Special Trajectory Research Articles

Effects of Equatorial Plasma Bubbles on Multi-GNSS Signals: A Case Study over South China

Equatorial plasma bubbles (EPBs) occur frequently in low-latitude areas and have a non-negligible impact on navigation satellite signals. To systematically analyze the effects of a single EPB event on multi-frequency signals of GPS, Galileo, GLONASS, and BDS, all-sky airglow images over South China are jointly used to visually determine the EPB structure and depletion degree. The results reveal that scintillations, or GNSS signal fluctuations, are directly linked to EPBs and that the intensity of scintillation is positively correlated with the airglow depletion intensity. The center of the airglow depletion often corresponds to stronger GNSS scintillation, while the edge of the bubble, which is considered to have the largest density gradient, corresponds to relatively smaller scintillation instead. This work also systematically analyzes the responses of multi-constellation and multi-frequency signals to EPBs. The results show that the L2 and L5 frequencies are more susceptible than the L1 frequency is. For different constellations, Galileo’s signal has the best tracking stability during an EPB event compared with GPS, GLONASS, and BDS. The results provide a reference for dual-frequency signal selection in precise positioning or TEC calculation, that is, L1C and L2L for GPS, L1C and L5Q for Galileo, L1P and L2C for GLONASS, and L1P and L5P for BDS. Notably, BDS-2 is significantly weaker than BDS-3. And inclined geosynchronous orbit (IGSO) satellites have abnormal data error rates, which should be related to the special signal path trajectory of the IGSO satellite.

Research on Climbing Robot for Transmission Tower Based on Foot-End Force Balancing Algorithm

This paper aims to introduce robot technology to carry out the safety inspection of transmission towers in long-distance power transmission, so as to improve the safety and efficiency of inspection. However, aiming at the problem that the existing climbing robots are mainly used for large load applications, which leads to the large size and lack of flexibility of the robot, we propose an innovative solution. Firstly, a lightweight quadruped climbing robot is designed to improve portability and operational flexibility. Then, a one-dimensional force sensor is added at the end of each leg of the robot, and a special swing phase trajectory is designed. The robot can judge whether the electromagnetic adsorption is effective and avoid potential safety hazards. Finally, based on the principle of virtual model control (VMC), a foot-end force balancing algorithm is proposed to achieve uniform distribution and continuous change in force, and improve safety and load capacity. The experiments show that the scheme has a stable climbing ability in the environments of angle steel, vertical ferromagnetic plane and transmission tower.

Comparison of Feedback Three-Axis Magnetic Attitude Control Strategies

In this article, five feedback magnetic attitude control algorithms are compared in terms of stabilization accuracy and implementation problems. The control strategies are classic Lyapunov control with scalar gain; the same control strategy with matrix gain and a specific gain-tuning procedure; sliding control with a variable surface; a linear quadratic regulator constructed for a special time-invariant system of a higher degree than the initial time-varying system; and a special controllable trajectory developed using particle swarm optimization. A new sliding surface construction method is proposed in this paper. Surface parameters were changed in every control iteration to ensure that the required control torque component along the geomagnetic induction vector was small. The advantages and drawbacks of the considered methods and their applicability for different target attitudes are discussed.

#4851 MOLECULAR FEATURES OF CIRCULATORY B CELLS AND RENAL CELLS AT THE SINGLE-CELL LEVEL IN AUTOANTIBODY-NEGATIVE PRIMARY MEMBRANOUS NEPHROPATHY PATIENTS

Abstract Background and Aims Primary membranous nephropathy (PMN) is an organ-specific autoimmune disease that is the most common cause of idiopathic nephrotic syndrome in adults. Furthermore, the incidence of PMN is increasing, especially in young adults and children. The landmark discovery of nephritogenic autoantibodies against podocyte antigens such as M-type phospholipase A2 receptor (PLA2R) and thrombospondin type-1 domain-containing protein 7A (THSD7A) has provided a paradigm shift in diagnosis and treatment of PMN. However, there are still few patients with negative serum and renal tissue autoantibodies. This study aims to explore the molecular features of antibody-negative PMN. Method We sorted CD19+ cells from the peripheral blood of a pediatric patient with seven nephritogenic autoantibodies-negative PMN (NEG) by flow cytometry and performed single-cell transcriptome sequencing (scRNA-seq) and single-cell B cell receptor sequencing (scBCR-seq). Meanwhile, scRNA-seq was performed on renal biopsy tissues from the same patient. In addition, we included the scRNA-seq data of renal from anti-PLA2R antibody positive patients (POS) and healthy controls (CTRL), and the scBCR-seq data of B cell from CTRL for integrative analysis. Results The NEG patient showed typical nephrotic syndrome and was diagnosed as stage Ⅲ membranous nephropathy by renal biopsy. There was no evidence of anti-PLA2R or anti-THSD7A antibodies in peripheral blood and seven nephritogenic autoantibodies such as anti-PLA2R antibodies in renal tissue. After excluding secondary factors, the patient was diagnosed with PMN. Through scRNA-seq of CD19+ cells, we found that the number, characteristic gene, function and clonotype of naÏve B cells and memory B cells in NEG were significantly changed. Expanded CD38+ naÏve B cells in NEG had the molecular characteristics of CD19+CD24+CD27-CD38+, defined as transitional B cells. This group of cells had distinct function features of cell activation, and its up-regulated genes were involved in multiple aspects of the BCR signaling pathway. Pseudotime trajectory analysis suggested CD38+ naÏve B cells were highly enriched in the beginning of B cell differentiation. There was a preference in the use of VJ gene segments of B cells between NEG and CTRL, especially an increase of the IGHV3-23 and IGLV2-14 in NEG. The stronger pairing frequencies, IGLV2-14/IGLJ3 and IGKV2D-29/IGKJ2, were indicated in NEG. We identified 14 distinct kidney cell types by marker genes. Through re-clustering of glomerular parietal epithelial cells (PECs), the patients were clearly distinct from their control counterparts, indicating a major shift in gene expression for this cell type. PECs in NEG showed significant up-regulation of cellular communication network factor-related genes (CCN1, CCN2), phospholipase A and acyltransferase-related genes (PLAAT4, PLAAT3), and septin protein-related genes (SEPTIN2, SEPTIN7), accompanied by significant down-regulation of podocyte-related genes. In addition, there are clearly distinct cellular functions and pseudotime trajectory in PECs from NEG and POS, and genes such as CCN2, PLAAT4, SEPTIN2 might drive the special trajectory of PECs in NEG. For the podocytes, the genes related with extracellular matrix and cell adhesion were significantly enhanced in NEG, which consistented with the functional enrichment analysis of the differentially expressed genes and gene set-based scores. We calculated the gene set-based scores including genes encoding lumen-to-blood sodium transporters. Results indicated the enhanced expression of sodium transporters in distal nephrons of MN patients. More surprisingly, a group of proximal tubule epithelial cells showed significantly higher expression levels of sodium transporters. Among them, the expression of SLC5A12 encoding SMCT2 increased significantly. Conclusion We have systematic revealed the cell-type specific molecular features of PMN patients from circulation to renal tissue. Our research provides valuable evidence for the molecular diagnosis of PMN in children and insights into pathogenic mechanism of classical nephritogenic autoantibody-negative PMN.

Раммохан Рай и Петр Чаадаев: философы на перекрестке культур Запада и Востока

Indian Rammohun Roy and Russian Pyotr Tchaadaev are juxtaposed as cross-cultural philosophers in Modern social thought. Being at the crossroads of the West and the East cultures in their countries, they have demonstrated the special resemblance in their worldviews and paradigm of thinking. Based on compara­tive analysis of philosophers’ existential circumstances and texts, the author de­scribes them as ‘problematic thinkers’ (M. Buber) who destruct quietness in their societies, form the problematic field of social thought and philosophy in the epoch of modernization, and create grounds for the self-understanding by Indian and Russian societies. The conventional description of paradigm of thinking by Ram­mohun Roy and Pyotr Tchaadaev is presented in the article. The universalistic approach is laid down in the paradigm ground; it permit to search for a unity and universality in diversity of natural and human worlds. The unity discovers through relation of their own social reality with the Other one (this role plays the West). Problems are raised and resolved in special trajectory “understanding of the Otner – thinking on their Own – a creation of some project of Eastern – Western synthesis”. Owing to the paradigm as well as the raised themes R. Roy and P. Tchaadaev have created the epochs in the history of thought and culture in India and Russia respectively.

Quantum Explosions of Black Holes and Thermal Coordinates

The Hawking temperature for a Schwarzschild black hole is T=1/8πM, where M is the black hole mass. This formula is derived for a fixed Schwarzschild background metric, where the mass M could be arbitrary small. Note that, for vanishing M→0, the temperature T becomes infinite. However, the Schwarzschild metric itself is regular when the black hole mass M tends to zero; it is reduced to the Minkowski metric, and there are no reasons to believe that the temperature becomes infinite. We point out that this discrepancy may be due to the fact that the Kruskal coordinates are singular in the limit of the vanishing mass of the black hole. To elucidate the situation, new coordinates for the Schwarzschild metric are introduced, called thermal coordinates, which depend on the black hole mass M and the parameter b. The parameter b specifies the motion of the observer along a special trajectory. The thermal coordinates are regular in the limit of vanishing black hole mass M. In this limit, the Schwarzschild metric is reduced to the Minkowski metric, written in coordinates dual to the Rindler coordinates. Using the thermal coordinates, the Schwarzschild black hole radiation is reconsidered, and it is found that the Hawking formula for temperature is valid only for large black holes, while for small black holes, the temperature is T=1/2π(4M+b). The thermal observer in Minkowski space sees radiation with temperature T=1/2πb, similar to the Unruh effect with non-constant acceleration. The thermal coordinates for more general spherically symmetric metrics, including the Reissner–Nordstrom, de Sitter, and anti-de Sitter, are also considered. In these coordinates, one sees a Planck distribution with constant temperature. One obtains that the thermal Planck distribution of massless particles is not restricted to the cases of black holes or constant acceleration, but is valid for any spherically symmetric metric written in thermal coordinates.

Multi-Scenario Trajectory Optimization for Vertical Takeoff and Vertical Landing Vehicles Using the Gauss Pseudospectral Method

Vertical takeoff and vertical landing (VTVL) vehicles, based on throttling liquid rocket engines, are attracting increasing attention for their validation of guidance and control techniques during landing. However, validation requires the vehicle to fly in a special trajectory with multiple constraints. Propellant consumption should be carefully calculated for the purpose of carrying more experimental devices during the flight, which makes conducting minimum-propellant trajectory optimization a necessity. This study focuses on the optimization of VTVL vehicles based on a throttling liquid rocket engine. Three flight scenarios applicable to this vehicle are proposed, namely, VTVL vehicles without horizontal movement, VTVL vehicles with horizontal movement, and vertical takeoff and autonomous landing with horizontal movement. Trajectory optimization using the Gauss pseudospectral method (GPM) was conducted during the abovementioned flight scenarios. The results show that the GPM provides excellent solutions for trajectory optimization in the different scenarios. In VTVL vehicles with horizontal movement, vertical takeoff, and autonomous landing with horizontal movement scenarios, the thrust appears in a similar bang–bang control. Meanwhile, in VTVL vehicles without a horizontal movement scenario, the thrust appears like a segmented bang–bang control, which we call regulative bang–bang control. Moreover, by introducing the thrust derivative into the optimization objective using a weighted method, thrust fluctuation can be restrained. To ensure the compatibility of switching the flight among the three scenarios, the carried propellant mass should be decided based on the third flight scenario.

Simulation study on cuttings transport of the wavy wellbore trajectory in the long horizontal wellbore

To improve the pay zone exposure and avoid hazardous interbed, the wellbore trajectory is necessary to be adjusted in real-time according to the geosteering data in a long horizontal wellbore, leading to a special wavy trajectory. At present, there are few pieces of research on hole cleaning and pressure management for the wavy wellbore trajectory. Besides, there is no quantitative definition of the trajectory. In this study, a transient solids-transport model with the modified mass flux is employed to assess the risk of hole cleaning and the feasibility of pressure management of the wavy trajectory. As a new quantitative definition, the wavy wellbore trajectory has the wellbore tortuosity with periodic variations. The wavy wellbore is classified as the up-dip wellbore, the down-dip wellbore, and the complex wellbore to evaluate the influences of wellbore trajectory on the cuttings bed height and the annulus pressure compared with the conventionally horizontal and smooth wellbore. A parametric analysis of build-up rate is conducted to assess its fluence on hole cleaning and pressure management. The result indicates that the wavy wellbore displays higher risks of drilling complicacy than the conventional wellbore. The down-dip wellbore has 1.36 times the volume of cuttings bed and 1.49 times the bottom hole pressure of the horizontal wellbore. The bottom hole pressure of the up-dip wellbore is 0.49 times that of the horizontal wellbore. In comparison to a smooth wellbore, the up-dip wellbore contains 43% hazardous sections. The build-up rate has an optimal value on hole cleaning and the larger build-up rate is beneficial to manage pressure. In the simulation of a field instance in West China, excessing drag and torque, wall instability, and lost circulation exist at the same time, of which inducements are predicted by the model very well. The findings serve as a useful guideline to risk prediction and control in drilling the long horizontal wellbore with wavy intervals.

Mechanism Design of a Transformable Crawling Robot and Feasibility Analysis for the Unstructured Environment

The better application of crawl robots depends on their ability to adapt to unstructured environments with significant variations in their structural shape and size. This paper presents the design and analysis of a novel robot with different locomotion configurations to move through varying environments. The leg of the robot, inspired by insects, was designed as a multi-link structure, including the Hoekens linkage and multiple parallel four-link mechanisms. The end trajectory was a symmetrical closed curve composed of an approximate straight line and a shell curve with a downward opening. The special trajectory allowed the robot to share drives and components to achieve structural deformation and locomotion. The structural characteristics of the crawl robot on the inner and outer arcs were obtained based on the working space. The constraint relationship between the structure size, the radius of the arc, and the coefficient of static friction with which the robot could crawl on the arc were established. The feasible support posture and support position of the robot under different arc radii were obtained. The simulation tested the locomotion of the robot on the plane, arc, and restricted space. The robot can be used for detection, search, and rescue missions in unstructured environments.

Optimized design and experiment of the three-arm transplanting mechanism for rice potted seedlings

The transplanting arm of two-arm transplanting mechanism is easy to cause seedlings injury and missing due to its faster speed relative to the seedlings. In order to solve the existed problems, a three-arm transplanting mechanism for rice potted seedlings was developed in this study. The developed three-arm transplanting mechanism for rice potted seedling can make the transplanting arm realize special trajectory and attitude through the unequal planetary gear transmission. The kinematic model of three-arm transplanting mechanism for rice potted seedling was established, and the optimal design software was developed. Based on the heuristic optimization algorithm named “parameter guide”, a set of satisfied mechanism parameters required by the rice potted seedling transplanting were obtained. The trajectory and attitude of three-arm transplanting mechanism used for the rice potted seedling were analyzed. Besides, the virtual simulation results were basically consistent with the optimization software results, and the correctness of theoretical analysis and virtual simulation were also verified by each other. When the developed transplanting mechanism picked up the seedling, the velocity of transplanting arm relative to the seedling was reduced by about 30%. The results showed that the injury rate of rice potted seedling transplanting mechanism was 0.04%, the missing rate of seedling was 1.4%, the integrity rate of seedling pot matrix was 96%, and the success rate of picking seedling was 99.92%. Keywords: agricultural machinery, transplanting mechanism, rice potted seedling, three-arm, optimal design DOI: 10.25165/j.ijabe.20211405.6844 Citation: Yin J J, Wang Z L, Zhou M L, Wu L N, Zhang Y. Optimized design and experiment of the three-arm transplanting mechanism for rice potted seedlings. Int J Agric & Biol Eng, 2021; 14(5): 56–62.

Is the internet the game changer? Disabled people and digital work in China

The marginalisation of disabled people in paid employment has been a longstanding issue. This article examines whether the recent proliferation of information and communication technologies (ICTs) can change the employment challenges for disabled people. It focuses on China, where digitalisation has happened almost simultaneously with industrialisation, and where a special disability employment trajectory is developing. Based on an exploratory study of the economic activities of Chinese disabled people, the article presents three types of digital work, in which physical labour, social relations and ICTs-related knowledge are commodified. These types of work are in general loosely organised, self-managed and unprotected. They have both empowering and debilitating effects. The article thus argues that the personal use of the Internet is just an entry point to disability employment, and it will be more effective if combined with policy interventions and broader structural changes. Points of interest People with impairments often face employment difficulties and some believe technological developments, such as the internet, can provide a solution to this. In China, people with physical impairments are working on the internet to earn money. Their work forms include levelling up online games for other players, opening online shops and developing ICTs products, such as software. Working online gives disabled people a chance to get paid and develop a better feeling about self. This however has significant limitations. Policy and social support should be provided to promote online employment for disabled people.

Corrections to the singlet-length distribution and the entanglement entropy in random singlet phases

We consider random singlet phases of spin-$\frac{1}{2}$, random, antiferromagnetic spin chains, in which the universal leading-order divergence $\frac{\ln 2}{3}\ln\ell$ of the average entanglement entropy of a block of $\ell$ spins, as well as the closely related leading term $\frac{2}{3}l^{-2}$ in the distribution of singlet lengths are well known by the strong-disorder renormalization group (SDRG) method. Here, we address the question of how large the subleading terms of the above quantities are. By an analytical calculation performed along a special SDRG trajectory of the random XX chain, we identify a series of integer powers of $1/l$ in the singlet-length distribution with the subleading term $\frac{4}{3}l^{-3}$. Our numerical SDRG analysis shows that, for the XX fixed point, the subleading term is generally $O(l^{-3})$ with a non-universal coefficient and also reveals terms with half-integer powers: $l^{-7/2}$ and $l^{-5/2}$ for the XX and XXX fixed points, respectively. We also present how the singlet lengths originating in the SDRG approach can be interpreted and calculated in the XX chain from the one-particle states of the equivalent free-fermion model. These results imply that the subleading term next to the logarithmic one in the entanglement entropy is $O(\ell^{-1})$ for the XX fixed point and $O(\ell^{-1/2})$ for the XXX fixed point with non-universal coefficients. For the XX model, where a comparison with exact diagonalization is possible, the order of the subleading term is confirmed but we find that the SDRG fails to provide the correct non-universal coefficient.

Synthesis of Programmed Motion Based on Special Optimal Control

A method is proposed for the synthesis of a closed-loop system with controls that ensure the movement of an object with minimal deviations from a given trajectory of the output coordinate and its higher derivatives and a transition to this set. To solve the problem, the Pontryagin maximum principle is used to study special situations without analysis of auxiliary variables, supplemented by the apparatus of general position conditions for nonlinear systems in an extended coordinate space, taking into account the object, a functional that is nonlinear regarding deviations of the output coordinate and the explicit occurrence of time. The combined use of these methods allows us, firstly, to find special trajectories of coordinates that are higher derivatives of the output coordinate, and after excluding time, a special phase trajectory is found, which is a switching line for reaching the final state, a given programmed motion along which in a closed system is carried out by special control. Secondly, access to a special phase trajectory from the initial state is carried out for linear objects by relay control, and for nonlinear objects, under certain boundary conditions, relay control is supplemented by a special control of the speed problem. Examples of control of programmed motion with oscillatory and aperiodic processes of a given duration for linear and nonlinear objects are given. Taking into account the nature of equilibrium states, determined by the methods of the qualitative theory of differential equations, and restrictions on control and coordinates, topologies of trajectories are obtained for the implementation of a continuous special control or sliding mode. New algorithms and structures of control systems are obtained. The results are accompanied by modeling, illustrating the effectiveness of algorithms and structures of control systems according to the proposed synthesis method and confirming analytical materials. The results of the work can be used to control linear and nonlinear objects in mechatronics, robotics, thermal processes and other industries.

Study on laser drilling induced defects of CFRP plates with different scanning modes based on multi-pass strategy

There are two kinds of scanning modes based on multi-pass strategy, including concentric scanning mode (CSM) and spiral scanning mode (SSM), which can realize 3D hole drilling of CFRP plates by a nanosecond UV laser. The mechanism of the CFRP laser drilling and defects formation under these two different scanning modes has been described. Several experiments are conducted to explore and compare the drilling defects including heat-affected zone (HAZ), dimension error, and machined surface micro-defects under these two different scanning modes. The results show that SSM can significantly reduce the width of HAZ compared with CSM. Under the most obvious reduction of parameters, the use of SSM (84.76 μm) is 33.42% less than the HAZ of CSM (127.3 μm). For MR, it is reduced by 24.83% (45.75–34.39 μm). Due to the special spiral trajectory of SSM, the dimension errors are increased when using SSM, including the taper error (maximum 26.11%) and slight circularity error. The micro-defects of laser processed surfaces with CSM are more serious than those with SSM, especially the obvious delamination, cracks, matrix loss, and fibre tip expansion formed fibre fusion caused by the significant thermal effect at a high laser repetition rate. This is consistent with the influence on HAZ at the hole edge.

Analytical trajectory prediction for near-first-cosmic-velocity atmospheric gliding using a perturbation method

This paper investigates a special atmospheric glide problem where the gliding speed is close to the first cosmic velocity (FCV). Here, the centrifugal force and gravity almost balance each other, and thus in the local vertical direction the lift force required to maintain the glide is almost zero. However, all the existing analytical solutions for 3-D gliding trajectories were derived under the condition that the vertical component of lift is large enough, and thus become invalid for the special glide case. To overcome the shortage of the existing studies, we abandon the vertical component of lift, but instead plan the profile of drag acceleration (aD) to derive the analytical solutions for the 3-D special gliding trajectory. By simplifying the nonlinear equations of motion properly, a reduced-order system is obtained and governed by aD and L2/D, where L2/D represents the ratio of the local horizontal component of lift to drag. Subsequently, by proposing a perturbation method to expand the system in Taylor series with finite terms, two analytically solvable subsystems are developed. As a result, the analytical trajectory solutions are obtained successfully. Additionally, as verified by the simulation results, the new solutions are also applicable to the conventional glide problem where the speed is much less than the FCV, and found to be much more accurate than the existing solutions because the new solutions give full consideration to the coupling of the longitudinal and lateral equations.

Trajectory planning and tracking control for 6‐DOF Stanford manipulator based on adaptive sliding mode multi‐stage switching control

AbstractThis article intends to investigate the trajectory planning and tracking control for six‐degrees‐of‐freedom (6‐DOF) Stanford manipulator consisting of 3‐DOF mechanical arm and 3‐DOF spherical wrist. By using Denavit–Hartenberg (DH) method, the Euler–Lagrange equations of motion of mechanical arm subsystem and spherical wrist subsystem are established, respectively. A new version of backstepping‐based adaptive sliding mode controller is proposed for trajectory tracking of each subsystem. In order to grasp an object from one point to another, a special smooth continuous trajectory is planned by inverse kinematics analysis which transforms the position of the end‐effector in the task space to the joint position in the joint space. After that, a multi‐stage switching control strategy is proposed to achieve trajectory tracking control. Simulation results are provided to demonstrate the performance of the proposed control strategy.

Methods of trajectory control of observation in air-based angle-measuring two-position radio monitoring systems. Part 2. Gradient methods

To control and monitor the electronic situation, air-based passive angle-measuring two-position systems radio monitoring can be used. A feature of the functioning of these systems is the fact that the accuracy of the estimation of the coordinates and parameters of the movement of radio emission sources (RES) depends largely on the configuration of the relative position of the receiving positions placed on the aircraft and the RES. Therefore, the problem of optimization the relative position of aircraft and AIR is relevant, and various gradient methods of trajectory control of observation have been developed to solve this problem. Usually in two-position systems one aircraft is the leader, and the second one provides information support. To implement gradient methods, the control of the information support aircraft is organized in such a way that the error of determining the position of the RES at any time is minimal. To fulfill this condition, the information support aircraft must move along a special trajectory, the parameters of which are determined by an algorithm based on gradient optimization methods. The dependence of the error in determining the position of the RES on the relative position of the aircraft and RES and the direction finding accuracy is used as an target function. The article provides information on the gradient methods of trajectory control in the angle-measuring two-position systems, which provide the fastest increase in the accuracy of estimating the coordinates and parameters of the motion of RES for various conditions of practical application in a volume sufficient to obtain a general idea of the ways to solve the problem of trajectory control of an aircraft in the angle-measuring two-position systems. For the trajectory control of the information support aircraft, the gradient method of course guidance was first developed. This method is a relatively simple iterative procedure based on information about the gradient of the quality functional. The disadvantage of this method is the low accuracy of determining the coordinates of the RES at the initial moment of time with a relatively small distance of the aircraft from each other at the beginning of the guidance, as well as in the greater fuel consumption on board the information support aircraft compared to the leading aircraft during the guidance process. To eliminate this disadvantage, trajectory control methods have been developed for two situations of practical application of anglemeasuring two-position systems. The first situation occurs when there is a two-stage procedure of target guidance. At the stage of long-range guidance, aircraft are brought to the RES detection zone by commands from the control center. At the second (short-range) stage of guidance, after the detection of the RES signals by the direction finders of the aircraft, the process of self-homing of leading aircraft to the RES begins and information support for the task solution by other aircraft. For this situation, a modified gradient method of trajectory control of information support aircraft has been developed. The second method to eliminate the disadvantage of the gradient method involves the rejection of the distribution functions of guidance and information support between the aircrafts. It can be used in a situation where the guidance of the aircraft on the RES begins from the moment it is detected on aircraft board. At the same time, the solution of the problem of minimizing the RES location errors is assigned not to one information support aircraft, but simultaneously to both aircrafts. However, mentioned methods do not take into account possible restrictions on the movement of the information support aircraft when forming the control parameters of this aircraft, associated with the presence of dangerous zones for flights, as a result, the flight safety of this aircraft is not guaranteed. For flights in the presence of dangerous zones, the method of trajectory control of the aircraft on the course and the corresponding algorithm of trajectory control of information support aircraft based on the method of gradient projection of the target function has been developed. However, this technique does not guarantee that the flight of the information support aircraft will be carried out exactly on the border of the dangerous zone. In order to eliminate this disadvantage, the method of trajectory control based on the gradient projection method was upgraded using the algorithm of the route guidance method of the aircraft.

A Magnetometer Calibration Method Using Single-Axis Motion Trajectory and Unscented Kalman Filter for Body Motion Capture Applications

Magnetometer calibration is a pre-processing step in the Attitude and Heading Reference Systems (AHRS) which has an essential role in many applications. The main purpose of this article is to derive an innovative and precise calibration approach for a magnetometer set installed on human body. To execute this calibration method, all the error parameters of multiple magnetometers are considered in an Unscented Kalman Filter (UKF) model for accurate estimation of calibration parameters. As achieving a precise estimation in Kalman filters-based algorithms needs an accurate and complete observation model, a special single-axis rotation trajectory for Inertial Measurement Unit (IMU) is performed to increase the observability rank of the calibration model. To evaluate the proposed method, five body-mounted sensors were experimented in the laboratory at the same time for applying in the body motion capture system. The results showed that all five sensors were well-calibrated without any need to be detached from the body and using any rotational robot arm. The resolution and precision of the proposed calibration method are assessed by the ellipsoid-fitting representation method. Consequently, all the body-mounted magnetometers were calibrated, on average, by about 1% uncertainty. The method can be used in every motion capture and AHRS applications due to its feasibility and simplicity.

Exact sharp-fronted travelling wave solutions of the Fisher–KPP equation

A family of travelling wave solutions to the Fisher–KPP equation with speeds c=±5∕6 can be expressed exactly using Weierstraß elliptic functions. The well-known solution for c=5∕6, which decays to zero in the far-field, is exceptional in the sense that it can be written simply in terms of an exponential function. This solution has the property that the phase-plane trajectory is a heteroclinic orbit beginning at a saddle point and ending at the origin. For c=−5∕6, there is also a trajectory that begins at the saddle point, but this solution is normally disregarded as being unphysical as it blows up for finite z. We reinterpret this special trajectory as an exact sharp-fronted travelling solution to a Fisher–Stefan type moving boundary problem, where the population is receding from, instead of advancing into, an empty space. By simulating the full moving boundary problem numerically, we demonstrate how time-dependent solutions evolve to this exact travelling solution for large time. The relevance of such receding travelling waves to mathematical models for cell migration and cell proliferation is also discussed.

Spontaneous-focusing and self-healing of Airy-like beams

Modulated by the spatial phase, Airy-like beams that possess the faster and better self-healing as well as the greater acceleration along the desired arbitrary trajectory are introduced. Airy-like beams have the strong spontaneous-focusing ability and the peak value of the focal plane is 5.4 times that of the initial plane when traveling along the quadratic function trajectory. Besides, the larger quadratic coefficient and the smaller constant term of the quadratic function can enhance the self-healing and the spontaneous-focusing of the beams. When the beams transmit along the snakelike trajectory, the original main lobe separates a new main lobe, and the energy will concentrate on the new main lobe. Airy-like beams, along a hyperbolic-secant trajectory, can remain non-diffraction over long distances. However, when traveling along a hyperbolic trajectory, the evolution process is very similar to that of Airy-Gaussian vortex beams. These excellent properties can be applied to the special beams’ modulation and optimization. Furthermore, it may provide a way for constructing beams along the special trajectory with the desired spontaneous-focusing and self-healing.