Curvature Constraints Research Articles

Mechanism for wrapping fiber around the Y fork

Fiber reinforcement on the practical parts with complex geometries (e.g., Y fork) is a challenge for the industrial development of composites fiber wrapping (FW). FW path planning for the Y fork is studied here, which is a prerequisite for the implementation of the FW process using a robotic work-cell. The feasibility of this work-cell is explored, and more precisely, two path generation algorithms for guiding the robot movement are proposed. One is used to calculate uniformly arranged paths at a constant angle to the axes of the tubular Y fork, where no overlaps and gaps are created under the assumption that the maximum geodesic curvature constraint in FW is ignored. Different from the first one, the second algorithm is presented where the curvature is restricted. Both of these algorithms are implemented by using the MATLABTM suite to carry out re-development of ABAQUS software. Finally, simulations are demonstrated to illustrate the validity of the methodology presented here.

An Optimized Trajectory Planner and Motion Controller Framework for Autonomous Driving in Unstructured Environments

This paper proposes an optimized trajectory planner and motion planner framework, which aim to deal with obstacle avoidance along a reference road for autonomous driving in unstructured environments. The trajectory planning problem is decomposed into lateral and longitudinal planning sub-tasks along the reference road. First, a vehicle kinematic model with road coordinates is established to describe the lateral movement of the vehicle. Then, nonlinear optimization based on a vehicle kinematic model in the space domain is employed to smooth the reference road. Second, a multilayered search algorithm is applied in the lateral-space domain to deal with obstacles and find a suitable path boundary. Then, the optimized path planner calculates the optimal path by considering the distance to the reference road and the curvature constraints. Furthermore, the optimized speed planner takes into account the speed boundary in the space domain and the constraints on vehicle acceleration. The optimal speed profile is obtained by using a numerical optimization method. Furthermore, a motion controller based on a kinematic error model is proposed to follow the desired trajectory. Finally, the experimental results show the effectiveness of the proposed trajectory planner and motion controller framework in handling typical scenarios and avoiding obstacles safely and smoothly on the reference road and in unstructured environments.

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza–Klein dimensional reduction from D+1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.

A Feedrate Planning Method for the NURBS Curve in CNC Machining Based on the Critical Constraint Curve

The curvature of the NURBS curve varies along its trajectory, therefore, the commonly used feedrate-planning method, which based on the acceleration/deceleration (Acc/Dec) model, is difficult to be directly applied in CNC machining of a NURBS curve. To address this problem, a feedrate-planning method based on the critical constraint curve of the feedrate (CCC) is proposed. Firstly, the problems of existing feedrate-planning methods and their causes are analyzed. Secondly, by considering both the curvature constraint and the kinematic constraint during the Acc/Dec process, the concept of CCC which represents the relationship between the critical feedrate-constraint value and the arc length is proposed. Then the CCC of a NURBS curve is constructed, and it has a concise expression conforming to the Acc/Dec model. Finally, a feedrate-planning method of a NURBS curve based on CCC and the Acc/Dec model is established. In the simulation, a comparison between the proposed method and the conventional feedrate-planning method is performed, and the results show that, the proposed method can reduce the Acc/Dec time by over 40%, while little computational burden being added. The machining experimental results validate the real-time performance and stability of the proposed method, and also the machining quality is verified. The proposed method offers an effective feedrate-planning strategy for a NURBS curve in CNC machining.

Spacelike translating solitons in Lorentzian product spaces: Nonexistence, Calabi–Bernstein type results and examples

We establish nonexistence results for complete spacelike translating solitons immersed in a Lorentzian product space [Formula: see text], under suitable curvature constraints on the curvatures of the Riemannian base [Formula: see text]. In particular, we obtain Calabi–Bernstein type results for entire translating graphs constructed over [Formula: see text]. For this, we prove a version of the Omori–Yau’s maximum principle for complete spacelike translating solitons. Besides, we also use other two analytical tools related to an appropriate drift Laplacian: a parabolicity criterion and certain integrability properties. Furthermore, under the assumption that the base [Formula: see text] is non-positively curved, we close our paper constructing new examples of rotationally symmetric spacelike translating solitons embedded into [Formula: see text].

Addendum to ‘EPRL/FK asymptotics and the flatness problem’

We show that, when an approximation used in this prior work is removed, the resulting improved calculation yields an alternative derivation, in the particular case studied, of the accidental curvature constraint of Hellmann and Kaminski. The result is at the same time extended to apply to almost all non-degenerate Regge-like boundary data and a broad class of face amplitudes. This resolves a tension in the literature.

Geometric model of the pursuit problem on a plane for the case of sets of targets and pursuers

This article examines a kinematic model of a group pursuing several targets by the method of parallel approach. The model is based on the fact that pursuers try to adhere to pre-designed trajectories. The pursuers’ trajectories have curvature constraints. The initial directions of the pursuers’ velocities are arbitrary, which changes the well-known method of parallel approach. In our model, targets are chased by the pursuers simultaneously. This is due to the change in the lengths of the predicted trajectories in such a way as to synchronize the time to reach the target. The change in the lengths of the predicted trajectories occurs due to an increase in the radius of curvature in the initial segment of the trajectory.

Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Ly$\alpha$ forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, $r_d$, from eight different samples and six measurements of the growth rate parameter, $f\sigma_8$, from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, $\Lambda$CDM model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization the BAO data provide nearly an order of magnitude improvement on curvature constraints. The RSD measurements indicate a growth rate that is consistent with predictions from Planck primary data and with General Relativity. When combining the results of SDSS BAO and RSD with external data, all multiple-parameter extensions remain consistent with a $\Lambda$CDM model. Regardless of cosmological model, the precision on $\Omega_\Lambda$, $H_0$, and $\sigma_8$, remains at roughly 1\%, showing changes of less than 0.6\% in the central values between models. The inverse distance ladder measurement under a o$w_0w_a$CDM yields $H_0= 68.20 \pm 0.81 \, \rm km\, s^{-1} Mpc^{-1}$, remaining in tension with several direct determination methods. (abridged)

МОДЕЛЬ ПАРАЛЛЕЛЬНОГО СБЛИЖЕНИЯ НА ПЛОСКОСТИ ГРУППЫ ПРЕСЛЕДОВАТЕЛЕЙ С ОДНОВРЕМЕННЫМ ДОСТИЖЕНИЕМ ЦЕЛИ

The article discusses a kinematic model of a group pursuing a single target by the method of parallel approach. The model is based on the fact that pursuers try to stick to pre-designed trajectories. The pursuer’s trajectories have curvature constraints. The initial directions of the pursuers’ velocities are arbitrary, which changes the well-known method of the parallel approach. In our model, the goal is achieved by the pursuers simultaneously. This is due to the change in the lengths of the predicted trajectories by time synchronization to reach the target. The change in length occurs due to an increase in the radius of curvature in the initial section of the trajectory.

Adaptive sampling point planning for free-form surface inspection under multi-geometric constraints

Free-form surfaces have been widely used in aerospace, automotive and other fields. Due to its complex geometry, free-form surface inspection is generally conducted by touch-trigger or measuring probe-based Coordinate Measurement Machines or On-machine Measurement. Sampling strategy plays a decisive role in improving both measurement accuracy and efficiency, which is determined by sample size and distribution of sample points. However, it is difficult to simultaneously take the surface curvature, sampling density and approximation error into account, considering the complexity of surface geometry. In this paper, triangle mesh simplification is innovatively adopted in sampling planning to achieve multi-geometric constraints. As triangle mesh has outstanding advantages in representing the surface features, strong stability and is easy to modify its structure, free-form surface is converted to a dense triangle mesh. Triangle mesh simplification is implemented by iteratively contracting triangle edges. An improved quadric error metric is established to decide contraction order and optimal target vertices under discrete curvature constraint. Sampling density is controlled by limiting the triangle edge length. Detailed adaptive sampling algorithm under multi-geometric constraints is then developed. Both simulation and experiment are conducted to validate feasibility and robustness of the proposed method. The results are compared with uniform sampling and existing adaptive sampling strategy to show that the proposed method can prominently reduce sampling error when sample size is small.

Signal denoising based on the Schrödinger operator's eigenspectrum and a curvature constraint

Signal denoising based on the Schrödinger operator's eigenspectrum and a curvature constraint

Adaptive surrogate-based harmony search algorithm for design optimization of variable stiffness composite materials

Having the advancement in automated fiber placement (AFP) and three-dimensional (3D) printing, fabricating novel composites reinforced with curvilinear fibers, namely variable stiffness composites (VSCs), have gradually become feasible. Contrasted to the traditional straight fiber-reinforced composites, VSCs possess significantly enhanced mechanical properties and increased mechanical performance. However, the optimization of a VSC panel is still a challenging problem, which can be attributed to the high non-convexity of the feasible design space and highly involved computation resources. To accelerate the design and optimization of VSC structures, in this study, we propose an effective and efficient adaptive surrogate-based harmony search algorithm (ASBHSA). The VSC is modeled using the fiber path methodology through which the fiber trajectory is generated by a mathematical formulation. In addition, the manufacturability and quality of the product are guaranteed by considering the curvature constraint. For the ASBHSA, a distance-based infill criterion in combination with a radial basis function (RBF) is proposed to guide the adaptive sampling. The global best harmony search (GHS) with a good ability to find the global minimum is integrated into the developed optimization framework. After solving some popular benchmark optimization problems as well as making comparisons of the optimal designs of VSCs with those in published works, the proposed optimization framework is demonstrated being able to effectively and efficiently find the global minimum. Then, a series of designs and optimizations of laminated VSC plates under various boundary conditions and different loading conditions are carried out systematically. The reported interesting findings may provide some insights and guidance in the design of laminated VSC composites. Moreover, our proposed optimization model provides a useful tool for solving various kinds of optimization problems.

Efficient curvature-constrained least cost route optimization on parallel architectures

When choosing a path for a linear infrastructure between two terminals, several types of constraints apply for installation and operational criteria. For offshore pipelines or cables, curvature constraints are typically important not only due to the flexural rigidity but also the maneuverability of the laying vessels. Roads are subject to similar curvature constraints to ensure the safety of users travelling at the design speed. Yet, such constraints are not taken into account in traditional least cost routing methods, often based on Dijkstra’s algorithm. Post-process smoothing is often necessary, resulting in non-optimal routes. We present a new method for least cost route optimization, allowing to incorporate the curvature constraints into the primary calculations as opposed to a post-determination consideration. With this technique, smoothing of the least cost route becomes unnecessary, preserving its optimal character. Optimization algorithms for the trajectories of forward-moving vehicles were adapted for the routing of linear infrastructures and modified to include an angular discretization of variable resolution, resulting in faster and more accurate results. In addition to the inclusion of curvature constraints, the proposed method offers a higher flexibility in terms of local route orientation compared to the traditional Dijkstra’s algorithm, producing routes of lower cost. The numerical solver was implemented on parallel architectures, to compute optimal routes on realistic domains in reasonable computational times. For personal computers with a few computing cores, the OpenMP implementation on Central Processing Units does not significantly increase the iteration count and provides significant speedups. For certain configurations, the use of Graphical Processing Units reduces further the computational time.

Path planning for endovascular catheterization under curvature constraints via two-phase searching approach

PurposePlanning a safe path for flexible catheters is one of the major challenges of endovascular catheterization. State-of-the-art methods rarely consider the catheter curvature constraint and reduced computational time of path planning which guarantees the possibility to re-plan the path during the actual operation. MethodsIn this manuscript, we propose a fast two-phase path planning approach under the robot curvature constraint. Firstly, the vascular structure is extracted and represented by vascular centerlines and corresponding vascular radii. Then, the path is searched along the vascular centerline using breadth first search (BFS) strategy and locally optimized via the genetic algorithm (GA) to satisfy the robot curvature constraint. This approach (BFS-GA) is able to respect the robot curvature constraint while keeping it close to the centerlines as much as possible. We can also reduce the optimization search space and perform parallel optimization to shorten the computational time. ResultsWe demonstrate the method’s high efficiency in two-dimensional and three-dimensional space scenarios. The results showed the planner’s ability to satisfy the robot curvature constraint while keeping low computational time cost compared with sampling-based methods. Path replanning in femoral arteries can reach an updating frequency at 6.4pm 2.3Hz. ConclusionThe presented work is suited for surgical procedures demanding satisfying curvature constraints while optimizing specified criteria. It is also applicable for curvature constrained robots in narrow passages.

Analysis of velocity and trajectory in the group pursuit tasks

This article discusses how to the goal pursuers can simultaneously achieve their goals in the group pursuit task. The proposed pursuit model suggests the pursuer to follow the set motion pattern, which is structured at each point of time. Such trajectory is a compound curve that takes into account the curvature constraints. The time of achieving the goal of each pursuer depends on the velocity and minimum radius of curvature of the trajectory. Multi-factor analysis of velocity modules and minimum radius of curvature of the trajectories of each pursuer for simultaneous achievement of their goals is the focus of this research

Geometrical constraints on curvature from galaxy-lensing cross-correlations

Accurate constraints on curvature provide a powerful probe of inflation. However, curvature constraints based on specific assumptions of dark energy may lead to unreliable conclusions when used to test inflation models. To avoid this, it is important to obtain constraints that are independent on assumptions for dark energy. In this paper, we investigate such constraints on curvature from the geometrical probe constructed from galaxy-lensing cross-correlations. We study comprehensively the cross-correlations of galaxy with magnification, measured from type Ia supernovae's brightnesses ("$g\kappa^{\rm SN}$"), with shear ("$g\kappa^{\rm g}$"), and with CMB lensing ("$g\kappa^{\rm CMB}$"). We find for the LSST and Stage IV CMB surveys, "$g\kappa^{\rm SN}$" , "$g\kappa^{\rm g}$" and "$g\kappa^{\rm CMB}$" can be detected with signal-to-noise ratio $S/N=104,\ 2291,\ 1842$ respectively. When combined with supernovae Hubble diagram ("SN") to constrain curvature, we find galaxy-lensing cross-correlation becomes increasingly important with more degrees of freedom allowed in dark energy. Without any priors, we obtain error on $\Omega_K$ of $0.723$ from "SN + $g\kappa^{\rm SN}$", $0.0417$ from "SN + $g\kappa^{\rm g}$", and $0.04$ from "SN + $g\kappa^{\rm g}$ + $g\kappa^{\rm CMB}$" for the LSST and Stage IV CMB surveys. The last one is more competitive than a Stage IV BAO survey ("BAO"). When galaxy-lensing cross-correlations are added to the combined probe of "SN + BAO + CMB", where "CMB" stands for Planck measurement for the CMB acoustic scale, we obtain constraint on $\Omega_K$ of $0.0013$, which is a factor of 7 improvement from "SN + BAO + CMB". We study improvements in these results from increasing the high redshift extension of supernovae.

A novel approach to optimising well trajectory in heterogeneous reservoirs based on the fast-marching method

To achieve efficient recovery of subsurface energy resources, a suitable trajectory needs to be identified for the production well. In this study, a new approach is presented for automated identification of optimum well trajectories in heterogeneous oil/gas reservoirs. The optimisation procedures are as follows. First, a productivity potential map is generated based on the site characterisation data of a reservoir (when available). Second, based on the fast-marching method, well paths are generated from a number of entrance positions to a number of exit points at opposite sides of the reservoir. The well trajectory is also locally constrained by a prescribed maximum curvature to ensure that the well trajectory is drillable. Finally, the optimum well trajectory is selected from all the candidate paths based on the calculation of a benefit-to-cost ratio. If required, a straight directional well path, may also be derived through a linear approximation to the optimised non-linear trajectory by least squares analysis. Model performance has been demonstrated in both 2D and 3D. In the 2D example, the benefit-to-cost ratio of the optimised well is much higher than that of a straight well; in the 3D example, laterals of various curvatures are generated. The applicability of the method is tested by exploring different reservoir heterogeneities and curvature constraints. This approach can be applied to determine the entrance/exit positions and the well path for subsurface energy system development, which is useful for field applications.

Phase diagrams and microstructures of aqueous short alkyl chain polyethylene glycol ether carboxylate and carboxylic acid triblock surfactant solutions

HypothesisThe surfactant C8EO8CH2COOH (Akypo LF2) and its salts have a small hydrophobic and a significantly longer hydrophilic part. As a consequence, there must be a significant steric constraint, once these surfactant molecules form micelles. In addition, the partially charged headgroups should bring some additional fine-tuning via electrostatic interactions to this “essentially non-ionic” surfactant. ExperimentsPhase diagrams of binary mixtures of water and C8EO8CH2COOH are established over large concentration and temperature ranges, also at different pHs and in the presence of sodium and calcium ions. Surface tensions and osmotic pressures are measured to understand the systems. To evaluate the microstructures, also Dynamic Light Scattering and Small-Angle X-ray Scattering are performed. FindingsApart from the formation of coacervates at very low surfactant concentrations, spherical micelles persist over the whole concentration and temperature range and do not change in size and shape. At very high surfactant concentrations, above 60% by weight, where the headgroups are no longer fully hydrated, the standard core-shell structure of micelles vanishes and highly stabilized aggregates of 8–26 octyl chains are suspended in interdigitated polyoxyethylene layers and form an “osmotic brush”. When the acid is partially transformed to a sodium salt, the repulsion between the micelles increases, whereas bridging between micelles prevails, when the counterions are calcium cations. Remarkably, the negative charges of the headgroups are randomly distributed in the hydrophilic ethylene oxide shell. Altogether, a phase diagram without lyotropic liquid crystalline phases and an extreme shift of the cloud-point in temperature and composition is found, similar to the phase diagram of C8EO8OH already known in literature. The phase properties can be explained by the curvature and packing constraints together with the Lindemann rule applied to short hydrocarbon chains.

Convergence Analysis of Gradient Algorithms on Riemannian Manifolds without Curvature Constraints and Application to Riemannian Mass

We study the convergence issue for the gradient algorithm (employing general step sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity (resp., weak sharp minima), local/global convergence (resp., linear convergence) results are established. As an application, the linear convergence properties of the gradient algorithm employing the constant step sizes and the Armijo step sizes for finding the Riemannian $L^p$ ($p\in[1,+\infty)$) centers of mass are explored, respectively, which in particular extend and/or improve the corresponding results in [B. Afsari, R. Tron, and R. Vidal, SIAM J. Control Optim., 51 (2013), pp. 2230--2260; G. C. Bento et al., J. Optim. Theory Appl., 183 (2019), pp. 977--992].

A global model of the magnetorotational instability in protoneutron stars

Context. Magnetars are isolated neutron stars characterized by their variable high-energy emission, which is powered by the dissipation of enormous internal magnetic fields. The measured spin-down of magnetars constrains the magnetic dipole to be in the range of 1014 − 1015 G. The magnetorotational instability (MRI) is considered to be a promising mechanism to amplify the magnetic field in fast-rotating protoneutron stars and form magnetars. This scenario is supported by many local studies that have shown that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown. Aims. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation. Methods. Using the pseudo-spectral code MagIC, we performed three-dimensional incompressible magnetohydrodynamics simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We performed a parameter study in which we varied the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations performed with the code Snoopy. Results. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of B ≥ 2 × 1015 G and a nondominant magnetic dipole, which represents systematically about 5% of the averaged magnetic field strength. Interestingly, this dipole is tilted toward the equatorial plane. By comparing these results with shearing box simulations, we find that local models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Moreover, overly large boxes allow for elongated structures to develop without any realistic curvature constraint, which may explain why these models tend to overestimate the field amplification. Conclusions. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae and gamma-ray bursts.