Search Results (47)

In this work, we introduce a novel class of $C^1$ rational quadratic interpolation splines defined by two symmetric parameters. This generalization encompasses the rational quadratic interpolation schemes given by Schmidt in 1987 as a special case. For data sets with convexity, monotonicity, or positivity constraints, we derive the necessary and sufficient conditions, ensuring that the interpolant preserves these properties. Furthermore, we propose an algorithm for selecting visually appealing and shape-preserving spline curves by minimizing a particular approximated curvature functional. Full article

This article presents an alternative variant of motion planning techniques for autonomous vehicles (AVs) centered on an inverse approach that concurrently optimizes both trajectory and speed. This method emphasizes searching for a trajectory and distributing its speed within a single road segment, regarded as a final element. The references for the road lanes are represented by splines that interpolate the path length, derivative, and curvature using Cartesian coordinates. This approach enables the determination of parameters at the final node of the road segment while varying the reference length. Instead of directly modeling the trajectory and velocity, the second derivatives of curvature and speed are modeled to ensure the continuity of all kinematic parameters, including jerk, at the nodes. A specialized inverse numerical integration procedure based on Gaussian quadrature has been adapted to reproduce the trajectory, speed, and other key parameters, which can be referenced during the motion tracking phase. The method emphasizes incorporating kinematic, dynamic, and physical restrictions into a set of nonlinear constraints that are part of the optimization procedure based on sequential quadratic optimization. The objective function allows for variation in multiple parameters, such as speed, longitudinal and lateral jerks, final time, final angular position, final lateral offset, and distances to obstacles. Additionally, several motion planning variants are calculated simultaneously based on the current vehicle position and the number of lanes available. Graphs depicting trajectories, speeds, accelerations, jerks, and other relevant parameters are presented based on the simulation results. Finally, this article evaluates the efficiency, speed, and quality of the predictions generated by the proposed method. The main quantitative assessment of the results may be associated with computing performance, which corresponds to time costs of 0.5–2.4 s for an average power notebook, depending on optimization settings, desired accuracy, and initial conditions. Full article

This paper tackles the highly challenging problem of automatic berthing for autonomous surface vessels (ASVs), encompassing trajectory planning, trajectory tracking, and collision avoidance. Firstly, a novel A* algorithm integrated with a quasi-uniform B-spline and quadratic interpolation method (A*QB) is proposed for generating a smooth trajectory from the initial position to the berth, utilizing an offline-generated scaled map. Secondly, the optimal nonlinear model predictive control (NMPC)-based trajectory-tracking framework is established, incorporating the model’s uncertainty, the input saturation, and environmental disturbances, based on a 3-DOF model of a ship. Finally, considering the collision risks during port berthing, a COLREGs-based collision avoidance method is investigated. Consequently, a novel trajectory-tracking and COLREGs-based collision avoidance (TTCCA) scheme is proposed, ensuring that the ASV navigates along the desired trajectory, safely avoids both static and dynamic obstacles, and successfully reaches the berth. To validate the TTCCA approach, numerical simulations are conducted across four scenarios with comparisons to existing methods. The experimental results demonstrate the effectiveness and superiority of the proposed scheme. Full article

In modern manufacturing, achieving high-speed laser cutting requires advanced robotic trajectory planning for smoothness and collision avoidance. Poorly optimized motion can cause frequent velocity changes, leading to mechanical vibrations that shorten machine service life. This study presents an innovative trajectory optimization approach for laser cutting machines equipped with a redundant standoff axis. A B-spline-based analytical model formulates rotational axes trajectories as quadratic programming problems to minimize jerk (the rate of acceleration change) under machining accuracy and kinematic constraints. Additionally, an M path, represented by the wrist center’s trajectory, refines translational axes by adjusting the standoff axis through a similar optimization model, thereby reducing mechanical stress. Collision avoidance is ensured through a concurrent iterative optimization process, considering the feasible domains of representative 3D geometric tool orientations. Simulation experiments on a complex B-pillar workpiece demonstrate the framework’s effectiveness, clearly indicating significant reductions in jerk and improved trajectory smoothness for both rotational and translational axes compared with conventional methods and a prior approach. This work advances high-speed machining capabilities by offering a novel, robust solution that leverages redundant structures to further improve trajectory smoothness and reliability in demanding industrial applications. Full article

In view of the large randomness, redundant path nodes, and low search efficiency of RRT-connect in a complex obstacle environment, this study intends to develop a path-planning method combining RRT-connect and Informed RRT*. First, to solve the problem of large sampling randomness, the Informed RRT* algorithm is combined to adopt a simpler rectangle and limit the sampling range to the rectangle. Second, for the poor quality of the search path, the dynamic step size is used for growth extension, the reverse greedy algorithm is used to delete redundant nodes, the spline curve is used to smooth the path such that the position meets the cubic spline curve and the speed meets the quadratic spline curve, and the final path is optimized. Finally, the proposed algorithm is verified in the simulation and real world using a self-developed quadrupedal robot. Compared with the original RRT-connect algorithm, the first solution time, total number of nodes, and initial path cost were reduced by more than 11%, 8.5%, and 2.5%, respectively. Full article

Maritime transportation is responsible for most global trade and is generally considered more environmentally efficient compared to other modes of transport, particularly for long-distance trade. With increasingly stringent emission regulations, however, accurately quantifying emissions and identifying their key determinants has become essential for effective environmental management. This study introduced a structured and comparative statistical modeling framework for ship-based emission modeling using gross tonnage (GT) as the primary predictor variable, due to its strong correlation with emission levels. Emissions for hydrocarbon (HC), carbon monoxide (CO), particulate matter with an aerodynamic diameter of less than 10 μm (PM10), carbon dioxide (CO₂), sulfur dioxide (SO₂), nitrogen oxides (NO_x), and volatile organic compounds (VOC) were estimated using a bottom-up approach based on emission factors and formulas defined by the U.S. Environmental Protection Agency (EPA), using data from 38,304 vessel movements through the Bosphorus in 2021. These EPA-estimated values served as dependent variables in the modeling process. The modeling framework followed a three-step strategy: (1) outlier detection using Rosner’s test to reduce the influence of outliers on model accuracy, (2) curve fitting with 12 regression models representing four curve types—polynomial (e.g., linear, quadratic), concave/convex (e.g., exponential, logarithmic), sigmoidal (e.g., logistic, Gompertz, Weibull), and spline-based (e.g., cubic spline, natural spline)—to capture diverse functional relationships between GT and emissions, and (3) model comparison using difference performance metrics to ensure a comprehensive assessment of predictive accuracy, consistency, and bias. The findings revealed that nonlinear models outperformed polynomial models, with spline-based models—particularly natural spline and cubic spline—providing superior accuracy for HC, PM₁₀, SO₂, and VOC, and the Weibull model showing strong predictive performance for CO and NO_x. These results underscore the necessity of using pollutant-specific and flexible modeling strategies to capture the intricacies of maritime emission dynamics. By demonstrating the advantages of flexible functional forms over standard regression techniques, this study highlights the need for tailored modeling strategies to better capture the complex relationships in maritime emission data and offers a scalable and transferable framework that can be extended to other vessel types, emission datasets, or maritime regions. Full article

The application of robotic arms in the industrial field is continuously becoming greater and greater. The impact force generated by a robotic arm in a gripping operation leads to vibration and wear. To address this problem, this paper proposes a trajectory planning method based on the improved Slime Mould Algorithm. An interpolation curve under the joint coordinate system is constructed by using seven non-uniform B-spline functions, with time and impact force as the optimization objectives and angular velocity, angular acceleration, and angular acceleration as the constraints. The original algorithm introduces Bernoulli chaotic mapping to increase the diversity of the population, adaptively adjusts the feedback factor, improves the crossover operator to accelerate the global convergence, and combines the original algorithm with an improved artificial bee colony search strategy guided by the global optimal solution, adding a quadratic interpolation method to increase the diversity of the population and to accelerate the global convergence speed. Combined with the improved artificial swarm search strategy guided by the global optimal solution, the quadratic interpolation method is added to enhance the local utilization ability. The simulation and real-machine experimental results show that the improved algorithm shortens the movement time of the robotic arm, reduces the joint impacts, minimizes the vibration and wear, and prolongs the service life of the robotic arm. Full article

Trajectory planning is a key task in unmanned aerial vehicle navigation systems. Although trajectory planning in the presence of obstacles is a well-understood problem, unknown and dynamic environments still present significant challenges. In this paper, we present a trajectory planning method for unknown and dynamic environments that explicitly incorporates the uncertainty about the environment. Assuming that the position of obstacles and their instantaneous movement are available, our method represents the environment uncertainty as a dynamic map that indicates the probability that a region might be occupied by an obstacle in the future. The proposed method first divides the free space into non-overlapping tetrahedral partitions using Delaunay triangulation. Then, a topo-graph that describes the topology of the free space and incorporates the uncertainty of the environment is created. Using this topo-graph, an initial path and a safe flight corridor are obtained. The initial safe flight corridor provides a sequence of control points that we use to optimize clamped B-spline trajectories by formulating a quadratic programming problem with safety and smoothness constraints. Using computer simulations, we show that our algorithm can successfully find a collision-free and uncertainty-aware trajectory in an unknown and dynamic environment. Furthermore, our method can reduce the computational burden caused by moving obstacles during trajectory replanning. Full article

The operational areas for unmanned aerial vehicles (UAVs) used in power line inspection are highly complex; thus, the best path planning under known obstacles is of significant research value for UAVs. This paper establishes a three-dimensional spatial environment based on the gridding and filling of two-dimensional maps, simulates a variety of obstacles, and proposes a new optimization algorithm based on the A-STAR algorithm, considering the unique dynamics and control characteristics of quadcopter UAVs. By utilizing a novel heuristic evaluation function and uniformly applied quadratic B-spline curve smoothing, the planned path is optimized to better suit UAV inspection scenarios. Compared to the traditional A-STAR algorithm, this method offers improved real-time performance and global optimal solution-solving capabilities and is capable of planning safer and more realistic flight paths based on the operational characteristics of quadcopter UAVs in mountainous environments for power line inspection. Full article

In practical missions, quadrotor drones frequently face the challenge of navigating through multiple predetermined waypoints in cluttered environments where the sequence of the waypoints is not specified. This study presents a comprehensive multi-waypoint motion planning framework for quadrotor drones, comprising multi-waypoint trajectory planning and waypoint sequencing. To generate a trajectory that follows a specified sequence of waypoints, we integrate uniform B-spline curves with a bidirectional A* search to produce a safe, kinodynamically feasible initial trajectory. Subsequently, we model the optimization problem as a quadratically constrained quadratic program (QCQP) to enhance the trackability of the trajectory. Throughout this process, a replanning strategy is designed to ensure the traversal of multiple waypoints. To accurately determine the shortest flight time waypoint sequence, the fast marching (FM) method is utilized to efficiently establish the cost matrix between waypoints, ensuring consistency with the constraints and objectives of the planning method. Ant colony optimization (ACO) is then employed to solve this variant of the traveling salesman problem (TSP), yielding the sequence with the lowest temporal cost. The framework’s performance was validated in various complex simulated environments, demonstrating its efficacy as a robust solution for autonomous quadrotor drone navigation. Full article

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth comparison of coupling and autoregressive flows, both based on symmetric (affine) and non-symmetric (rational quadratic spline) bijectors, considering four different architectures: real-valued non-Volume preserving (RealNVP), masked autoregressive flow (MAF), coupling rational quadratic spline (C-RQS), and autoregressive rational quadratic spline (A-RQS). We focus on a set of multimodal target distributions of increasing dimensionality ranging from 4 to 400. The performances were compared by means of different test statistics for two-sample tests, built from known distance measures: the sliced Wasserstein distance, the dimension-averaged one-dimensional Kolmogorov–Smirnov test, and the Frobenius norm of the difference between correlation matrices. Furthermore, we included estimations of the variance of both the metrics and the trained models. Our results indicate that the A-RQS algorithm stands out both in terms of accuracy and training speed. Nonetheless, all the algorithms are generally able, without too much fine-tuning, to learn complicated distributions with limited training data and in a reasonable time of the order of hours on a Tesla A40 GPU. The only exception is the C-RQS, which takes significantly longer to train, does not always provide good accuracy, and becomes unstable for large dimensionalities. All algorithms were implemented using TensorFlow2 and TensorFlow Probability and have been made available on GitHub. Full article

Herein, to address the challenges faced by Automatic Guided Vehicles (AGVs) in construction site environments, including heavy vehicle loads, extensive road search areas, and randomly distributed obstacles, this paper presents a hierarchical trajectory planning algorithm that combines coarse planning and precise planning. In the first-level coarse planning, lateral and longitudinal sampling is performed based on road environment constraints. A multi-criteria cost function is designed, taking into account factors such as deviation from the road centerline, shortest path cost, and obstacle collision safety cost. An efficient dynamic programming algorithm is used to obtain the optimal path. Considering nonholonomic constraints of vehicles, eliminating inflection points using improved B-Spline path fitting, and a quadratic programming algorithm is proposed to enhance path smoothness, completing the coarse planning algorithm. In the second-level precise planning, the coarse planning path is used as a reference line, and small-range sampling is conducted based on AGV motion constraints, including lateral displacement and longitudinal velocity. Lateral and longitudinal polynomials are constructed. To address the impact of randomly appearing obstacles on vehicle stability and safety, an evaluation function is designed, considering factors such as jerk and acceleration. The optimal trajectory is determined through collision detection, ensuring both safe obstacle avoidance and AGV smoothness. Experimental results demonstrate the effectiveness of this method in solving the path planning challenges faced by AGVs in construction site environments characterized by heavy vehicle loads, extensive road search areas, and randomly distributed obstacles. Full article

The direct ink writing (DIW) process, used for creating components with functionally graded materials, holds significant promise for advancement in various advanced fields. However, challenges persist in achieving complex gradient variations in small-sized parts. In this study, we have developed a customized pin shape for an active screw mixer using a combination of quadratic B-Spline, the response surface method, and global optimization. This tailored pin design was implemented in a two-material extrusion-based printing system. The primary objective is to facilitate the transformation of material components with shorter transition distances, overcoming size constraints and enhancing both printing flexibility and resolution. Moreover, we characterized the transition delay time for material component changes and the mixing uniformity of the extruded material by constructing a finite element simulation model based on computational fluid dynamics. Additionally, we employed a particle tracking method to obtain the Lyapunov exponent and Poincaré map of the mixing process. We employed these metrics to represent and compare the degree of chaotic mixing and dispersive mixing ability with two other structurally similar mixers. It was found that the optimized pin-type mixer can reduce the transition delay distance by approximately 30% compared to similar structures. Finally, comparative experiments were carried out to verify the printing performance of the optimized pin-type active mixer and the accuracy of the finite element model. Full article

Curvature-based damage detection has been previously applied to identify damage in concrete structures, but little attention has been given to the capacity of this method to identify distributed damage in multiple damage zones. This study aims to apply for the first time an enhanced existing method based on modal curvature analysis combined with wavelet transform curvature (WTC) to identify zones and highlight the damage zones of a beam made of ultra-high-performance fiber-reinforced concrete (UHPFRC), a construction material that is emerging worldwide for its outstanding performance and durability. First, three beams with a 2 m span of UHPFRC material were cast, and damaged zones were created by sawing. A reference beam without cracks was also cast. The free vibration responses were measured by 12 accelerometers and calculated by operational modal analysis. Moreover, for the sake of comparison, a finite element model (FEM) was also applied to two identical beams to generate numerical acceleration without noise. Second, the modal curvature was calculated for different modes for both experimental and FEM-simulated acceleration after applying cubic spline interpolation. Finally, two damage identification methods were considered: (i) the damage index (DI), based on averaging the quadratic difference of the local curvature with respect to the reference beam, and (ii) the WTC method, applied to the quadratic difference of the local curvature with respect the reference beam. The results indicate that the developed coupled modal curvature WTC method can better identify the damaged zones of UHPFRC beams. Full article

In this paper, we propose algorithms for the real-time simulation of grass deformation and wind flow in complex scenes based on the Navier–Stokes fluid. Grasses play an important role in natural scenes. However, accurately simulating their deformation due to external forces such as the wind can be computationally challenging. We propose algorithms that minimize computational cost while producing visually appealing results. We do this by grouping the grass blades and then applying the same force to the group to reduce the computation time. We also use a quadratic equation to deform the blades affected by the wind force rather than using a complicated spline technique. Wind force is fully modeled by the Navier–Stokes fluid equation, and the blades react to this force as if they were being swept by the wind. We also propose the AGC interface (Arrow-Guided wind flow Control), which allows the direction and intensity of the wind to be manipulated using an arrow-shaped interface. Through this interface, users can have grass sway in response to user-defined wind forces in a real-time rate. We verified that the proposed algorithms can simulate 900% more grass blades than the compared paper’s algorithms. Full article