Route-Planning Method for Plant Protection Rotor Drones in Convex Polygon Regions

Aiming at the problem of low operating efficiency due to the poor endurance of plant protection rotor drones and the small volume of pesticide carried, this paper proposes a route-planning algorithm for convex polygon regions based on the initial heading angle. First, a series of coordinate conversion methods ranging from the Earth coordinate system to the local plane coordinate system are studied. Second, in the local plane coordinate system, a route generation method based on subregion is proposed; therefore, multiple routes can be generated with different initial heading angles. Lastly, the optimal route and the best initial heading angle can be obtained after the comparison according to the three evaluation criteria: number of turns, route distance, and pesticide waste rate. The simulation results show that, compared with the common grid method, the route generation method based on subregion reduces the route distance and pesticide waste rate by 2.27% and 13.75%, respectively. Furthermore, it also shows that, compared with the route generated by the initial heading angle of 0°, the optimal route reduces the number of turns, route distance, and pesticide waste rate by 60%, 17.65%, and 38.18%, respectively. The route was optimized in three aspects and reached the best overall result using this method, which in turn proved its feasibility.

Local wave numbers on an n-spheres

We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them in terms of their local plane wave behavior. We estimate the local spectrum of wave numbers by approximating the Spherical harmonics in the locally flat neighborhood around a point on the Spheres. These local wave numbers are shown to obey an interesting Pythagorean type relation. Based on this relation, we propose a question whether there are integer triples for 2-spheres and their generalization to n-spheres. We apply the local spectrum to define quantities such as phase velocity and group velocity on a sphere and outline the relevance of the analysis for the case fields on de Sitter space.

Semi-exact local absorbing boundary condition for seismic wave simulation

An absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.

Large Common Plansets-4-Points Congruent Sets for Point Cloud Registration

Point cloud registration combines multiple point cloud data sets collected from different positions using the same or different devices to form a single point cloud within a single coordinate system. Point cloud registration is usually achieved through spatial transformations that align and merge multiple point clouds into a single globally consistent model. In this paper, we present a new segmentation-based approach for point cloud registration. Our method consists of extracting plane structures from point clouds and then, using the 4-Point Congruent Sets (4PCS) technique, we estimate transformations that align the plane structures. Instead of a global alignment using all the points in the dataset, our method aligns 2-point clouds using their local plane structures. This considerably reduces the data size, computational workload, and execution time. Unlike conventional methods that seek to align the largest number of common points between entities, the new method aims to align the largest number of planes. Using partial point clouds of multiple real-world scenes, we demonstrate the superiority of our method compared to raw 4PCS in terms of quality of result (QoS) and execution time. Our method requires about half the execution time of 4PCS in all the tested datasets and produces better alignment of the point clouds.

Signature-causality reflection generated by Abelian gauge transformations

In this paper, we want to better understand the causality reflection that arises under a subset of Abelian local gauge transformations in geometrodynamics. We proved in previous papers that in Einstein–Maxwell spacetimes, there exist two local orthogonal planes of gauge symmetry at every spacetime point for non-null electromagnetic fields. Every vector in these planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. The vectors that span these local orthogonal planes are dependent on electromagnetic gauge. The local group of Abelian electromagnetic gauge transformations has been proved isomorphic to the local groups of tetrad transformations in these planes. We called LB1 the local group of tetrad transformations made up of SO(1, 1) plus two different kinds of discrete transformations. One of the discrete transformations is the full inversion two by two which is a Lorentz transformation. The other discrete transformation is given by a matrix with zeroes on the diagonal and ones off-diagonal two by two, a reflection. The group LB1 is realized on this plane, we call this plane one, and is spanned by the time-like and one space-like vectors. The other local orthogonal plane is plane two and the local group of tetrad transformations, we call this LB2, which is just SO(2). The local group of Abelian electromagnetic gauge transformations is isomorphic to both LB1 and LB2, independently. It has already been proved that a subset of local electromagnetic gauge transformations that leave the electromagnetic tensor invariant induces a change in sign in the norm of the tetrad vectors that span the local plane one. The reason is that one of the discrete transformations on the local plane one that belongs to the group LB1 is not a Lorentz transformation, it is a flip or reflection. It is precisely on this kind of discrete transformation that we have an interest since it has the effect of changing the signature and the causality. This effect has never been noticed before.

2D anisotropic multicomponent Gaussian-beam migration under complex surface conditions

Elastic-wave migration in anisotropic media is a vital challenge, particularly for areas with irregular topography. Gaussian-beam migration (GBM) is an accurate and flexible depth migration technique, which is adaptable for imaging complex surface areas. It retains the dynamic features of the wavefield and overcomes the multivalued traveltimes and caustic problems of Kirchhoff migration. We have extended the GBM method to work for 2D anisotropic multicomponent migration under complex surface conditions. We use Gaussian beams to calculate the wavefield from irregular topography, and we use two schemes to derive the down-continued recorded wavefields. One is based on the local slant stack as in classic GBM, in which the PP- and PS-wave seismic records within the local region are directly decomposed into local plane-wave components from irregular topography. The other scheme does not perform the local slant stack. The Green’s function is calculated with a Gaussian beam summation emitted from the receiver point at the irregular surface. Using the crosscorrelation imaging condition and combining with the 2D anisotropic ray-tracing algorithm, we develop two 2D anisotropic multicomponent Gaussian-beam prestack depth migration (GB-PSDM) methods, i.e., using the slant stack and nonslant stack, for irregular topography. Numerical tests demonstrate that our anisotropic multicomponent GB-PSDM can accurately image subsurface structures under complex topography conditions.

Online dictionary learning method for extracting GPR diffractions

Diffractions in a Ground-Penetrating Radar (GPR) data carry significant responses from near-surface small-scale fractures or karsts. However, this geological information is generally difficult to extract because of the shielding effect of strong reflections from subsurface layers. In order to solve this problem, a GPR diffraction extraction method is proposed for individually separating and imaging of GPR diffractions that incorporates a local plane-wave destruction filter with an online dictionary learning algorithm. The strong reflections are estimated and eliminated by the local plane-wave destruction method and the weak GPR diffractions are extracted by a sparse coding algorithm. In solving this model, a trust-region algorithm is used for accelerating the sparse coding procedures that can scale up gracefully to a large GPR data processing. A numerical experiment demonstrates the good performance of the proposed method in destroying strong reflections and enhancing weak diffractions from small-scale void holes. Real data application further verifies its potential value in resolving fine details of subsurface small-scale buried targets, such as pipes or void holes.