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Dual Quaternion-Based Powered Descent Guidance with State-Triggered Constraints

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2020年第9期43卷 1584-1599页

作者： Reynolds, Taylor P. Szmuk, Michael Malyuta, Danylo Mesbahi, Mehran Acikmese, Behcet Carson, John M., III Univ Washington Aeronaut & Astronaut Seattle WA 98195 USA NASA Johnson Space Ctr Houston TX 77058 USA

This paper presents a numerical algorithm for computing six-degree-of-freedom free-final-time powered descent guidance trajectories. The trajectory generation problem is formulated using a unit dual quaternion representation of the rigid body dynamics and several standard path constraints. Our formulation also includes a special line-of-sight constraint that is enforced only within a specified band of slant ranges relative to the landing site: a novel feature that is especially relevant to terrain and hazard relative navigation. We use the newly introduced state-triggered constraints to formulate these range constraints in a manner that is amenable to real-time implementations. The resulting nonconvex optimal control problem is solved iteratively as a sequence of convex second-order cone programs that locally approximate the nonconvex problem. Each second-order cone program is solved using a customizable interior point method solver. Also introduced are a scaling method and a new heuristic technique that guide the convergence process toward dynamic feasibility. To demonstrate the capabilities of our algorithm, two numerical case studies are presented. The first studies the effect of including a slant-range-triggered line-of-sight constraint on the resulting trajectories. The second study performs a Monte Carlo analysis to assess the algorithm's robustness to initial conditions and real-time performance.

关键词： Powered Descent Guidance Quaternions Three Degrees of Freedom Pontryagin's Maximum Principle Monte Carlo Analysis Parallel Computing Techniques numerical algorithms Model Predictive Control Nonlinear Programming Sensor Technology

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Gradient crystal plasticity including dislocation-based work hardening and dislocation transport

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INTERNATIONAL JOURNAL OF PLASTICITY 2015年 69卷 152-169页

作者： Wulfinghoff, Stephan Boehlke, Thomas KIT Inst Engn Mech Continuum Mech D-76131 Karlsruhe Germany

This work aims at the formulation of a gradient crystal plasticity model which incorporates some of the latest developments in continuum dislocation theory and is, at the same time, well-suited for a three-dimensional numerical implementation. Specifically, a classical continuum crystal plasticity framework is extended by taking into account continuous dislocation density and curvature field variables which evolve according to partial differential equations (Hochrainer et al., 2014;Ebrahimi et al., 2014). These account, for dislocation transport and curvature-induced line-length production and have been derived from a higher-dimensional continuum dislocation theory. The dislocation density information is used to model work hardening as a consequence of dislocation entanglement. A composite microstructure is simulated consisting of a soft elasto-plastic matrix and hard elastic inclusions. The particles are assumed to act as obstacles to dislocation motion, leading to pile-ups forming at the matrix inclusion interface. This effect is modeled using gradient plasticity with a simplified equivalent plastic strain gradient approach (Wulfinghoff et al., 2013) which is used here in order to allow for an efficient numerical treatment of the three-dimensional numerical model. A regularized logarithmic energy is applied which is intended to approximate the higher order gradient stress of the statistical theory of Groma et al. (2003). (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Crystal plasticity Dislocations Particulate reinforced material numerical algorithms Gradient plasticity

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NONREFLECTING BOUNDARY-CONDITIONS FOR EULER EQUATION CALCULATIONS

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AIAA JOURNAL 1990年第12期28卷 2050-2058页

作者： GILES, MB Massachusetts Institute of Technology Cambridge Massachusetts 02139

This paper presents a unified theory for the construction of steady-state and unsteady nonreflecting boundary conditions for the Euler equations. These allow calculations to be performed on truncated domains without the generation of spurious nonphysical reflections at the far-field boundaries. The general theory, developed perviously by mathematicians, is presented in a more easily understood form based upon fundamental ideas of linear analysis. The application to the Euler equations is given, and the relation to standard "quasi-one-dimensional" boundary conditions is explained. Results for turbomachinery problems show the effectiveness of the new boundary conditions, particularly the steady-state nonreflecting boundary conditions.

关键词： Primitive Variable Turbomachinery Flow Conditions Vorticity Stagnation Enthalpy Boundary Value Problems Mach Numbers Wake Vortices numerical algorithms Oblique Shock

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Elastoplastic deformation and damage process in duplex stainless steels studied using synchrotron and neutron diffractions in comparison with a self-consistent model

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INTERNATIONAL JOURNAL OF PLASTICITY 2016年 81卷 102-122页

作者： Baczmanski, A. Zhao, Y. Gadalinska, E. Le Joncour, L. Wronski, S. Braham, C. Panicaud, B. Francois, M. Buslaps, T. Soloducha, K. AGH Univ Sci & Technol WFiIS Al Mickiewicza 30 PL-30059 Krakow Poland Univ Technol Troyes ICD LASMIS UMR CNRS 6281 12 Rue Marie CurieCS 42060 F-10004 Troyes France Inst Aviat Al Krakowska 110-114 PL-02256 Warsaw Poland Arts & Metiers ParisTech ENSAM PIMM UMR CNRS 8006 151 Bd Hop F-75013 Paris France ESRF 6 Rue J Horowitz F-38500 Grenoble France

In situ time of flight neutron diffraction and X-ray synchrotron diffraction methods were applied to measure lattice strains in duplex steels during a tensile test. The experimental results were used to study slips on crystallographic planes and the mechanical effects of damage occurring during plastic deformation. For this purpose the prediction of an elastoplastic self-consistent model was compared with the experimental data. The used methodology allowed to determine the elastic limits and parameters describing work hardening in both phases of studied polycrystalline materials. In the second part of this work the developed elastoplastic model was applied to study damage occurring in the ferritic phase. The theoretical results showed a significant reduction of stresses localized in the damaged phase (ferrite) and confirmed the evolution of the lattice strains measured in the ferritic and austenitic phases. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Polycrystalline material Yield condition Fracture mechanisms numerical algorithms Diffraction measurements

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FINDING SHORTEST PATHS ON SURFACES USING LEVEL SETS PROPAGATION

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1995年第6期17卷 635-640页

作者： KIMMEL, R AMIR, A BRUCKSTEIN, AM TECHNION ISRAEL INST TECHNOL DEPT COMP SCIIL-32000 HAIFAISRAEL

We present a nerv algorithm for determining minimal length paths between two regions on a three dimensional surface, The numerical implementation is based on finding equal geodesic distance contours from a given area, These contours are calculated as zero sets of a bivariate function designed to evolve so as to track the equal distance curves on the given surface, The algorithm produces all paths of minimal length between the source and destination areas on the surface given as height values on a rectangular grid.

关键词： CURVE EVOLUTION EQUAL DISTANCE CONTOURS GEODESIC PATH numerical algorithms MINIMAL GEODESICS

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Using high-order accurate essentially nonoscillatory schemes for aeroacoustic applications

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AIAA JOURNAL 1996年第2期34卷 244-250页

作者： Casper, J Meadows, KR VIGYAN INC ADV TECHNOL GRPHAMPTONVA 23666 NASA LANGLEY RES CTRDIV FLUID MECH & ACOUSTHAMPTONVA 23681

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, particularly when shock waves are involved, Because of their dual capacity for high-order accuracy and high-resolution shock capturing, the recently developed class of essentially nonoscillatory (ENO) schemes has generated considerable interest in regard to such problems. The use of ENO schemes for aeroacoustic applications is investigated, with particular attention to the control of the adaptive stenciling procedure. A modification of previously developed stencil-biasing procedures is proposed. This nonlinear stencil biasing allows a freer adaptation near discontinuities than is allowed by the previous biasing methods, without disturbing the biased, stable stencils that are desired in smooth regions. The accuracy of these new methods is validated through the study of a shocked nozzle flow. An axisymmetric shock-vortex interaction is then investigated, numerical results indicate a reduction in error when compared with results in which other stencil-biasing procedures are used.

关键词： Vortex Filaments Axisymmetric Flow Mach Number Adaptive Stencil algorithms Runge Kutta Methods Riemann Problem Computational Aeroacoustics Supersonic Combustion numerical algorithms Aerospace Sciences

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EULER SOLUTIONS FOR AIRCRAFT CONFIGURATIONS EMPLOYING UPPER-SURFACE BLOWING

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JOURNAL OF AIRCRAFT 1987年第3期24卷 188-194页

作者： ATTA, E RAGAB, S BIRCKELBAW, L Lockheed Georgia Company Marietta Georgia

A zonal method has been developed for computing the flow field around aircraft configurations using uppersurface blowing. The method is based on a zonal grid generation approach coupled with an Euler flow solver algorithm. In this method the flowfield is divided into a number of nonoverlapped regions, each containing a component of the aircraft such as a wing, a fuselage, or a nacelle. H-type grids are generated independently in each region using a hybrid elliptic/algebraic grid generation scheme. An explicit finite-volume Euler algorithm has been developed that is applicable to the multiregion H-type grids. The present method has been applied to a three-dimensional upper-surface blowing model and a realistic aircraft configuration consisting of a wing/fuselage with two integrated nacelles. numerical results indicate that the computational method is effective in predicting the flowfield about upper-surface blowing-type configurations and complex aircraft geometries. © American Institute of Aeronautics and Astronautics, Inc., 1987. All rights reserved.

关键词： Aircraft Configurations Computational Methods Computing Angle of Attack Aerodynamic Simulation Velocity Profiles numerical algorithms Supersonic Flow Static Pressure Wing Root

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Enhanced High-Order Scheme for High-Resolution Rotorcraft Flowfield Analysis

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AIAA JOURNAL 2022年第1期60卷 144-159页

作者： Hong, Yoonpyo Lee, Dawoon Yee, Kwanjung Park, Soo Hyung Seoul Natl Univ Dept Aerosp Engn Seoul 08826 South Korea Seoul Natl Univ Inst Adv Aerosp Technol Seoul 08826 South Korea Konkuk Univ Dept Mech & Aerosp Engn Seoul 05029 South Korea

The recent growing interest in urban air mobility (UAM) worldwide has led to the demand for physical analyses of the aerodynamic performance and aeroacoustic characteristics of electric vertical takeoff and landing (eVTOL) rotorcraft. In a UAM eVTOL rotorcraft, the smaller vortices generated from multiple propulsors interact with lifting surfaces such as wings, fuselage, and propellers in a complex manner. Therefore, to accurately predict the performance and noise of UAM eVTOL rotorcraft, vortices should be preserved with little dissipation;and their interactions must be modeled precisely. These requirements need a numerical algorithm with a refined resolution than that allowed by conventional schemes. This paper proposes a newly modified enhanced multidimensional limiting process (eMLP) for vorticity conservation (eMLP-VC), which improves the original eMLP by accounting for the fact that most rotorcraft flowfields are vortex dominated and subsonic. For advanced capability in preserving vortices, the distinguishing criterion was modified through vortex profile analysis, and low-Mach-number adjustment was performed by reconstructing the interpolated primitive variables. The proposed scheme was applied to wave propagation, shock discontinuity, double Mach reflection, propeller-wing interaction, and Second Higher-Harmonic Control Aeroacoustic Rotor Test problems. The computed results confirmed that eMLP-VC exhibits superior resolution, numerical stability, and computational time efficiency as compared to the multidimensional limiting process, eMLP, and weighted essentially nonoscillatory methods.

关键词： Multirotor Wingtip Vortices Reynolds Averaged Navier Stokes Freestream Mach Number Propeller Blades Urban Air Mobility Primitive Variable Aircraft Configurations Vertical Takeoff and Landing numerical algorithms

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A BSP-Based Algorithm for Dimensionally Nonhomogeneous Planar Implicit Curves with Topological Guarantees

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ACM TRANSACTIONS ON GRAPHICS 2009年第2期28卷 1–24页

作者： Gomes, Abel J. P. Morgado, Jose F. M. Pereira, Edgar S. Univ Beira Interior Inst Telecommun Dept Informat P-6200001 Covilha Portugal

Mathematical systems (e. g., Mathematica, Maple, Matlab, and DPGraph) easily plot planar algebraic curves implicitly defined by polynomial functions. However, these systems, and most algorithms found in the literature, cannot draw many implicit curves correctly;in particular, those with singularities (self-intersections, cusps, and isolated points). They do not detect sign-invariant components either, because they use numerical methods based on the Bolzano corollary, that is, they assume that the curve-describing function f flips sign somewhere in a line segment (AB) over bar that crosses the curve, or f (A). f (B) < 0. To solve these problems, we have generalized the False Position ( FP) method to determine two types of zeros: (i) crossing zeros and (ii) extremal zeros (local minima and maxima without function sign variation). We have called this method the Generalized False Position (GFP) method. It allows us to sample an implicit curve against the Binary Space Partitioning (BSP), say bisection lines, of a rectangular region of R-2. Interestingly, the GFP method can also be used to determine isolated points of the curve. The result is a general algorithm for sampling and rendering planar implicit curves with topological guarantees.

关键词： algorithms Implicit curves binary space partitioning numerical algorithms geometric computing

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SUBOPTIMAL FEEDBACK VIBRATION CONTROL OF A BEAM WITH A PROOF-MASS ACTUATOR

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1989年第5期12卷 691-697页

作者： POLITANSKY, H PILKEY, WD MINIST DEF HAIFAISRAEL

A clamped-free beam, damped by a proof-mass actuator, is selected for small-scale model research of flexible structures in space. Because of the short length of the actuator, the dynamic behavior of this system is strongly influenced by the constraints on the motion of the proof mass and by the maximum control forces available. An optimal solution is presented, in which a linear programming algorithm is used. Then, by special consideration of the constraints, a simplified suboptimal feedback position control is used, controlling the system by imposing position commands on the proof mass rather than using direct force inputs. The resulting time response closely fits the optimal solution. An adequate response is achieved in the linear and nonlinear regions, even when the proof mass violates its constraints.

关键词： Actuators numerical algorithms Vibration Control Flexible Structures Modern Control Theory Algebraic Riccati Equation Accelerometer Large Space Structures Electromagnetic Forces Real Time System

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