Curvature Discontinuities Research Articles

Cultural relics fragment assembly based on fracture surface contour features

Addressing the issue of registration deviations caused by local fragment loss and shape diversity during the process of cultural relics fragment assembly, this paper proposes a method for assembling cultural relics fragments based on the contour features of fracture surfaces. Initially, the curvature of discrete point clouds is calculated using the quartic surface method and the Weingarten matrix, and curvature discontinuity points are identified using a proportional method as a candidate feature point set. Subsequently, the angle difference between a point and its neighboring points’ directed segments is defined as a neighborhood feature parameter, which further optimizes the feature point set and selects the optimal matching set. Then the 4-points congruent sets (4PCS) algorithm is utilized for the initial registration of the fragments, and the unit quaternion method is employed to calculate the rigid body transformation matrix during the iteration process. Finally, corresponding point pairs are determined by the intersection of a point’s normal with a set of points, improving the iterative closest point (ICP) algorithm to achieve precise assembly of the fragments. The experimental results show that, compared to other assembly algorithms, the proposed method is more accurate in feature point extraction, robust, and effectively enhances the accuracy and efficiency of fragment assembly.

Five-axis path smoothing based on sliding convolution windows for CNC machining

Tiny linear toolpaths widely used in five-axis CNC machine tools only meet G0 continuity at the junctions of adjacent paths, the tangential and curvature discontinuities at the corners result in decelerations and fluctuations of machine tools. Although the corner smoothing for the three-axis tool path is relatively mature, the five-axis tool pose path smoothing is still difficult to plan due to the nonlinear motions of the rotational axes and the parameter synchronization between the tool center point (TCP) path and the tool orientation vector (TOV) path. Therefore, this paper aims to extend the smoothing scopes of previously presented mixed tiny path smoothing method based on sliding convolution windows for three-axis CNC machining (Zhang et al. in Journal of Manufacturing Process 102:685–699, [19]). Compared with the previous work, this paper converts the five-axis tool pose path into the tool position signal and tool orientation signal, and the interpolation points of the two path signals in the convolution window are directly processed on the basis of the synchronous motions of all axes. The original parameter synchronization relationship between the TCP path and the TOV path is still maintained. Besides, the smoothing error prediction model is constructed. The proposed five-axis path smoothing method has been integrated into a self-developed open-architecture CNC system and its effectiveness for the five-axis path optimization is validated via the simulation and experiment.

A new grinding trajectory adaptive adjustment algorithm for circular-arc end mill flank based on grinding contact zone control

As one of the key structural features of the circular-arc end mill, the flank directly affects its service performance such as tool life and milling efficiency. Due to the curvature discontinuity of the flank edge curves and the inflexible posture of the grinding wheel, the existing grinding trajectory algorithms are difficult to accurately control the important end mill parameters such as the relief angle and flank width, and grinding interference is easy to occur. Therefore, this paper proposes a new grinding trajectory adaptive adjustment algorithm for circular-arc end mill flanks based on grinding contact zone control. Firstly, the edge curve equations are constructed through structural feature decomposition of the end mill, and the second flank is modeled based on uniform offset densification of edge curves. Then, the grinding wheel posture model is established and the contact zone between the grinding wheel and the first flank of the end mill is calculated. A grinding trajectory adaptive adjustment algorithm is then proposed, which iteratively modifies the lifting angle and swing angle of the grinding wheel and can avoid the abrupt change of grinding postures and the grinding interference, thus realizing accurate flank grinding. Finally, the corresponding algorithm module is developed on the VC++ platform, and the effectiveness of the proposed algorithm is verified by machining simulation and grinding experiments, therefore providing technical support for the accurate grinding of circular-arc end mills.

Interactive modelling of fair ship hulls with B-spline surfaces avoiding gaps and discontinuities

ABSTRACT Ship hull surfaces are commonly represented as parametric B-spline or NURBS 1 surfaces. The shape of a surface is controlled by a regular mesh of vertices with constant numbers of vertices in each parametric direction. This restriction complicates the modelling of complex features like bulbous bows, stern bulbs, transoms. Multiple surface patches may be used to overcome the limitations of a regular control mesh, but it is challenging to keep the patches properly aligned at the seams. This paper presents a systematic methodology to design fully featured ship hulls without any gaps, overlaps or tangent and curvature discontinuities. With proper layout of the control vertex mesh and exploitation of the geometrical properties inherent to the B-spline/NURBS definition, the resulting three-dimensional hull models are readily transferred to analysis and manufacturing systems.

Research on Automatic Vertical Parking Path-Planning Algorithms for Narrow Parking Spaces

Narrow parking spaces pose difficulties in path planning and spot turning caused by sudden changes and discontinuities in path curvature. To address these problems, this paper investigates the performance of three path-planning algorithms and proposes a path-optimization algorithm. First, a narrow parking space is defined based on single-step parking using the arc-line combination parking algorithm. Second, to compare the arc-line combination algorithm, Hybrid A* algorithm, and particle swarm optimization parking algorithm with respect to different narrow parking spaces, a multi-objective evaluation function is proposed, including three evaluation indicators, namely, the path length, the number of positive and negative conversions of vehicle speed, and the smoothness of the path. Their performance is compared using a simulation conducted in MATLAB. With the same starting point and different parking space widths, the three algorithms are simulated to generate different planned paths. Then, the evaluation indices are obtained to compare the performance of the algorithms based on the multi-objective function, the values of which indicate the fitness of the algorithm in a narrow parking environment. The results show that the Hybrid A* algorithm is better than the others for narrow parking spaces. Third, to smooth the planning path, a path optimization algorithm based on the cubic B-spline curve and gradient descent is proposed. Finally, the results of a simulation conducted on the proposed algorithm and the Hybrid A* algorithm are provided: the average minimum curvature of the path was reduced by 0.005 m−1, and the path meets the requirements of the minimum turning radius constraint of the analyzed vehicle. The results show that the proposed algorithm can effectively eliminate the curvature mutation point and constrain the path curvature to meet the requirements of a smooth path.

Novel design of variable Mach number nozzle operated by a single jack

The increasing demand for the wide-range aircraft technique requires the ground test facilities with continuous variation of the Mach number. Owing to the rigorous aerodynamic foundation and simple operation, the single-jack flexible nozzle is widely used. However, there are still some problems in the original single-jack flexible nozzle, such as low Mach number and insufficient flow uniformity. This paper presents a novel design of the single-jack flexible nozzle with high flow uniformity and continuous variable Mach number, adopting flow field inverse design and elasticity inverse design. The new nozzle adopts a three-order transonic asymptotic solution and a B-spline axial velocity distribution, designed by the method of characteristics. By comparing with the original nozzle, the new nozzle no longer requires the conical flow assumption, and the flow fields are more uniform. Another improvement is the continuous contour curvature to ensure the coincidence of the aerodynamic profile and the elastic profile, avoiding the negative Mach waves generated by the curvature discontinuity. In addition, the new nozzle has the advantage of two Mach number design points. Similar to the squeeze theorem, the flow fields are uniform at the non-design points between two design points. The numerical results show that the new nozzle eliminates the Mach waves at different Mach number cases. Within the design range of Mach 2.0–4.0, the flow angle's maximum deviations do not exceed 0.2°, and the average deviations do not exceed 0.1°, meeting the national standard of 0.3°. The Mach number's maximum deviations are around 0.5% of Ma¯, the average deviations are less than 0.2% of Ma¯, and the standard deviations meet the national advanced standard. Even at Mach 1.5 and Mach 4.5 outside the design range, the new nozzle still performs well. The evaluation results validate the feasibility of the novel design, supporting the future construction of the variable Mach number facility.

Automatic parking trajectory planning based on random sampling and nonlinear optimization

The current parking trajectory planning algorithms based on geometric connections or formulation of optimization problems in automatic parking systems have strict requirements on the starting position, lower planning efficiency and discontinuous curvature of the reference trajectory. In order to solve these problems, a hierarchical planning algorithm which is combined with nonlinear optimization and the improved RRT* algorithm (Rapidly-exploring Random Tree Star) with Reeds-Shepp curve is proposed in this paper. First, the improved RRT*RS algorithm with the rapid repulsion-straddle experiment is designed for enhancing the efficiency of path planning. Second, because of the shortcomings of the Reeds-Shepp curve that can meet the minimum turning radius but not realize the continuous curvature of the path, a nonlinear optimization problem based on convex-set obstacle constraints is formulated and solved. Finally, simulation results show that the proposed parking trajectory planning algorithm in this paper can plan an effective parking trajectory with continuous curvature in different starting positions and multiple parking scenarios.

Dissipative hyperbolic mean curvature flow for closed convex plane curves

This paper considers one dimensional dissipative hyperbolic mean curvature flow. To analysis the asymptotic behavior of this dissipative hyperbolic curvature flow, we investigate the evolution of a family of circles. Particularly, we give some propositions and prove the main result. If the minimum of initial velocity is nonnegative, the flow will converge either to a point or a limit curve which has the discontinuous curvature in finite time. If the maximum of initial velocity is positive, the flow will expand firstly and then converge either to a point or a limit curve which has the discontinuous curvature in finite time.

Research on transonic flow of nozzle contractions for providing an asymptotic solution

The effect of a contraction on the flow in a supersonic nozzle is investigated, and improvements are made to provide an accurate asymptotic solution of transonic flow. Owing to the elliptical characteristic of the governing equation, supersonic nozzle contractions are not rigorously designed from aerodynamics theory. The contraction effect is often masked by the design defects of the supersonic nozzle contours and, therefore, is hard to evaluate independently. In this study, the authors use a sufficiently advanced supersonic contour to support numerical and theoretical research on various contractions. The results show that the commonly used contractions lead to abrupt changes in transonic flow field parameters, and the degree does not vary with the nozzle Mach number. Based on the work of Hall, the accurate asymptotic solution of the sonic line in the nozzle is derived. Most practical sonic lines provided by various contractions are inconsistent with the accurate asymptotic solution, which further affects the uniformity of the supersonic flow. By iterating the shift of the Witoszynski contraction, the end point curvature is found to be the core parameter. On this basis, three improved contractions are proposed. These new contractions allow discontinuities in wall curvature and avoid the problem inherent in Sivells' cylindrical-quartic–conical-quartic contraction. Each improved contraction successfully coincides with theoretical transonic flow, helping the supersonic nozzle eliminate waves completely and achieve a high degree of flow uniformity.

Trajectory Tracking of Autonomous Vehicle Using Clothoid Curve

This paper proposes a clothoid-curve-based trajectory tracking control method for autonomous vehicles to solve the problem of tracking errors caused by the discontinuous curvature of the control curve calculated by the pure pursuit tracking algorithm. Firstly, based on the Ackerman steering model, the motion model is constructed for vehicle trajectory tracking, Then, the position of the vehicle after the communication delay of the control system is predicted as the starting point of the clothoid control curve, and the optimization interval of the curve end point is determined. The clothoid control curves are calculated, and their parameters are verified by the vehicle motion and safety constraints, so as to obtain the optimal clothoid control curve satisfying the constraints. Finally, considering the servo system response delay time of the steering system, the steering angle target control value is obtained by previewing the curvature of the clothoid control curve. The field experiment is conducted on the test road, which consists of straight, right-angle turns and lane-change elements under three sets of speed limitations, and the test results show that the proposed clothoid-curve-based trajectory tracking control method greatly improved the tracking accuracy compared with the pure pursuit method; in particular, the yaw deviation is improved by more than 50%.

Integrated Vehicle Controller for Path Tracking with Rollover Prevention of Autonomous Articulated Electric Vehicle Based on Model Predictive Control

This paper presents an integrated controller for an autonomous articulated electric vehicle (AAEV) for path tracking and rollover prevention. The AAEV is vulnerable to rollover due to the characteristics of the articulated frame steering (AFS) mechanism, which shows improved maneuverability and agility but not front wheel steering. In addition, the ratio between height and track width is high, so the AAEV is prone to rolling over. Therefore, the proposed controller was designed to achieve the two goals, following the reference path and managing the velocity to improve the safety of the AAEV. Vehicle behavior was modeled by a kinematic model with actuation delay. A local linearization was used to improve the accuracy of the vehicle model and reduce the computational load. Reference states of the position and heading were determined to follow the reference path and prevent the rollover. A model predictive control (MPC)-based reference state tracker was designed to optimize the articulation angle rate and longitudinal acceleration commands. The simulation study was conducted to evaluate the proposed algorithm with a comparison of the base algorithms. The reference path for the simulation was an S-shaped path with discontinuous curvature. Simulation results showed that the proposed algorithm reduces the path tracking error and load-transfer ratio.

Corner smoothing for CNC machining of linear tool path: A review

Computer numerical control (CNC) machine tools are widely used in various industrial fields ranging from aerospace, automotive, ship building, and the die/mould to manufacture products. However, tool paths of most CNC machine tools are composed of a series of linear motion commands (G01), which will inevitably cause the discontinuity in curvature and feedrate at the junctions between adjacent linear tool path segments, deteriorating the surface quality with unfavorable marks and decreasing the machining efficiency. To solve this problem for obtaining the steady and continuous motions of machine tools, the local corners have to be smoothed. Generally, the existing corner smoothing methods can be classified as the global smoothing and the local corner smoothing, where the specially designed transition curves or the directly planned motion of machine tools are adopted to generate the geometrically corner-free tool path. Moreover, some new methods that focus on developing different transition or rounding strategies are also developed for further improving the kinematics performance of machine tools. In this paper, the recent advances and researches on corner smoothing methods are reviewed from different categories, and the conclusions, remaining challenges and future directions in corner smoothing are also presented.

Research on parallel parking path planning and tracking control of unmanned vehicles

Aiming at the problems of discontinuous curvature of the planned path, difficulty in finding the optimal reference path and high control accuracy requirements in tracking control for unmanned vehicles in the process of parallel parking, an optimal reference path planning method based on arc line and multi-objective optimization function and a path tracking control strategy based on nonlinear model predictive control are proposed. Firstly, the upper and lower boundaries of the exercisable area are obtained by the tangent of the arc and the straight line, and the multi-objective optimization function is designed to obtain the optimal arc-line combination, and the optimal reference path is obtained by polynomial curve fitting. Secondly, a path-following controller is designed using nonlinear model predictive control. Finally, a comparative analysis is carried out in MATLAB/Simulink and Carsim with the controller based on pure tracking design. The results show that the optimal reference path curvature obtained by the proposed method is continuous without sudden change, and the designed tracking controller has better tracking accuracy.

Research on dynamic prediction of tubular extension limit and operation risk in extended-reach drilling

Extended-reach wells have been widely applied to efficient development of oil and gas resources in complex areas such as oceans, beaches, lakes and mountains. Extended-reach drilling has the characteristics of many constraints, high implementation difficulty and high operation risk, and the accurate prediction of tubular extension limits and operation risks is very significant for safe drilling. Firstly, local tubular deflection curves and additional contact forces due to discontinuity effects are firstly deduced, and an amended torque & drag model of tubular strings is built. Secondly, a dynamic inversion method of friction factors was presented by introducing the weight function related to well depth and considering the difference of friction factors on cased and open-hole sections. Next, a dynamic prediction of tubular extension limit and operation risk is built by combining the amended tubular mechanical model, inversion model of friction factors. At last, the above theoretical models are applied to a case study. The results indicate that curvature discontinuity and stiffness discontinuity increase contact forces obviously in build-up and azimuth turning sections, which further increase friction force and torque a lot. The long-term, short-term and real-time tubular extension limits and operation risks can be obtained by setting different values of p.

Whale optimization algorithm based on Levy flight and memory for static smooth path planning

In this paper, a whale optimization algorithm based on Levy flight and memory (WOALFM) is proposed to solve the curvature discontinuity problem in the global path planning of unmanned vehicles. Levy flight and chaotic mapping are introduced to disturb the solutions of each generation and enhance the diversity of solutions. A memory strategy based on fractional-order expansion is presented to remember the influence of the positions of individuals in previous generations on the positions of current generation. This strategy based on Levey flight and memory can enhance searching ability and avoid falling into local optimum. Furthermore, the ratio of global searching to local searching can be adjusted to achieve desired results in WOALFM algorithm. The proposed WOALFM algorithm is tested and compared with five algorithms including whale optimization algorithm (WOA), Moth-Flame Optimization (MFO), particle swarm optimization (PSO), Fractional-Order Velocity based Particle Swarm Optimization (FOPSO) and Grey Wolf Optimizer (GWO) on 23 standard benchmark functions. The experimental results show the effectiveness of WOALFM. The proposed algorithm is applied to smooth path planning problem of unmanned vehicles. Three factors, including the length, curvature and curvature derivative of a path are considered in order to obtain the shortest smooth path without collisions. The experimental results show that more collision-free paths can be obtained in lower computational cost by the presented method.

Manipulating Interfacial Thermal Conduction of 2D Janus Heterostructure via a Thermo‐Mechanical Coupling

Abstract2D Janus transition metal dichalcogenide (TMD) semiconductor materials have attracted great interest for their potential applications. Because of the increased requirement for thermal management in 2D devices with single‐atom thickness, a fundamental understanding of interfacial thermal conduction (ITC) has emerging significance. In this work, the ITC of in‐plane heterostructures constructed using MoSSe and WSSe is reported. In addition to the interface connected normally by MoSSe and WSSe with the same type of chalcogen atoms are on the same side of left and right sections, inversional interface by rotation of 180° of WSSe is also considered, in which S atoms are on the opposite side of the left and right sections. Interestingly, the ITC in the normally connected heterostructure is found to be almost twice as much as that in the inversely connected heterostructure. The unusually large change in ITC is attributed to the bending curvature and additional discontinuity in the inversely connected heterostructure. Euler–Bernoulli beam model gives further insight into the origin of such interface bending. The findings offer the very first insight into the phonon transport in Janus heterostructures, and benefit thermal management of 2D devices based on Janus monolayers.

Smooth Three-Dimensional Route Planning for Fixed-Wing Unmanned Aerial Vehicles With Double Continuous Curvature

This paper presents a smooth flight path planner for maneuvering in a 3D Euclidean space, which is based on two new space curves. The first one is called “Elementary Clothoid-based 3D Curve (ECb3D)”, which is built by concatenating two symmetric Clothoid-based 3D Curves (Cb3D). The combination of these curves allows to reach an arbitrary orientation in 3D Euclidean space. This new curve allows to generate continuous curvature and torsion profiles that start and finish with a null value, which means that they can be concatenated with other curves, such as straight segments, without generating discontinuities on those variables. The second curve is called “Double Continuous Curvature 3D Curve (DCC3D)” which is built as a concatenation of three straight line segments and two ECb3D curves, allowing to reach an arbitrary configuration in position and orientation in the 3D Euclidean space without discontinuities in curvature and torsion. This trajectory is applied for autonomous path planning and navigation of unmanned aerial vehicles (UAVs) such as fixed-wing aircrafts. Finally, the results are validated on the FlightGear 2018 flight simulator with the UAV kadett 2400 platform.

The edge profile of liquid spills

The Young–Laplace (Y–L) equation relates the curvature of the interface between two fluids to the pressure difference across that interface. The link between the surface curvature and pressure discontinuity underpins numerous phenomena in hydrostatics, including the profiles of sessile (immobile) drops, pendant drops, capillary bridges, and liquid pearls. In most cases, the application of the Y–L equation readily yields the governing differential equations of the fluid surface but often these equations have no analytic solutions; this is the case, for example, with the profile of a dew drop or a liquid pendant. There are, however, some cases for which the differential equations have closed form solutions; one is the edge profile of a liquid spill or puddle on a horizontal surface. Here, we review the Y–L equation and apply it to obtain the governing differential equations of the edge profile for a liquid spill. The solution of the differential equations results in a universal function that describes the edge profile of any fluid. One important finding is that the profile curve begins its descent very gradually from the flat top of the fluid far away from the edge and terminates at the point, where the angle between the profile curve and the horizontal matches the equilibrium contact angle of the liquid on the substrate.

Research on Path Planning and Tracking Control of Automatic Parking System

In this paper, we focus on the parking path planning and path tracking control under parallel parking conditions with automatic parking system as the research object. In order to solve the problem of discontinuity of curvature in the path planning of traditional arc-straight combined curve, a quintic polynomial is used to smooth the path. we design a path tracking controller based on the incremental model predictive control (MPC). The preview control based on pure tracking algorithm is used as the comparison algorithm for path tracking. The feasibility of the controller is verified by building a Simulink/CarSim co-simulation platform. In addition, the practicality of the parking controller is further verified by using the ROS intelligent car in the laboratory environment.

Parking Planning Under Limited Parking Corridor Space

Automatic parking systems are increasingly used in daily life, and the restriction of parking spaces will make parking more difficult. This paper proposes parallel parking and forwards vertical parking path planning algorithms considering the park-ing corridor space. First, an anthropomorphic parallel parking path planning using parking space is proposed for the limited space over the length of the parking corridor. Second, a for-ward vertical parking path planning algorithm is proposed con-sidering the width of the parking space corridor. Third, the tar-get line set for parallel parking and vertical parking paths is generated. At the same time, the target line set considers the error factor and then selects the target line. Fourth, the clothoid solves the problem of discontinuous curvature of the parking path. Finally, a driver model is constructed to follow the gener-ated parking path, and the parking planning method proposed in this paper is compared with other methods.