensive computational resources and iterative processes. This paper presents GEO-DSGA, a novel framework integrating hybrid geometric neural networks with deep symbiotic genetic algorithms for enhanced airfoil optimization. The methodology employs graph-based representations of airfoil geometries through a hybrid architecture combining graph convolutional networks with traditional deep learning, enabling precise capture of spatial geometric relationships. The parametric modeling stage utilizes CST, Bézier curves, and PARSEC methods to generate mathematically robust airfoil representations, subsequently transformed into graph structures preserving local and global shape characteristics. The optimization framework incorporates a deep symbiotic genetic algorithm enhanced with dominant feature phenotyping, applying biological symbiotic principles where design parameters achieve superior performance through mutual enhancement rather than independent optimization. This systematic exploration maintains geometric feasibility and aerodynamic validity throughout the design space. Experimental results demonstrate an 88.6% reduction in computational time while maintaining prediction accuracy within 1.5% error margin for aerodynamic coefficients across diverse operating conditions. The methodology successfully identifies airfoil geometries outperforming baseline NACA profiles by up to 12% in lift-to-drag ratio while satisfying manufacturing and structural constraints, establishing GEO-DSGA as a significant advancement in computational aerodynamic design optimization. Full article