B-spline Curve Research Articles

Research on the End Effector and Optimal Motion Control Strategy for a Plug Seedling Transplanting Parallel Robot

Due to the phenomenon of holes and inferior seedlings in trays, it is necessary to remove and replenish unqualified seedlings. The traditional operation is labor-intensive, and the degree of mechanization is low. This paper took broccoli seedlings as the research object and developed an image recognition system suitable for seedling health recognition and pose judgement, researched and designed a plug-in end effector that reduces leaf damage, and conducted orthogonal tests to obtain a substrate parameter combination containing the moisture content, seedling age, and transplanting acceleration suitable for culling operations. A parallel robot kinematics and dynamics model was built. The fifth degree B-spline curve was used to construct the joint space motion curve for seven nodes, and the motor speed, torque, and end-effector acceleration were used to construct the joint space motion curves. The end-effector acceleration was the constraint condition to plan the optimal trajectory of the joint space in time, and the optimal time was obtained using the artificial fish swarm–particle swarm hybrid optimization algorithm. A single operation time was greatly reduced; the whole machine was systematically built; the average time of single-time seedling removal was measured; and the transplanting efficiency of the whole machine was high. In the seedling damage rate gap test, the leaf damage rate was low. This research provides a reference for the localized development of greenhouse high-speed and low-loss seedling removal equipment.

Path Planning for UAV Based on Improved PRM

In this paper, an improved probabilistic roadmap (IPRM) algorithm is proposed to solve the energy consumption problem of multi-unmanned aerial vehicle (UAV) path planning with an angle. Firstly, in order to simulate the real terrain environment, a mathematical model was established; secondly, an energy consumption model was established; then, the sampling space of the probabilistic roadmap (PRM) algorithm was optimized to make the obtained path more explicit and improve the utilization rate in space and time; then, the sampling third-order B-spline curve method was used to curve the rotation angle to make the path smoother and the distance shorter. Finally, the results of the improved genetic algorithm (IGA), PRM algorithm and IPRM algorithm were compared through a simulation. The data analysis shows that the IGA has significant advantages over other algorithms in some aspects, and can be well applied to the path planning of UAVs.

Bayesian Shape Reconstruction Using B-Spline Level Set in Electrical Impedance Tomography

A new shape reconstruction framework that incorporates sparse Bayesian learning (SBL) and the B-spline level set (BLS) is proposed for difference electrical impedance tomography (EIT). To begin with, the conductivity distribution to be reconstructed is assumed to be piecewise constant under the BLS framework. Second, the boundaries of the inclusions are represented by the B-spline curves in a parametric and explicit way. Next, the optimal shapes are found by solving the unknown variables using the SBL method. Then, the proposed method takes full advantage of B-spline flexible representation and Bayesian learning capability, resulting in improvements in reconstruction performance, noise robustness, and computational efficiency. Finally, a series of numerical and experimental tests are performed to verify the feasibility of the proposed method. Furthermore, the robustness studies are also investigated considering the inhomogeneous background, different numbers of control points, and different initial guesses. The results show that the proposed method leads to reliable and robust shape reconstructions, as evaluated by several quantitative metrics. Specifically, the forced vital capacity (FVC) tests of ten healthy volunteers show that the mean error in the 1-s rate of the shape reconstructions is less than 5% compared with simultaneous spirometry measurements. Hence, the proposed method is promising in providing an effective assessment for lung imaging.

UAV safe route planning based on PSO-BAS algorithm

In order to solve the current situation that unmanned aerial vehicles (UAVs) ignore safety indicators and cannot guarantee safe operation when operating in low-altitude airspace, a UAV route planning method that considers regional risk assessment is proposed. Firstly, the low-altitude airspace is discretized based on rasterization, and then the UAV operating characteristics and environmental characteristics are combined to quantify the risk value in the low-altitude airspace to obtain a 3D risk map. The path risk value is taken as the cost, the particle swarm optimization-beetle antennae search (PSO-BAS) algorithm is used to plan the spatial 3D route, and it effectively reduces the generated path redun dancy. Finally, cubic B-spline curve is used to smooth the plan ned discrete path. A flyable path with continuous curvature and pitch angle is generated. The simulation results show that the generated path can exchange for a path with a lower risk value at a lower path cost. At the same time, the path redundancy is low, and the curvature and pitch angle continuously change. It is a flyable path that meets the UAV performance constraints.

A path smoothing scheme for micro-line tools using cubic B-spline fitting with dominant points

To obtain higher order continuous tool path, a cubic B-spline curve fitting method is presented in this paper to process the linear tool path. First, a local cubic polynomial fitting with bidirectional scanning scheme is proposed to determine some initial dominant points. Based on these dominant points, the initial knot vector is generated by average method, and the initial B-spline is constructed. To constrain the fitting error, a Newton’s method based fitting error estimation scheme and a fitting error based dominant point insertion scheme are proposed to modify the B-spline. Simulation results prove that our method can compress data and smooth tool path. Compared with another existing curve fitting method, the number of control point has decreased by 9.43%, and the machining time has decreased by 94.45% compared with traditional point-to-point (P2P) motion.

A study on longitudinal motion stability of a variable-structure SWATH USV with and without twin hydrofoils

The form-changeable unmanned surface vehicle (USV) have a high research enthusiasm due to its far-ranging applicability, strong combat capability and low operating cost. This paper constructs a variable-structure Small Waterplane Area Twin Hull (SWATH) USV with twin hydrofoils, and aims at assessing its longitudinal motion stability (LMS) in the catamaran-form state (CFS) by parametric model and CFD method. The parametric representation of the torpedo, double struts and hydrofoils was conducted by uniform B-spline curves, 3-D coordinates conversion and surface generation method. The CFD code was verified, and used to calculate the LMS of the vessel with different strut configurations, form-states and CG position. Based on numerical results, the causes of different instability behaviors were expounded. Further, the LMS of the models with and without hydrofoils was compared at Fr = 0.1–0.8, the adjustment method of fore and aft hydrofoils to sailing attitudes was explained, the rational allocation of attack angles was also offered. The results show that the slender double struts arranged at both ends of torpedo is more conducive to the LMS and resistance, the vessel should sail in the CFS of γs ≤ 10° at Fr > 0.6; the hydrofoils slightly weakens the LMS at low Fr, makes the bow appear slight updip at Fr = 0.4–0.6, but still can sails stably; adjusting attack angles can inhibit the instability, and the most effective allocation of the fore and aft hydrofoil's attack angles is linearly arranged at Fr = 0.7, 0.8, also the adjusting can reduce the upward trim at Fr = 0.9, 1.0, but the hull is lifted higher and arises the bow updip due to the free surface suction force, at this time, the attack angle's graduation should be refined to realize the finer adjustment to the dynamic trim.

Imitation of a Pre-Designed Irregular 3D Yarn in Given Fabric Structures

The 3D CAD software has obvious advantages in appearance imitating and geometric structure modeling for fabrics. In contemporary 3D CAD fabric systems, only uniform yarns are involved in studies on fabric geometric structures, due to technological limitations, whereas objectives such as irregular/uneven 3D yarns have not been considered much. As the fabric structure or the central curve of the yarn changes, it is difficult to reflect the changed positions of the effect spots of the pre-designed uneven 3D yarns accordingly. In this paper, a key-point-mapping algorithm between the source yarn and the target curve is proposed to reflect the position change in effect spots when the fabric structure changes. By using the shape-preserving quasi-uniform cubic B-spline curve, a simple 3D irregular source yarn is designed using key points and setting their corresponding base cross-sections. The mapping is based on the principle that the lengths of the curve between the key points and the contours of the corresponding base cross-sections of the source yarn remain unchanged. Finally, the control grid of the new 3D yarn in the fabric structure is automatically generated. According to the examples and error analysis, the mapping technique can be applied to arbitrary given fabric structures, and the effect spots of the irregular 3D yarn are reasonably distributed as expected.

B-Spline Curve Fitting of Hungry Predation Optimization on Ship Line Design

The ship line often describes by the offset table of discrete data points, which leads to the problems that three view coordinates may not correspond, the fitting error is large and the fitted curve cannot be easily modified. This will seriously affect the subsequent ship performance evaluation and op-timization. To solve this problem, this paper develops a B-spline curve fitting of hunger predation optimization on ship line design (HPA), which contains knot guidance technology, hungry preda-tion optimization technology and adaptive adjustment of algorithm input parameters. HPA transforms the discrete ship line into a continuous B-spline curve description, which improves the accuracy and modifiability of the ship line design. Through the real-time feedback of the results of each round of iteration, the knot vector is adaptively adjusted towards a better fitness, and then the optimal control point set that satisfies the error threshold can be obtained. The effectiveness and superiority of HPA are verified by comparing with related research and engineering software.

Shape optimization of corrugated tube using B-spline curve for convective heat transfer enhancement based on machine learning

Shape optimization of corrugated tube using B-spline curve for convective heat transfer enhancement based on machine learning

Tolerance analysis of a compliant assembly using random Non-Uniform Rational B-Spline curves and isogeometric method

Abstract Non-Uniform Rational B-Spline (NURBS) is one of the most versatile tools of computer-aided design. The concept of random NURBS curves is introduced for modeling the geometrical errors in mechanical parts and assemblies. The proposed idea is utilized to solve an example problem involving deformable components. For this purpose, profile tolerances of the parts are transformed into covariance matrices of NURBS control polygon parameters. Then, the control polygons are used as vector chains to calculate geometrical error propagation. Afterwards, isogeometric analysis (IGA) is invoked to express deformations of the parts during the assembly process as changes in the shape of the underlying control polygons. Finally, the result of the calculations is translated back into the tolerance zone of the assembly. Numerical examples are employed to examine the effect of NURBS structure (degree, knot vector, and control points) on convergence and stability of results. Outcomes of the theory are compared with direct measurements of actual assemblies and results of a Monte Carlo finite element simulation to illustrate the validity of the results. Furthermore, the developed model is used to obtain practical guidelines regarding the reduction of geometrical errors by the optimum design of the assembly.

Trajectory optimization of the redundant manipulator with local variable period under multi-machine coordination

AbstractThe coordinated motion between the press and the feeding mechanism directly determines the production efficiency of the high-speed stamping line. In order to generate the high-performance trajectory of the feeding mechanism, this paper investigates the optimization of the trajectory with the local variable period. Based on the quintic B-spline curve and normal distribution, the smooth interpolation method of variable-time interval is proposed to generate the collision-free and energy-jerk-minimal trajectory with variable-time intervals. The advantage of the proposed method is that it can make the feeding mechanism transition smoothly between districts of variable-time and fixed-time intervals. It is beneficial to avoid re-performing the entire process of trajectory planning. ADAMS and actual experiments are used to validate the effectiveness of the proposed method. Results show that the proposed method can maintain the high performance of the initial trajectory, and there is no sharp point in the displacement-time and velocity-time curves. The investigation provides a new direction for the direct generation of local variable-period trajectories in the multi-machine coordination of the stamping line.

Autonomous Obstacle Avoidance Path Planning for Grasping Manipulator Based on Elite Smoothing Ant Colony Algorithm

Assembly robots have become the core equipment of high-precision flexible automatic assembly systems with a small working range. Among different fields of robot technology, path planning is one of the most important branches. In the present study, an elite smoothing ant colony algorithm (ESACO) is proposed for spatial obstacle avoidance path planning of the grasping manipulator. In this regard, the state transition probability and pheromone update strategies are improved to enhance the search capability of path planning symmetry and the convergence of the algorithm. Then a segmented B-spline curve is presented to eliminate path folding points and generate a smooth path. Finally, a manipulator control system based on the Arduino Uno microcontroller is designed to drive the manipulator according to the planned trajectory. The experimental results show that the performance of the ESACO algorithm in different scenarios has symmetry advantages, and the manipulator can efficiently complete the simulation trajectory with high accuracy. The proposed algorithm provides a feasible scheme for the efficient planning of manipulators in equipment manufacturing workshops.

A C2 continuous trajectory planning method for 6-DOF rotational robot manipulators

PurposeThe purpose of this paper is to propose a smooth double-spline interpolation method for six-degree-of-freedom rotational robot manipulators, achieving the global C2 continuity of the robot trajectory.Design/methodology/approachThis paper presents a smooth double-spline interpolation method, achieving the global C2 continuity of the robot trajectory. The tool center positions and quaternion orientations are first fitted by a cubic B-spline curve and a quartic-polynomial-based quaternion spline curve, respectively. Then, a parameter synchronization model is proposed to realize the synchronous and smooth movement of the robot along the double spline curves. Finally, an extra u-s function is used to record the relationship between the B-spline parameter and its arc length parameter, which may reduce the feed rate fluctuation in interpolation. The seven segments jerk-limited feed rate profile is used to generate motion commands for algorithm validation.FindingsThe simulation and experimental results demonstrate that the proposed method is effective and can generate the global C2-continuity robot trajectory.Originality/valueThe main contributions of this paper are as follows: guarantee the C2 continuity of the position path and quaternion orientation path simultaneously; provide a parameter synchronization model to realize the synchronous and smooth movement of the robot along the double spline curves; and add an extra u-s function to realize arc length parameterization of the B-spline path, which may reduce the feed rate fluctuation in interpolation.

Research on the S-shaped time-rounding series feedrate scheduling based on NURBS curve

The inconsistency between continuous feedrate scheduling and discrete interpolation of Non-Uniform Rational B-Splines (NURBS) curves as toolpath interpolation affects the interpolation accuracy and motion smoothness of computer numerical control (CNC) machining. The S-shaped series feedrate scheduling method of the NURBS curve is presented to meet the consistency between feedrate scheduling and interpolation, and the needs of the motor to receive accurate discrete pulses to avoid chatter. The acceleration and deceleration margin factor models are respectively established in the acceleration and deceleration stages to compensate for the velocity loss in the discrete process, so that the feedrate scheduling can be accurately reached in each acceleration and deceleration stage. Based on this, 17 kinds of acceleration and deceleration situations are summarized according to the comparison of displacement, start and end velocity, and the number of interpolation cycles. The butterfly three-segment trajectories are selected for simulation in Matlab. The experimental platform is built based on the Codesys platform programing, and the series feedrate scheduling of the proposed method for a NURBS toolpath is carried out. Both simulations and experiments have verified the effectiveness of the algorithm.

Motion Planning and Tracking Control of Autonomous Vehicle Based on Improved A ∗ Algorithm

The traditional A ∗ algorithm, applied to the motion planning of autonomous vehicles, easily causes high computational costs and excessive turning points generated in the planning path. In addition, the vehicle cannot track the path due to the unsmooth inflection point. To overcome these potential limitations, an improved A ∗ algorithm-based motion planning algorithm and a tracking control strategy based on model predictive control theory were proposed in this work. The method of expanding the search neighborhood is adopted to improve the planning efficiency of A ∗ algorithm. The artificial potential field method is also incorporated into the proposed A ∗ algorithm. The resultant force generated by each potential field is further introduced into the evaluation function of A ∗ algorithm to plan the driving path, which could be suitable for autonomous vehicles. The sharp nodes in the path are smoothed by cubic quasi-uniform B-spline curve. The tracking control strategy is designed based on model predictive control theory to realize the accurate tracking of the planned path. Typical obstacle avoidance conditions were selected for co-simulation test verification. The experimental results show that the proposed motion planning algorithm and tracking control strategy can effectively plan the obstacle avoidance path and accurately track the path in different environments.

The Impact Force of Large Boulders with Irregular Shape in Flash Flood and Debris Flow

The impact force of large boulders carried by flash floods and debris flows is one of the main causes of structural damage. The elastoplastic modification model of the impact force was derived, and it was found that the impact force was significantly affected by large boulders with irregular shapes. However, a large boulder with an irregular shape is often simplified as an isovolumetric sphere or ellipsoid, which may lead to inaccurate calculation of the impact force. In this paper, a method to obtain the irregular shape of a large boulder in the field is proposed by combining field investigation, image processing, and graphic analysis. The irregular shape is described by a nonuniform rational B-spline (NURBS) curve. The curvature radii corresponding to the potential impact contact points on the surface of a large boulder, which can reflect the influence of the irregular shape, are extracted according to the concavity and convexity analysis. The results demonstrate that NURBS curves can describe irregular shapes both conveniently and accurately. The impact force was corrected by the elastic—plastic model, the impact force increased with increasing curvature radius, and the increase ratio of the impact force gradually decreased with increasing velocity. Compared with the isovolumetric sphere model and ellipsoid model, the impact force calculated by the ellipsoid model is closer to the results obtained in this paper. The reduction factor of the impact force is 0.03–0.16, which first increases significantly and then linearly increases with increasing curvature radius. In addition, the reduction factor of the impact force initially exhibits a significant decline with increasing velocity and then gradually stabilises. To simplify parameter selection, we suggest using the maximum curvature radius in the ellipsoid model as the calculation parameter in calculating the impact force of large boulders.

Research on smooth path planning method based on improved ant colony algorithm optimized by Floyd algorithm.

Aiming at the problems of slow convergence and easy fall into local optimal solution of the classic ant colony algorithm in path planning, an improved ant colony algorithm is proposed. Firstly, the Floyd algorithm is introduced to generate the guiding path, and increase the pheromone content on the guiding path. Through the difference in initial pheromone, the ant colony is guided to quickly find the target node. Secondly, the fallback strategy is applied to reduce the number of ants who die due to falling into the trap to increase the probability of ants finding the target node. Thirdly, the gravity concept in the artificial potential field method and the concept of distance from the optional node to the target node are introduced to improve the heuristic function to make up for the fallback strategy on the convergence speed of the algorithm. Fourthly, a multi-objective optimization function is proposed, which comprehensively considers the three indexes of path length, security, and energy consumption and combines the dynamic optimization idea to optimize the pheromone update method, to avoid the algorithm falling into the local optimal solution and improve the comprehensive quality of the path. Finally, according to the connectivity principle and quadratic B-spline curve optimization method, the path nodes are optimized to shorten the path length effectively.

Mixed isogeometric collocation for geometrically exact 3D beams with elasto-visco-plastic material behavior and softening effects

A geometrically nonlinear, shear-deformable 3D beam formulation with inelastic material behavior and its numerical discretization by a mixed isogeometric collocation method are presented. In particular, the constitutive model captures elasto-visco-plasticity with damage/softening from Mullin’s effect, which applies to the modeling of metallic and polymeric materials, e.g., in additive manufacturing applications and metamaterials. The inelastic material behavior is formulated in terms of thermodynamically consistent internal variables for viscoelastic and plastic strains and isotropic and kinematic hardening variables, as well as accompanying evolution equations. A mixed isogeometric collocation method is applied for the discretization of the strong form of the quasi-static nonlinear differential equations. Thus, the displacements of the centerline curve, the cross-section orientations, and the stress resultants (forces and moments) are discretized as B-spline or NURBS curves. The internal variables are defined only locally at the collocation points, and an implicit return-mapping algorithm is employed for their time discretization. The method is verified in comparison to 1D examples as well as reference results for 3D beams. Furthermore, its applicability to the simulation of beam lattice structures subject to large deformations and instabilities is demonstrated.

A data-driven non-intrusive polynomial chaos for performance impact of high subsonic compressor cascades with stagger angle and profile errors

The impact of geometric variations due to manufacturing errors on the aerodynamic performance of compressor blades is considerable in engineering practice. Accurate uncertainty quantification (UQ) of aerodynamic performance based on actual statistical information of manufacturing errors is helpful for error detection, aerodynamic shape design, etc. However, the actual manufacturing errors may not be independent of each other, and their marginal distributions are often not standard. To apply UQ to dependent input variables with arbitrary distributions, the present paper first introduced a decorrelation algorithm and proposed a novel data-driven Non-Intrusive Polynomial Chaos (DNIPC) model. The subsequent tests based on high-dimensional function experiments and UQ of the performance for a high subsonic compressor cascade have validated its generality, effectiveness, and efficiency. Then, the simultaneous impact of stagger angle and profile errors on the performance of the compressor cascade was investigated by the proposed DNIPC and Sobol's sensitivity analysis. The distributions of manufacturing error were determined by kernel density estimation based on finite measurement data, then using the parametric B-spline and Bezier curves to build the manufactured geometry of the cascade. Finally, the influence of the manufacturing errors on aerodynamic performance was further discussed through the UQ of the cascade flow field. The results show that the performance impact in the off-design conditions, especially for those below the design incidence, is the most important. It suggested that the uncertainty of profile error should be checked carefully in the process of detecting machining error when the operation condition is at or below the design incidence; in contrast, the influence of stagger angle error calls for more attention when the cascade works at high incidences. The fluctuation of the overall aerodynamic loss is mainly associated with the manufacturing error near the leading edge, for it affects the velocity spike and the development of its downstream boundary layer. Therefore, the leading edge error should be the top focus.

Application of Low Bit Rate Coding Based on Nonlinear Data Prediction in Wireless Network Multimedia Communication

In order to realize the application of low bit rate video coding in wireless multimedia communication, this paper analyzes the principle of video coding and highlights the importance of low bit rate in wireless multimedia communication. For this, the iterative optimization method of contour height map contour, B-spline curve approximate contour, and control points is carried out to ensure that hearing and vision can achieve the clarity of video under appropriate conditions. The results show that compressing the original video to a suitable size for decoding and completing the output in a compatible format can realize the operation efficiency of the encoder and improve the coding speed.