Intelligent Perception and Seam Tracking System for Thick Plate Weldments Based on Constant-Focus Optical Path

To achieve the goal of high-speed and highly accurate machining, this paper proposes a real-time control algorithm based on Taylor's expansion for implementing variable feed rate non-uniform rational B-spline (NURBS) curve. To efficiently compute the NURBS curve and its derivatives in real-time, some effective methods are proposed. In contrast to the existing linear and circular interpolators, the proposed interpolator can maintain small contour errors and feedrate fluctuations. It also can shorten the size of machining code effectively compared with the linear and circular interpolators. At the same time, the NURBS-format milling codes adapting the dual NURBS Curve interpolation algorithm for 5 axis high-speed machining are adopted in this study. Besides, an effective algorithm is adopted to minimize the kinematics error by means of the shortest path scheme.

Aiming at the problem of speed fluctuation caused by the large error between the ideal interpolation step and the actual interpolation step in the traditional non-uniform rational B-spline ( NURBS ) curve interpolation, a NURBS curve interpolation algorithm based on Mline-Gear is proposed. The differential and derivative definitions are derived to transform the Mline and Gear formulas respectively, and the prediction and correction formulas of the interpolation parameters are obtained. Then, it is judged whether the interpolation parameter values obtained by the correction formula meet the speed fluctuation rate requirements, and the interpolation can be continued. Otherwise, the Steffensen descent formula is used to iteratively correct the interpolation parameter values. In order to ensure the calculation accuracy and avoid solving high-order derivatives, the fourth-order Runge-Kutta method is used to solve the initial two interpolation parameters. Finally, the algorithm is simulated. The simulation results show that the algorithm reduces the feed speed fluctuation rate while ensuring a small number of iterations.

In the industrial applications of intersecting curve welding, in order to improve the accuracy and quality of welding, the automation program of weld seam positioning, data processing, and the actual welding is widely used. In this paper, a lot of research has been carried out, and a method based on non-uniform rational B-spline (NURBS) curve fitting is presented, while the trajectory of the welding torch is planned. The method can use the position data of the discrete weld seam points obtained by manual teaching or weld seam location. By the improved least squares method and the White rule, the outliers are eliminated and the weld seam points for intersecting curve fitting are obtained. These points are fitted based on NURBS, and then the parameter expressions of the fitted intersecting curve are given. For the purpose of obtaining the orientation of the welding torch, the coordinate system which can describe the feature of the fitted intersecting curve is established. The coordinate system is combined with the theoretical intersecting curve model and the fitted intersecting curve model and gives a novel approach to compute the orientation of the welding torch according to the position of the fitted intersecting curve. In the process of planning the welding trajectory, a fitted intersecting curve discrete algorithm based on the equal arc length principle is proposed to reduce the fluctuation of the feed rate according to the restriction of chord error. Finally, this method gives the position and orientation of the welding torch in the form of a homogeneous matrix and verifies the correctness and flexibility of the algorithm by MATLAB simulation and intersecting curve welding experiment.

Eulerian analysis of bulk metal forming processes based on spline-based meshfree method

In order to solve the problem of complicated Non-Uniform Rational B-Splines (NURBS) modeling and improve the real-time performance of the high-order derivative of the curve interpolation process, the method of NURBS modeling based on the slicing and layering of triangular mesh is introduced. The research and design of NURBS curve interpolation are carried out from the two aspects of software algorithm and hardware structure. Based on the analysis of the characteristics of traditional computing methods with Taylor series expansion, the Adams formula and the Runge-Kutta formula are used in the NURBS curve interpolation process, and the process is then optimized according to the characteristics of NURBS interpolation. This can ensure accuracy, and avoid the calculation of higher-order derivatives. Furthermore, the hardware modules for the Adams and Runge-Kutta formulas are designed by using the parallel hardware construction technology of Field Programmable Gate Array (FPGA) chips. The parallel computing process using FPGA is compared with the traditional serial computing process using CPUs. Simulation and experimental results show that this scheme can improve the computational speed of the system and that the algorithm is feasible.

In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V≈1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: Vmax=1 m/s, Amax=2 m/s2, and Jmax=5 m/s3. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

Soil particle-size distribution or soil texture presents one of the most important physical properties. There are various systems of the classification systems for soil particle-size fractions with different boundaries. Our effort was concentrated on the mathematical approach to evaluate the existing data and convert it to the form of a reconstructed cumulative particle-size curve which will allow reading concentration of any desired particle size. Non-Uniform Rational B-Splines (NURBS) curves therefore represent a generalization of B-splines and BĂŠzier curves by extending the definition by an element of rationality, which is represented by the weights of the control points, and a nodal vector of parametrization, which represents the element of uniformity. The NURBS curve was used for smooth (depending on the degree of the curve used) and as tight as possible approximation of the arranged control points, the connecting lines of which forms a convex envelope for its individual parts. The NURBS approximation curve is therefore determined by the ordered control points and their connecting lines, the weights of these points, the degree of the curve and the nodal vector of parametrization. However, the construction of the approximation curve is primarily dependent on a limited number of points of the experimentally determined particle-size distribution curves, and for curves with significant breaks in the course, one must consider either a lower accuracy of the approximation or the necessity of “improving” the approximation using the weights of individual points, inserting additional points or working with a nodal vector of parametrization. For basic approximation, the PUGIS system (Czech soil information system) offers automatic approximation using all variants mentioned in the article as well as the possibility of individual changes in the weights of control points, in their number and position, and in the nodal vector of parametrization.

This paper proposes a real-time coplanar Non-Uniform Rational B-Spline (NURBS) curves fitting and interpolation for 6-DOF robot arm to improve the fitting and interpolation quality, and reduce the calculation effort. The process consists of (1) reading discrete points, (2) discrete points extraction, (3) curve fitting, (4) interpolation, and (5) inverse kinematics transformation. According to the simulation and experimental results, the proposed approach certainly raises the fitting and interpolation quality, and the efficiency of calculation.

The coupling of geometric descriptions and finite elements using NURBs — A study in shape optimization

The study of neural connectivity has grown rapidly in the past decade. Revealing brain anatomical connection improves not only clinical measures but also cognition understanding. In order to achieve this goal, we have to track neural fiber pathways first. Aiming to estimate 3D fiber pathways more accurately from orientation distribution function (ODF) fields, we presented a novel tracking method based on nonuniform rational B-splines (NURBS) curve fitting. First, we constructed ODF fields from high angular resolution diffusion imaging (HARDI) datasets using diffusion orientation transform (DOT) method. Second, under the angular and length constraints, the consecutive diffusion directions were extracted along each fiber pathway starting from a seed voxel. Finally, after the coordinates of the control points and their corresponding weights were determined, NURBS curve fitting was employed to track fiber pathways. The performance of the proposal has been evaluated on the tractometer phantom and real brain datasets. Based on several measure metrics, the resulting fiber pathways show promising anatomic consistency.

The utilization of the non-uniform rational B-spline (NURBS) toolpaths becomes more important than ever before. However, in traditional milling electrical discharge machining (EDM) of parametric curves, there commonly exist problems such as speed loss and an overincreased sampling period, which directly cause a decrease in machining efficiency. Moreover, traditional approaches normally suffer from a complex toolpath planning. In this paper, a real-time interpolator with a constant segment length is proposed to improve the milling EDM of NURBS curves. The proposed interpolator can directly process NURBS curves with their definition information. The toolpath planning can thus become simpler. A new two-stage interpolation method is adopted such that both a high speed accuracy and a relatively short sampling period can be achieved, and the magnitude of chord errors can also be reduced. While the first-stage interpolation samples a NURBS curve with a constant-length segment, the second-stage interpolation, or the re-interpolation, executes multiple interpolations in a sampling period to generate the required feed rate. A loop buffer is designed for the implementation of the real-time interpolator. Experimental results show that the proposed interpolator demonstrates a superior machining performance to that by traditional interpolators, especially in terms of chord errors and erosion rate.

Based on the non-uniform rational B-spline(NURBS)curve theory,the general rule of how the knot vector affects the shape of the NURBS curve is put forward.The local support property on how a knot affects the NURBS curve is demonstrated.The quantitative computation formula on how a knot affects the NURBS curve is obtained.An experiment performed on the example in computer aided geometric design(CAGD)proves that it is possible that the NURBS curve can be modified locally and be designed interactively by modifying a single knot.And another experiment performed on the measurement of the edge of the vane of the aero-engine compressor proves that the fitting model with the minimum errors can be achieved by the knot factor method(KFM)that is based on the rule.Both experiments prove that the rule proposed here is correct,practical and feasible.

In this paper, an adaptive parametric curve interpolator with a real-time look-ahead function is developed for non-uniform rational B-spline curves (NURBS) interpolation, which considers the maximum acceleration/deceleration of the machine tool. In the proposed interpolator, both constant feedrate and high accuracy are achieved while the inconsistency of feedrate is reduced dramatically as well. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, a look-ahead function is introduced to detect and adjust the feedrate adaptively. Two cases were respectively studied to evaluate the feasibility of the developed interpolator: one is for feedrate sensitive arc corner; the other is for feedrate sensitive sharp corner.

Circular arches are often used as parts of engineering structures due to their effectiveness in resisting vertical loads. An understanding of nonlinear structural behavior of circular arches is crucial to obtaining their good designs. Points of interest are the effects of the rise-to-span ratio on their nonlinear structural behavior. In this paper, large displacement analysis of pinned-fixed circular arches with different rise-to-span ratios using an isogeometric approach is presented. In the analysis, the Euler-Bernoulli beam theory is used. The exact reference axis of each arch and its deformed axis are represented by non-uniform rational B-spline (NURBS) curves. The effects of the rise-to-span ratio on the nonlinear structural behavior of the arches are studied. Some well-established examples, exhibiting snap-through and snap-back phenomena, are considered, and the accuracy and efficiency of the proposed approach are discussed.KeywordsIsogeometric analysis (IGA)Non-uniform rational B-spline (NURBS)Large displacement analysisThin circular archRise-to-span ratio

To improve the carrying capacity and reduce the weight of telescopic boom structure in a truck crane, a Collaborative optimization (CO) approach was applied to solve the problems of strength, stiffness and local stability in the telescopic boom structure. First, the complex optimization problem of the telescopic boom structure was decomposed into two-level optimizations: the system level and two subsystem levels for strength and local stability. Second, the underside curve of the boom’s cross-section was constructed by the Non-uniform rational B-Splines (NURBS) curve. 3D parametric solid model and the parametric finite element analysis model for the strength and the local stability were then established. Third, the mathematical models of the strength and local stability for the subsystem levels, and the system level were optimized, respectively. The adaptive relaxation factor algorithm and the penalty function approach were applied to improve the efficiency of CO. Next, the CO process which integrates the ANSYS package with ISIGHT platform was implemented. The optimal results show that the carrying capacity of the telescopic boom structure can be significantly improved and its weight efficiently is reduced. Finally, with the comparison of the stress values obtained from both the experimental test and the theoretical computation, highly coincident results could be obtained to verify the reliability of CO of a telescopic boom.