Search Results (23)

Global path planning for autonomous orchard robots must balance obstacle clearance, path smoothness, and trajectory trackability. This balance is difficult to achieve in unstructured orchards, where irregular tree rows, scattered trunks and ground obstacles, and narrow inter-row passages can cause conventional planners to generate low-clearance paths with frequent local turns. This study proposes SDF-Theta*, a safety- and smoothness-aware global path planning framework for orchard robots in unstructured environments. The framework constructs a Euclidean signed distance field (ESDF) from a two-dimensional occupancy planning map and defines a safe navigable domain using the robot width and a grid-discretization approximation margin. Within this domain, the bidirectional SDF-Theta* search performs candidate-node screening, applies Safe LOS checks along candidate connection segments, and uses safety–geometry multi-criteria state selection based on minimum clearance, mean clearance, path length, and turning cost. The resulting initial discrete path is processed through path skeleton refinement and local Bézier curve smoothing. Differential-flatness-based time parameterization then converts the smoothed geometric path into a time-indexed motion reference. In the Orchard Field Experiment, SDF-Theta* increased the minimum obstacle clearance by 16.6% compared with Theta* (ESDF) and achieved a safe path ratio of 100.00%. It also reduced the 99th-percentile curvature, maximum curvature, and total curvature variation by 54.3%, 85.5%, and 82.1%, respectively. Trajectory Tracking Validation yielded a path-overlap ratio of 94.65% at a nearest-path distance threshold of 0.03 m, with no physical collision or map-boundary violation. These results show that SDF-Theta* improved path safety and geometric smoothness and demonstrated trajectory trackability under the tested orchard conditions. Full article

In complex environments, tower cranes not only need to efficiently transport loads to specified target points but also must avoid obstacles present in their surroundings. This poses a significant challenge for the load positioning control of tower cranes. To tackle this problem, an accurate model-based approach is developed for trajectory planning and tracking control, enabling both obstacle avoidance and precise load positioning during the crane’s lifting process. Specifically, the paper formulates smooth parameterized load trajectories in the tower crane task space using piecewise Bézier curves. The positions of curve control points are designed to allow independent adjustment of each trajectory segment, thus avoiding obstacles during load movement and ensuring operational safety. A novel method for defining the load swing angle is introduced, which employs the system’s differential flatness to map the smooth parameterized trajectories from the task space to the system’s generalized state space without requiring model linearization, thereby ensuring the designed trajectories’ precision and traceability. A meticulously designed high-order sliding mode controller is employed to ensure the jib and trolley accurately follow the prescribed reference trajectory, while effectively suppressing load swing angle, thereby achieving precise load positioning. Finally, the proposed control strategy was tested on a tower crane experimental platform. Experimental validation reveals that the maximum radial swing angle is limited to 3.264°, while the maximum slew swing angle reaches 3.599°, with residual oscillations reduced to 0.425° and 0.343°, respectively. Compared with conventional input-shaping methods, the maximum radial swing and residual oscillation are reduced by 72.7% and 88.9%, respectively. These results demonstrate that the designed trajectory planning and tracking control strategy enables the tower crane load to avoid obstacles smoothly and position precisely at the target point. Full article

This study presents a reinforcement learning (RL)-based framework for the aerodynamic optimization of the Lotte airship, combining mid-fidelity dynamic simulations with adaptive learning strategies. To address the complex nonlinear coupling between the hull shape and tail configuration, a staged, data-driven optimization strategy is developed. In the first stage, single-parameter RL experiments are conducted to independently analyze the aerodynamic sensitivity of key design variables. This conceptual stage isolates pure aerodynamic potential, focusing on the unconstrained optimization of the hull’s Bézier parameterized profile, alongside the individual sensitivities of empennage area, longitudinal shift, lift slope factor, and efficiency. These experiments yield a comprehensive sensitivity map, clarifying each parameter’s independent influence on the average lift-to-drag ratio ($\overline{L/D}$) of the airship. In the second stage, the obtained sensitivities are utilized to structure an integrated multi-parameter optimization scenario. Crucially, this unified environment integrates the hull and tail while enforcing rigorous longitudinal trim constraints via a dynamic bisection search. This forces the RL agent to balance system-level aerodynamic recovery against inevitable trim drag penalties. The proposed framework is implemented in MATLAB R2023b using the SILCROAD airship dynamics environment and trained by the Deep Deterministic Policy Gradient (DDPG) algorithm. Results demonstrate that the initial single-parameter sensitivity extraction not only accelerates algorithmic convergence but also significantly improves the interpretability and physical validity of the final trimmed full airship configuration. This hierarchical approach establishes a systematic path from isolated parameter understanding to holistic, physics-informed aerodynamic design, offering a transferable methodology for future autonomous airship optimization. Full article

Rapid and robust trajectory planning for the Terminal Area Energy Management (TAEM) phase of horizontal-landing Reusable Launch Vehicles (RLVs) is critical but challenging due to large initial deviations, stringent terminal constraints, and strong model nonlinearities. To address the limitations of existing methods in convergence reliability and computational speed, this paper proposes a novel online trajectory optimization framework based on analytical lateral planning and equivalent dynamic decoupling. First, a cubic Bézier curve is employed to parameterize the lateral ground track, enabling the rapid generation of analytical expressions for the lateral states that strictly satisfy boundary constraints. Leveraging these analytical solutions, the original six-degree-of-freedom dynamics are exactly decoupled and reduced to a lower-dimensional model governing only the longitudinal motion. To further mitigate nonlinearity, the third derivative of height with respect to range is introduced as a virtual control variable, transforming the problem into a smoother form. The resulting equivalent longitudinal optimization problem is then efficiently solved using the Gauss Pseudospectral Method. Numerical simulations demonstrate that the proposed method significantly outperforms traditional approaches in computational efficiency: it generates feasible trajectories satisfying all constraints within 0.26 s (3$\sigma$ value). Furthermore, the method exhibits remarkable insensitivity to initial guesses, achieving stable convergence even with simple linear initialization. This approach provides a robust and real-time capable solution for complex TAEM trajectory optimization problems characterized by high nonlinearity and multiple constraints. Full article

Compliant mechanisms have contributed to many advances in soft robotics, and there is strong motivation to translate these ideas to assistive devices where adaptive motion at the human interface is required. This work presents novel reconfigurable compliant joints (RCJs) as a parameterized joint element for functional biomimicry in lower-extremity joints for prosthetic knees and ankle–foot orthoses, with concepts that extend to other limb joints. The RCJ uses a rigid hub and outer ring joined by an array of flexible links with centerlines defined by cubic Bézier curves. Link shapes are organized into four Bézier classes (A–D), with base types using 10, 12, or 14 uniformly distributed link slots and variants generated by modifying active-link count and distribution, forming a structured morphology space of 12 configurations for machine design. Dual-extrusion 3D-printed prototypes are characterized by a custom testing apparatus using a 2.2 kN load cell at 25 mm/s over a 0–90° rotation range across six recorded load cycles to measure torque–angle curves and stiffness under large deformations. Angle-dependent stiffness is evaluated over three fixed intervals (0–30°, 30–60°, and 60–90°) to quantify multi-stage behavior. A 2-dimensional corotational frame model and a Simscape Multibody model, including a rolling-contact knee configuration, use the same parameterization to relate geometry, nonlinear mechanics, and system-level motion. Experiments and simulations show multi-stage torque–angle profiles and predictable stiffness modulation across all configurations, with both magnitude and transition angle tunable through Bézier class and active-link distribution, positioning the RCJ as a CAD/CAE-compatible joint architecture for assistive devices or wearable robotic systems and a basis for advancing functional biomimicry in compliant mechanism design. Full article

Chinese font generation is important for digital typography, cultural preservation, and personalized user interfaces. However, existing methods often face challenges in maintaining structural consistency, supporting diverse stylistic variations, and achieving computational efficiency simultaneously, especially in cloud-based environments. A key application is bandwidth-efficient font delivery, where compact structural templates replace large font files for on-demand style customization. To address these issues, this paper proposes Stroke2Font—a hierarchical vector model with AI-driven optimization for dynamic Chinese font generation. The core model decouples structural representation from style rendering through stroke element decomposition and Bézier curve parameterization. To further balance structural fidelity, style diversity, and real-time performance, we introduce a three-module optimization framework: (1) a reinforcement learning policy for dynamic selection of Bézier control parameters to minimize rendering latency; (2) a genetic algorithm for exploring style vector spaces and generating novel font variants; and (3) an adaptive complexity-aware optimization strategy that dynamically configures parameters based on character structural complexity. Experimental results on a dataset of 150 Chinese characters with 1123 stroke trajectories and 5287 feature points demonstrate that the adaptive complexity-aware optimization achieves the highest trajectory similarity of 65.2%, representing a 6.4% relative improvement over baseline (61.3%). The evaluation covers characters ranging from 1 to 18 strokes across 6 stroke types, with standard deviation reduced to ±5.7% (compared to ±6.5% baseline), indicating more consistent performance. Quantitative analysis confirms that the method generalizes effectively across varying character complexity, with the optimization showing stable improvement regardless of stroke count distribution. These results validate that Stroke2Font provides an effective solution for high-quality, efficient, and scalable Chinese font generation in cloud-based applications. Full article

Drag reduction forms a key area of focus in aerodynamics with a significant emphasis on delaying the laminar-to-turbulent transition of boundary layers over the wings of aircraft. There is enough evidence to suggest that achieving such transition delays is particularly challenging for backward-swept wings with large leading-edge sweep angles, which give rise to crossflow and attachment-line instabilities, in addition to Tollmien–Schlichting waves. The sustenance of extended laminar flow regions at high sweep angles has been demonstrated in recent studies, by designing airfoils with specially curated leading-edge profiles, which generate pressure distributions that can suppress crossflow. Such airfoils are called Crossflow Attenuating Natural Laminar Flow (CATNLF) airfoils. However, the design of such airfoils is presently restricted to inverse methodologies due to the inability of the conventional geometry parameterization techniques in representing the specialized leading-edge profiles of CATNLF airfoils. The aim of this study is to illustrate that a parametric representation of CATNLF airfoils can be realized using Bezier curves, thereby enabling their forward multi-point design using gradient-free Bayesian optimization. The developed design framework in terms of geometry parameterization and optimization formulation is able to deliver airfoils that can sustain natural laminar flow up to around 50% chord length on the upper surface, with a leading-edge sweep angle greater than 27 degrees at a Mach number of 0.78 and a Reynolds number of 20 million within a range of lift coefficients $C_l=0.5\pm 0.1$, making them a suitable design choice for a medium-range transport aircraft. Full article

Autonomous underwater vehicle (AUV) motion planning in complex three-dimensional ocean environments remains challenging due to the simultaneous requirements of obstacle avoidance, dynamic feasibility, and energy efficiency. Current approaches often decouple these factors or exhibit high computational overhead, limiting applicability in real-time or large-scale missions. This work proposes a hierarchical trajectory planning framework designed to address these coupled constraints in an integrated manner. The framework consists of two stages: (i) a current-biased sampling-based planner (CB-RRT*) is introduced to incorporate ocean current information into the path generation process. By leveraging flow field distributions, the planner improves path geometric continuity and reduces steering variations compared with benchmark algorithms; (ii) spatial–temporal alternating optimization is performed within underwater safe corridors, where Bézier curve parameterization is utilized to jointly optimize spatial shapes and temporal profiles, producing dynamically feasible and energy-efficient trajectories. Simulation results in dense obstacle fields, heterogeneous flow environments, and large-scale maps demonstrate that the proposed method reduces the maximum steering angle by up to 63% in downstream scenarios, achieving a mean maximum turning angle of 0.06 rad after optimization. The framework consistently attains the lowest energy consumption across all tests while maintaining an average computation time of 0.68 s in typical environments. These results confirm the framework’s suitability for practical AUV applications, providing a computationally efficient solution for generating safe, kinematically feasible, and energy-efficient trajectories in real-world ocean settings. 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

End-to-end autonomous driving demands precise perception, robust motion planning, and efficient trajectory generation to navigate complex and dynamic environments. This paper proposes BETAV, a novel framework that addresses the persistent challenges of low 3D perception accuracy and suboptimal trajectory smoothness in autonomous driving systems through unified BEV-Transformer encoding and Bézier-optimized planning. By leveraging Vision Transformers (ViTs), our approach encodes multi-view camera data into a Bird’s Eye View (BEV) representation using a transformer architecture, capturing both spatial and temporal features to enhance scene understanding comprehensively. For motion planning, a Bézier curve-based planning decoder is proposed, offering a compact, continuous, and parameterized trajectory representation that inherently ensures motion smoothness, kinematic feasibility, and computational efficiency. Additionally, this paper introduces a set of constraints tailored to address vehicle kinematics, obstacle avoidance, and directional alignment, further enhancing trajectory accuracy and safety. Experimental evaluations on Nuscences benchmark datasets and simulations demonstrate that our framework achieves state-of-the-art performance in trajectory prediction and planning tasks, exhibiting superior robustness and generalization across diverse and challenging Bench2Drive driving scenarios. Full article

This research investigates the optimization of airfoil design for fixed-wing drones, aiming to enhance aerodynamic efficiency and reduce drag. The research employs Kulfan CST and Bézier surface parameterization methods combined with global sensitivity analysis (GSA) and machine learning techniques to improve airfoil performance under various operational conditions. Particle swarm optimization (PSO) is utilized to optimize the airfoil design, minimizing drag in cruise and ascent conditions while ensuring lift at takeoff. Computational fluid dynamics (CFD) simulations, primarily using XFOIL, validate the aerodynamic performance of the optimized airfoils. This study also explores the generative design approach using a neural network trained on 10 million airfoil simulations to predict airfoil geometry based on desired performance criteria. The results show important improvements in drag reduction, especially during low-speed cruise and ascent phases, contributing to extended flight endurance and efficiency. These results can be used for small unmanned aerial vehicles (UAVs) in real-world applications to develop better-performance UAVs under mission-specific constraints. Full article

NURBS curve parameter interpolation is extensively employed in precision trajectory tasks for industrial robots due to its smoother performance compared to traditional linear or circular interpolation methods. The trajectory planning systems for industrial robots necessitate four essential functional modules: first, the spline curve discretization technique ensuring chord error compliance; second, the contour scanning technique for determining the maximum feasible feed rate for multi-constraint and multi-segment paths; third, the technique for achieving a smooth feed rate profile; and fourth, the continuous curve parameter interpolation technique. Therefore, this paper proposes a high-precision planar NURBS interpolation system for industrial robots. Firstly, a segmentation method for NURBS curves based on a closed-loop chord error constraint is proposed, which segments the original global NURBS curve into a collection of Bezier curves that strictly meet the chord error constraint. Secondly, a bidirectional scanning technique is presented to meet the joint space constraint, establishing an analytical mapping between the tool tip kinematic constraint and the joint kinematic constraint. Then, based on the traditional S-shaped feed rate profile, an adaptive algorithm with a displacement constraint is introduced, considering the real-time speed adjustment requirements of robots. Finally, a compensation interpolation strategy based on arc length parameterization is adopted to solve the accumulated error problem in parameter interpolation. The effectiveness of and potential for enhancing the quality of planar machining of the proposed planar NURBS interpolation system for industrial robots are validated through simulations and experiments. The results demonstrate the system’s applicability and accuracy, and its ability to improve planar machining quality. Full article

The modeling and simulation of biological tissue is the core part of a virtual surgery system. In this study, the geometric and physical methods related to soft tissue modeling were investigated. Regarding geometric modeling, the problem of repeated inverse calculations of control points in the Bezier method was solved via re-parameterization, which improved the calculation speed. The base surface superposition method based on prior information was proposed to make the deformation model not only have the advantages of the Bezier method but also have the ability to fit local irregular deformation surfaces. Regarding physical modeling, the fitting ability of the particle spring model to the anisotropy of soft tissue was improved by optimizing the topological structure of the particle spring model. Then, the particle spring model had a more extensive nonlinear fitting ability through the dynamic elastic coefficient parameter. Finally, the secondary modeling of the elastic coefficient based on the virtual body spring enabled the model to fit the creep and relaxation characteristics of biological tissue according to the elongation of the virtual body spring. Full article

This paper considers the problem of minimum-time smooth trajectory planning for wheeled mobile robots. The smooth path is defined by several Bézier curves and the calculated velocity profiles on individual segments are minimum-time with continuous velocity and acceleration in the joints. We describe a novel solution for the construction of a 5th order Bézier curve that enables a simple and intuitive parameterization. The proposed trajectory optimization considers environment space constraints and constraints on the velocity, acceleration, and jerk. The operation of the trajectory planning algorithm has been demonstrated in two simulations: on a racetrack and in a warehouse environment. Therefore, we have shown that the proposed path construction and trajectory generation algorithm can be applied to a constrained environment and can also be used in real-world driving scenarios. Full article

In order to reduce the dependence on fossil fuels, the concept of distributed electric propulsion (DEP) has been introduced. At present, there are a few studies on the small electric propulsion engines of DEP vertical take-off and landing (VTOL) UAVs. According to the design requirements of DEP VTOL UAV ducted fans, the aerodynamic design of a ducted fan is carried out in this paper. Firstly, the initial model is established by referring to theoretical derivations. Then, Bezier curves are used to control the mid-arc and thickness distributions of the blade profiles at different blade heights in order to realize the parameterization as design variables. Finally, the objective function that can represent the performance of the rotor is selected, and a multi-objective genetic algorithm is used to optimize the performance. The optimal results are obtained, and the aerodynamic characteristics are analyzed. Compared with the initial model, the total pressure ratio and isentropic efficiency of the optimized model are increased by 5.3% and 7.8%, respectively, reaching 1.20 and 90.37%. Meanwhile, the aerodynamic performance of the optimized model is improved, indicating that the performance of the rotor is significantly enhanced and that the design task is completed. Full article