Descent Path Research Articles

The Efficient Method for Calculating the Physical Optics Scattered Fields from the Concave Surfaces

In this work, the numerical steepest descent path (NSDP) method is proposed to compute the highly oscillatory physical optics (PO) scattered fields from the concave surfaces, including both the monostatic and the bistatic cases. Quadratic variations are adopted to approximate the integrands of the PO type integral into the canonical form. Then, on involving the NSDP method, we deform the integration paths of the integrals into several NSDPs on the complex plain, through which the highly oscillatory integrands are converted to exponentially decay integrands. The RCS results of the PO scattered field are calculated and are compared with the high frequency asymptotic (HFA) method and the brute force (BF) method. The results demonstrate that the proposed NSDP method for calculating PO scattered fields from concave surfaces is frequency-independent and error-controllable. Numerical examples are provided to verify the efficiencies of the NSDP method.

Study on a Fixed Point Vertical Landing Method Using the Flat Spin for a Fixed-wing UAV

A runway for the operation of a fixed-wind UAV cannot be always available in practical missions and there is no handy method for landing in confined space while a catapult can be used for launch. The purpose of this paper is to develop a new vertical landing method using the flat spin. Flat spin is the motion that an aircraft rotates horizontally while it is descending vertically. In order to control its touchdown position to a desired position, it is necessary to generate centripetal force to control UAV's descent path to target direction while descending vertically. This paper shows the method to change the path during vertical descent, as well as the result of flight tests and wind tunnel tests.

Topological computation of some Stokes phenomena on the affine line

Let $\mathcal M$ be a holonomic algebraic $\mathcal D$-module on the affine line, regular everywhere including at infinity. Malgrange gave a complete description of the Fourier-Laplace transform $\widehat{\mathcal M}$, including its Stokes multipliers at infinity, in terms of the quiver of $\mathcal M$. Let $F$ be the perverse sheaf of holomorphic solutions to $\mathcal M$. By the irregular Riemann-Hilbert correspondence, $\widehat{\mathcal M}$ is determined by the enhanced Fourier-Sato transform $F^\curlywedge$ of $F$. Our aim here is to recover Malgrange's result in a purely topological way, by computing $F^\curlywedge$ using Borel-Moore cycles. In this paper, we also consider some irregular $\mathcal M$'s, like in the case of the Airy equation, where our cycles are related to steepest descent paths.

The descent and bouncing path of the Hayabusa2 lander MASCOT at asteroid (162173) Ryugu

Images from the Optical Navigation Camera system (ONC) onboard the Hayabusa2 spacecraft show the MASCOT lander during its descent to the surface of asteroid (162173) Ryugu. We used results from a previous stereo-photogrammetric analysis that provided precise ONC image orientation data (camera position and pointing), ONC orthoimages, and an ONC-based 3D surface model to combine them with the visibilities of MASCOT itself and its shadow on-ground within the ONC images. We integrated additional information from instruments onboard MASCOT (MASMag, MARA, MASCam) and derived MASCOT’s release position and modeled its free-fall descent path and its velocity over 350 s from its release at ∼41 m altitude above ground until its first contact with the surface of Ryugu. After first contact, MASCOT bounced over the surface of Ryugu for 663 s and came to rest at its first settlement point after four intermediate surface contacts. We again used ONC images that show MASCOT and partly its shadow and reconstructed the bouncing path and the respective velocities of MASCOT. The achieved accuracy for the entire descent and bouncing path is ∼0.1 m (1σ).

A comparison of methods for traversing regions of non-convexity in optimization problems

This paper considers the well-known problem of dealing with non-convexity during the minimization of a non-linear function f(x) by Newton-like methods. The proposal made here involves a curvilinear search along an approximation to the continuous steepest descent path defined by the solution of the differential equation The algorithm we develop and describe has some features in common with trust-region methods and we present some numerical experiments in which its performance is compared with other ODE-based and trust-region methods.

The Two-Dimensional Numerical Steepest Descent Path Method for Calculating the Physical Optics Scattered Fields From Different Quadratic Patches

In this article, the Two-Dimensional numerical steepest descent path (TD-NSDP) method is proposed to calculate the physical optics (PO) scattered fields from the quadratic patches. Compared with the NSDP method, the TD-NSDP method avoids adopting the complementary error function, and hence, the TD-NSDP method could significantly improve the accuracy of the PO scattered fields by around four to five digits. Moreover, the computational workload is also frequency independent. To demonstrate the efficiencies of the TD-NSDP method, numerical examples for both quadratic convex and concave surface patches are conducted. Finally, the radar cross section (RCS) simulation from the realistic and complex scatterer is conducted to verify the practicability of this method in electromagnetic (EM) scattering application.

Analyzing fundamental problem of designing incinerated payload fairings made from composite polymer materials

The article considers fundamental engineering problem of designing the payload fairing (PLF) for a launch vehicle (LV) made from polymer composite material (PCM) with high temperature resistance and minimum mass, with the PLF being incinerated after separation from the launch vehicle on the atmospheric section of the descent path. The energetic material (EM) is introduced into the PCM, which provides heating of the PCM structure to the ignition temperature and subsequent PLF combustion under the conditions of the incoming air flow. A comparative analysis of the problems arising at different life cycle stages in creating and operating traditional (PLFT) and incinerated (PLFI) payload fairings is carried out. Example options for energetic materials and possible designs of the individual PLFI elements are given.

Reformulation of wavenumber integrals describing transient waves

A principal-value integral in wavenumber appears in the description of water waves generated by a wavemaker in wave tank. Its integrand is highly oscillatory and has a pole at the prescribed wavenumber associated with the oscillation frequency of wavemaker. Our analysis starts with transforming the wavenumber integral into two canonic integrals by changing the integral variable. The canonic integrals are then studied in three complex planes. Three contour integrals along appropriate steepest descent paths yield several components including residues’ contribution and integral terms. By regrouping integral terms according to their integrand, a new formulation is derived and composed of an explicit steady-state component, an explicit initial component, and two integrals. The wavefront component in integral form is analysed and expressed in a close form involving the complementary error function. The local component is further expressed as the sum of an asymptotic term and remaining integral which is well suited for numerical computations. Numerical results confirm that the new formulation gives exactly the same as the original one but in a much more efficient and accurate way. Furthermore, the new formulation providing explicit expressions of different components and could be used to reveal insightful features of transient waves.

New Exact Image Methods for Impedance Boundary Half-Space Green’s Function and Their Fast Multipole Expansion

Two foremost barriers to the development of fast and efficient simulation algorithms for electromagnetic problems in half-space and planar media are efficient Sommerfeld integral evaluation techniques and fast solvers. In this paper, we focus on challenging these two difficulties in the impedance boundary half-space, which is a proper model for common air-lossy media half-space. Based on the Laplace transformation, we first propose an alternative exact image representation for the Sommerfeld integral in half-space Green's function. In addition to its fast and absolute convergence property, this new exact image version does not contain any singularities and interprets the Sommerfeld integral as an integral over real image line. Furthermore, this representation allows a rigorous fast multipole expansion (FME), and thus it can be applied to the development of fast multipole solver with controllable precision. However, this exact image representation is not valid for the all Sommerfeld integrals in half-space Green's function. Therefore, a more generalized single mirror image representation, also exact and computationally efficient, is then presented. The strength of the mirror image is obtained through Weyl's method and steep descent path approach. Subsequently, an approximated FME scheme for this representation is proposed and studied via numerical examples. We find this approximated FME scheme has a higher accuracy than that of previous work. Numerical results show that the proposed work provides exact and efficient evaluations for Sommerfeld integrals in impedance boundary half-space Green's function and valuable insights into the development of fast multipole solver for half-space electromagnetic problems.

ВДОСКОНАЛЕННЯ ПАРАШУТНО-РЕАКТИВНОЇ СИСТЕМИ З ДЕСАНТУВАННЯ БОЙОВОЇ ТЕХНІКИ АБО КРУПНО ГАБАРИТНИХ ОБ’ЄКТІВ

The paper is devoted to the study of the prospects for improving the parachute-retrorocket airdrop system (PRS) in order to increase its reliability and enable the ability to adjust the orientation of a load in the horizontal plane depending on the slope of the earth's surface at the landing site. The primary task is to improve the accuracy of the altimeter, which determines the triggering moment of the PRS jet engines. The replacement of a mechanical altimeter of an outdated design with a modern electronic radio altimeter based on phased array radar is proposed, which allows to improve the accuracy of determining the absolute altitude(distance to the ground) and to take into account a roll of the load during the descent. The ways of determining the slope of earth's surface at the estimated landing site are also discussed. The results obtained make it possible to increase the accuracy of radio altimeter operation and significantly reduce the probability of an error in determining the absolute altitude due to rocking or static roll of the object. In addition to determining the current values of the height and speed of the descent of the vehicle, the use of a scanning radar makes it possible to estimate the inclination angle of the Earth’s surface at the landing site (in the radar scanning plane). If a certain angle of inclination of the earth surface at the landing site turns out to be too large, the probability of a successful landing can be increased by correcting the object's descent path, taking into account the information received. One of the easiest ways to correct a descent trajectory is to equip an object with small aerodynamic elements (rudders) and electromechanical actuators, ensuring their necessary orientation based on the results of determining the surface relief with radar. As one of the options, the authors propose the use of additional jet engines, which are structurally located on opposite sides of the object of landing in such a way as to form a torque of rotation of the object in a space from 0 ° to 90 ° in the horizontal plane due to the kinetic energy of motion from the actuation of jet engines. The triggering moment of the squibs is calculated based on determining the optimal distance of the object to the ground surface, and the need for triggering the squibs to rotate the object (correcting its position in space) depends on a certain value of the slope angle of the earth surface and comparing it with the admissible critical values of the angle, at which the object loses its stability during landing.

Integration of the ground-based augmentation system in continuous descent operations

Predictability is a necessity in today's commercial flight operations if delays are to be minimized. Possible mitigations, such as the implementation of continuous descent arrivals (CDAs), may help generate the required procedural predictability to curtail these delays. However, on the basis of its individual avionics suite, each aircraft follows a different barometric vertical descent path; furthermore, the aircraft may be given additional level-off segments by air traffic control to compensate for possible deviations in the vertical profile. Therefore, aircraft flying the current descent profiles are too unpredictable and thus the procedures cannot be implemented in complex airspace structures or when traffic is moderate to high. This study introduces a mitigation to this problem by taking the global positioning system (GPS) one step further by integrating the GPS-based ground-based augmentation system (GBAS) into the new optimized continuous decent arrival procedure, subsequently, allowing for the introduction of a geometrical vertical guidance, namely, the GBASCDA, which will make the aircraft flying the descent profile predictable. With the increase in availability of GBAS aircraft equipage, specifically the GPS landing system (GLS), and the approaching amendment of the Appendix E of the Minimum Operational Performance Standards for GPS Local Area Augmentation System Airborne Equipment–RTCA DO-253D, this idea of the integration of the GBAS on the arrival/descent segment as a viable solution may be finally coming within reach.

Development of proposals for the synthesis of polymer composite materials capable of combustion after the mission

One of the ways of solving the problem of reducing the man-made impact of rocket and space activities on the environment, based on the reduction of the impact areas of separating launch vehicle component (LVC) in the process of launching payloads into orbit are considered. Known particular solutions to this problem, for example, the return of spent LV stage accelerators to the point of launch, a multiple reduction in the impact areas of spent LV stage accelerators due to their controlled descent, however, there is open the question of how to deal with such LVC as payload fairings (PF) and aft-interstage (AIS) having significant areas of the impact areas. The possibility of burning LVC, such as PF and AIS, made of a composite material based on carbon fiber is considered. The thermal conditions of LVC during their movement on the descent path are investigated, the necessary amount of heat for heating the LVC to the ignition temperature is determined and various options of energy materials (EM) are considered. On the example of a typical PF, having a design of a polymer composite material (carbon fiber) with an aluminum honeycomb core (AHC), another structure is proposed, where a filler based on a mixture of polymer films such as ABS structure and energy material is used instead of AHC. The proposed design of the polymer composite material allows to provide the necessary operation parameters of the PF (strength, thermal protection, etc.) at the stage of preparation of the PF for a launch, LV ascent in the active section of the trajectory. And the possibility of burning after the mission with minimal energy costs allows to provide.

Dynamic guidance of orbiter gliders: alignment, final approach, and landing

A new algorithm capable of guiding an orbiter glider to a target point with a prescribed alignment and descent path angle is presented. This algorithm can initiate Terminal Area Energy Management (TAEM) before reaching steady state and perform the Final Approach and Landing (FA&L). During TAEM, runway alignment is done through a moving virtual target derived from steady state, while during FA&L, a transient (or flare) is used to reach the extremely shallow descent path angles. All decisions are made dynamically relying solely on local information (position, speed, attitude, and atmospheric parameters), and all structural limits of the glider are respected at all times. As a proof of concept, a Space Shuttle return flight is simulated. For a large multitude of initial conditions and targets, the algorithm is able to consistently deliver distance errors below 19 m (transverse errors below 4 m), alignment errors below $$1^{\circ }$$ , descent path angles at the intended $$-\,2^{\circ }$$ , and vertical descent speeds below 8.5 m/s with control time intervals of 0.1 s.

Photoinduced hydrogen-transfer reactions in pyridine-water clusters: Insights from excited-state electronic-structure calculations

Recent experiments have shown that photoexcited pyridine can abstract a hydrogen atom from a water molecule in pyridine-water clusters containing at least four water molecules. To explain these findings, we explored the electron-driven proton-transfer reaction from water to pyridine in pyridine-(H2O)n, n = 1–4, complexes with ab initio methods. It is shown that the photoinduced electron/proton transfer reaction is energetically possible for all clusters. The calculations reveal that the hydrogen bond between pyridine and the adjacent water molecule is weakened (strengthened) in the 1nπ∗ (1ππ∗) excited state, which is unfavorable (favorable) for the H-atom transfer reaction. For pyridine-(H2O)n clusters with n = 1–3, the steepest descent path leads to a local minimum of 1nπ∗ character, while for the pyridine-(H2O)4 cluster, this path leads to a local minimum of 1ππ∗ character. The transition state calculations show the presence of this 1ππ∗ minimum substantially reduces the barrier height for the H-atom transfer reaction. These results provide a tentative explanation of the experimental observations.

Steepest descent integration: A novel method for computing wavefields radiated from borehole sources

Borehole sources, including chemical explosives, air gun, water gun, and piezoelectric transducers in the borehole, generate seismic waves inside and outside the borehole. Modeling the wavefield is of key importance in acoustic logging, crosshole tomography, mining geophysics, and deep sounding seismic for interpretation of amplitude information of real data and prediction of energy-radiation patterns. Classic methods for modeling the wavefield inside a borehole, such as real-axis integration, are challenged by highly oscillatory integrals encountered when modeling the wavefield outside the borehole. We have developed a novel method, called steepest descent integration (SDI), which evaluates the oscillatory wavenumber integration by numerically integrating along the steepest descent path. The oscillation along the new integration path is significantly reduced. The contributions of poles and branch cuts are added if they are located between the steepest descent path and the real axis. The SDI is applicable to arbitrary frequency and source-receiver distance. Comparison with real-axis integration shows that the method can compute highly oscillatory integrals with better efficiency and accuracy. In addition, the SDI is more numerically robust because it generates no spurious arrivals, which are evident in the real-axis integration. Analysis of numerical examples at different source-receiver distance shows that SDI is more efficient when computing far-field seismograms. This SDI can also be used to compute highly oscillatory integral in other wave-propagation problems.

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

The non-equilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed non-planar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansion diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward effective field theory description of hydrodynamics. Our findings indicate that anisotropic hydrodynamics is an effective theory for far-from-equilibrium fluid dynamics which resums the Knudsen and inverse Reynolds numbers to all orders.

Hybrid Trajectory Planning for Autonomous Driving in Highly Constrained Environments

In this paper, we introduce a novel and efficient hybrid trajectory planning method for autonomous driving in highly constrained environments. The contributions of this paper are fourfold. First, we present a trajectory planning framework that is able to handle geometry constraints, nonholonomic constraints, and dynamics constraints of cars in a humanlike and layered fashion and generate curvature-continuous, kinodynamically feasible, smooth, and collision-free trajectories in real time. Second, we present a derivative-free global path modification algorithm to extract high-order state information in free space for state sampling. Third, we extend the regular state-space sampling method widely used in on-road autonomous driving systems to a multi-phase deterministic state-space sampling method that is able to approximate complex maneuvers. Fourth, we improve collision checking accuracy and efficiency by using a different car footprint approximation strategy and a two-phase collision checking routine. A range of challenging simulation experiments show that the proposed method returns high-quality trajectories in real time and outperforms existing planners, such as hybrid A* and conjugate-gradient descent path smoother in terms of path quality, efficiency, and computation resources used.

Autonomous Tracking of Intermittent RF Source Using a UAV Swarm

The localization of a radio-frequency transmitter with intermittent transmissions is considered via a group of unmanned aerial vehicles (UAVs) equipped with omnidirectional received signal strength sensors. This group embarks on an autonomous patrol to localize and track the target with a specified accuracy, as quickly as possible. The challenge can be decomposed into two stages: 1) estimation of the target position given previous measurements (localization) and 2) planning the future trajectory of the tracking UAVs to get lower expected localization error given current estimation (path planning). For each stage, we compare two algorithms in terms of performance and computational load. For the localization stage, we compare a detection-based extended Kalman filter (EKF) and a recursive Bayesian estimator. For the path planning stage, we compare a steepest descent posterior Cramer–Rao lower bound path planning and a bioinspired heuristic path planning. Our results show that the steepest descent path planning outperforms the bioinspired path planning by an order of magnitude, and recursive Bayesian estimator narrowly outperforms detection-based EKF.

Spherical Bessel transform via exponential sum approximation of spherical Bessel function

A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.

Lava flow hazard prediction and monitoring with UAS: a case study from the 2014\u20132015 P\u0101hoa lava flow crisis, Hawai\u2018i

Accurately predicting lava flow path behavior is critical for active crisis management operations. The advance and emplacement of pāhoehoe flows modifies and inverts pre-existing topography, prompting the need for rapid and accurate updates to the topographic models used to forecast flow paths. The evolution and velocity of pāhoehoe flows are dependent on macro and micro topography, the slope of the descent path, effusion rate, and rheology. During the 2014–2015 Pāhoa crisis on the island of Hawai‘i, we used a low-altitude unmanned aerial system (UAS) to quickly and repeatedly image the active front of a slowly advancing pāhoehoe lava flow. This imagery was used to generate a series of 1 m resolution bare-earth digital elevation models (DEMs) and associated paths of steepest descent over the study area. The spatial resolution and timeliness of these UAS-derived models are an improvement over the existing topographic data used by managers during the crisis. Results from a stepwise resampling experiment suggest that the optimum DEM resolution for generating accurate pāhoehoe flow paths through lowland tropical forest environments is between 1 and 3 m. Our updated models show that future flows in this area will likely be deflected by these newly emplaced flows, possibly threatening communities not directly impacted by the original 2014–2015 lava flow. We demonstrate the value of deploying UAS during a dynamic volcanic crisis and suggest that this technology can fill critical monitoring gaps for Kīlauea and other active volcanoes worldwide.