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Terminal-Velocity-Based lambert algorithm

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2020年第8期43卷 1529-1539页

作者： Zhang, Gang Harbin Inst Technol Res Ctr Satellite Technol Harbin 150001 Peoples R China

This paper provides an alternative lambert solution based on the terminal velocity vector. The chordal terminal velocity component is selected as the independent variable since it is the final required parameter in lambert's problem and it can be directly solved in the minimum-fuel free-time impulsive targeting problem. The transfer time for arbitrary conic transfer is written as a function only of the terminal velocity component. The admissible ranges of the new independent variable are analytically derived for different trajectory types. The 180 deg case and the multiple-revolution case are also considered. The analytical derivative of transfer time is provided to improve computational efficiency in numerical iterations. Compared with the existing lambert methods, the proposed approach is direct from the viewpoint of problem and physically more intuitive, although it is not superior in numerical performance.

关键词： Terminal Velocity lambert algorithm Newton Raphson Method Orbital Elements Eccentric Anomaly Boundary Value Problems Flight Path Angle Orbit Rendezvous Perigee Transfer Orbit

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Fast Solver for J2-Perturbed lambert Problem Using Deep Neural Network

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第5期45卷 875-884页

作者： Yang, Bin Li, Shuang Feng, Jinglang Vasile, Massimiliano Nanjing Univ Aeronaut & Astronaut Adv Space Technol Lab 29 Yudao St Nanjing 211106 Peoples R China Univ Strathclyde Dept Mech & Aerosp Engn 75 Montrose St Glasgow G1 1XJ Lanark Scotland

This paper presents a novel and fast solver for the J2-perturbed lambert problem. The solver consists of an intelligent initial guess generator combined with a differential correction procedure. The intelligent initial guess generator is a deep neural network that is trained to correct the initial velocity vector coming from the solution of the unperturbed lambert problem. The differential correction module takes the initial guess and uses a forward shooting procedure to further update the initial velocity and exactly meet the terminal conditions. Eight sample forms are analyzed and compared to find the optimum form to train the neural network on the J2-perturbed lambert problem. The accuracy and performance of this novel approach will be demonstrated on a representative test case: the solution of a multirevolution J2-perturbed lambert problem in the Jupiter system. The performance of the proposed approach will be compared against a classical standard shooting method and a homotopy-based perturbed lambert algorithm. It will be shown that, for a comparable level of accuracy, the proposed method is significantly faster than the other two.

关键词： lambert algorithm Artificial Neural Network Pearson Correlation Coefficient Orbital Elements MATLAB Orbital Inclination Boundary Value Problems Monte Carlo Simulation Trajectory Optimization Numerical Simulation

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Autonomous Maneuver Targeting Around Small Bodies Using Continuous-Thrust Propulsion

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第3期45卷 499-516页

作者： Kuettel, Donald H. H. McMahon, Jay W. Univ Colorado Orbital Res Cluster Celestial Applicat Smead Dept Aerosp Engn Boulder CO 80303 USA

This paper presents a novel fuel-efficient continuous-thrust maneuver targeting (CTMT) algorithm that is capable of planning finite, continuous maneuvers in a larger autonomous spacecraft guidance architecture. This is accomplished using a constant-thrust bilinear tangent guidance law in conjunction with an optimal lambert algorithm and a Newton-Raphson predictor-corrector targeting scheme. This simple approach is capable of planning a plethora of different free-time and fixed-time single-burn, burn-coast intercept, or burn-coast-burn bilinear tangent maneuvers from an initial state/orbit to a desired state/orbit. For the study case of asteroid Bennu, when used with thrust levels that are greater than 5% of the surface acceleration of asteroid Bennu, the CTMT algorithm is able to converge on 99% of orbital transfers initiated from a circular, 1.5 km, terminator orbit. Furthermore, many of the continuous-thrust maneuvers calculated by the CTMT algorithm are the optimal constant-thrust trajectories between two states in the small-body dynamical environment, and they are able to be calculated hundreds of times faster with the CTMT algorithm than with state-of-the-art nonlinear optimization algorithms. Ultimately, the CTMT algorithm shows promise as a candidate for future autonomous guidance applications.

关键词： Thrust Propulsion System Optimal Impulsive Maneuvers Broyden Fletcher Goldfarb Shanno Guidance Laws Asteroids lambert algorithm Spacecraft Trajectories Sparse Nonlinear Optimizer algorithms Convergence

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Multi-Objective Hidden Genes Genetic algorithm for Multigravity-Assist Trajectory Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第7期45卷 1269-1285页

作者： Ellithy, Ahmed Abdelkhalik, Ossama Englander, Jacob Iowa State Univ Aerospace Engn Dept 1200 Howe Hall Ames IA 50011 USA Iowa State Univ Dept Aerosp Engn 1200 Howe Hall Ames IA 50011 USA Johns Hopkins Appl Phys Lab Space Explorat Sect 11101 Johns Hopkins Rd Laurel MD 20723 USA

In multigravity-assist trajectory optimization, the size of the design space is a variable itself. The objective functions are usually replete with local minima. This paper presents a multi-objective hidden genes genetic algorithm (MOHGGA) for trajectory optimization. The length of the chromosome is selected large enough to enable modeling a given maximum number of swing-bys and maximum number of deep space maneuvers (DSMs). Binary tags are appended to those genes that control the swing-bys and DSMs. These binary tags are used to remove/add swing-bys and DSMs to a trajectory solution, and hence enable optimization among solutions of different sizes (different topologies). The MOHGGA generates Pareto fronts that have solutions of, in general, different number of swing-bys, swing-by planets, launch and arrival dates, and number of DSMs. Two objectives are considered in this paper: the total mission cost and total time of flight. An elitist nondominated sorting genetic algorithm is used. Local optimization is conducted on one objective function, holding the other objective function constant, to further improve the resulting Pareto front. Numerical results of four benchmark test cases for missions to Mars, Jupiter, Saturn, and Mercury are presented. The results demonstrate the capability of MOHGGA in searching for optimal trajectory topologies while optimizing two objectives.

关键词： Hidden Genes Genetic algorithms Trajectory Optimization Neptune Deep Space Maneuver Pericenter Multi Objective Evolutionary algorithms Interplanetary Trajectories lambert algorithm Cassini Mission MATLAB

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lambert algorithm Using Analytic Gradients

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2013年第6期36卷 1751-1761页

作者： Ahn, Jaemyung Lee, Sang-Il Korea Adv Inst Sci & Technol Dept Aerosp Engn Taejon 305701 South Korea

This paper proposes a new approach to solve lambert's problem using analytic gradient information. The initial flight-path angle has been selected as an iterator variable, and the gradient of the transfer time with respect to the iterator variable has been derived using conditions for an orbital two-point boundary value problem for update of the flight-path angle at each iteration step. A comprehensive experimental study has been conducted to demonstrate the validity of the proposed algorithm. The study results indicate that the proposed algorithm converges in all problem instances generated in the experiments and its efficiency is comparable to that of one of the best published methodologies.

关键词： lambert algorithm Flight Path Angle Boundary Value Problems Orbital Boundary Value Aerospace Engineering Target Spacecraft Orbital Elements Operating Systems Transfer Orbit Secant Method

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Dynamic selection of zero-revolution lambert algorithms using performance comparison map

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AEROSPACE SCIENCE AND TECHNOLOGY 2016年第Apr.期51卷 96-105页

作者： Lee, Sang-il Ahn, Jaemyung Bang, Jun Korea Adv Inst Sci & Technol Dept Aerosp Engn Daejeon 34141 South Korea

This paper proposes a dynamic algorithm selection procedure to accelerate the lambert's problem routine composed of two phases - the preparation phase and the execution phase. In the preparation phase, a performance comparison framework for different lambert algorithms using their characteristic parameters and cost formulae is used to generate a performance map containing the information on best algorithms for test problem instances. In the execution phase, the best algorithm for the given problem instance is selected based on the algorithm selection parameters and the performance map created in the preparation phase, and the instance is solved using the selected algorithm. The comparison results of experiments to solve a large number of test problem instances using the proposed procedure and the traditional static algorithm selection for three popular lambert algorithms demonstrate the effectiveness of the dynamics algorithm selection. (C) 2016 Elsevier Masson SAS. All rights reserved.

关键词： lambert algorithm Dynamic selection Performance comparison framework

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Robust Planning of Nonlinear Rendezvous with Uncertainty

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2017年第8期40卷 1954-1967页

作者： Yang, Zhen Luo, Ya-zhong Zhang, Jin Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Hunan Peoples R China

Practical uncertainties are not considered by optimal rendezvous trajectory designs proposed in many current studies. In this study, a robust optimization method for on-ground rendezvous trajectory design is proposed by considering the uncertainties and orbital replanning process. Two robust performance indices related to the final rendezvous errors and the total velocity increment v are first defined, then a multi-objective optimization model (including the minimum v and minimum rendezvous errors) is formulated. The unscented transformation method is used to efficiently compute the robust indices in optimization process, and a multi-objective, nondominated sorting genetic algorithm is employed to obtain a Pareto-optimal solution set. It is shown that the proposed approach can be used to design a rendezvous trajectory with the v and final rendezvous errors that are both robust against uncertainties. Furthermore, the proposed approach can identify the most preferable design space in which specific solutions for practical application of rendezvous control are selected.

关键词： Genetic algorithm Sequential Quadratic Programming Elliptical Transfer Orbit lambert algorithm Robust Design Probability Density Functions Orbital Mechanics Target Spacecraft Trajectory Optimization Model Apogee Altitude

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Partial Derivatives of the Solution to the lambert Boundary Value Problem

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2015年第9期38卷 1563-1572页

作者： Arora, Nitin Russell, Ryan P. Strange, Nathan Ottesen, David CALTECH Jet Prop Lab Pasadena CA 91011 USA Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

Two methods for deriving first-order partial derivatives of the outputs with respect to the inputs of the lambert boundary value problem are presented. The first method assumes the lambert problem is solved via the universal vercosine formulation. Taking advantage of inherent symmetries and intermediate variables, the derivatives are expressed in a computationally efficient form. The typical added cost of computing these partials is found to be approximate to 15 to 35% of the lambert computed cost. A second set of the same partial derivatives is derived from the fundamental perturbation matrix, also known as the state transition matrix of the Keplerian initial value problem. The equations are formulated in terms of Battin's partitions of the state transition matrix and its adjoint. This alternative approach works with any lambert formulation, including one that solves a perturbed lambert problem, subject to the availability of the associated state transition matrix. The analytic partial derivatives enable fast trajectory optimization formulations that implicitly enforce continuity constraints via embedded lambert problems.

关键词： Boundary Value Problems lambert algorithm Computing Effort Computing Cost Trajectory Optimization Eccentric Anomaly Orbit Determination FORTRAN Finite Difference Method Optimization algorithm

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Computational Solutions to lambert's Problem on Modern Graphics Processing Units

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2015年第7期38卷 1306-U15页

作者： Wagner, Sam Wie, Bong Kaplinger, Brian Iowa State Univ Dept Aerosp Engn Asteroid Deflect Res Center Ames IA 50010 USA Florida Inst Technol Dept Mech & Aerosp Engn Melbourne FL 32901 USA

The Battin, Gooding, and Sun algorithms are able to converge for nearly 100% of all orbit combinations. Both the Gooding and Sun algorithms have approximately the same performance, whereas the Battin algorithm is consistently slower. The performance for each lambert algorithm, when run on the graphics processing unit (GPU), has been compared. Each lambert solution algorithm is able to compute tens of millions of solutions per second, with Sun's method having the best performance at nearly 32 million solutions per second. This represents an increase in performance of two orders of magnitude when using GPUs over standard CPU algorithms. Although even the grid search CPU run times are not high when compared with common high-performance computing algorithms, mission optimization algorithms often require run times ranging from hours to multiple days. By offloading computations for solutions to lambert's problem to GPU(s) and sufficiently parallelizing optimization algorithms, performance increases of up to two orders of magnitude can be realized when compared with standard CPU algorithms. This will allow mission designers to quickly compute complex trajectories when evaluating potential mission architectures.

关键词： lambert algorithm Graphics Processing Unit algorithm Performance Application Programming Interface Orbit Determination Highly Elliptical Orbit High Performance Computing Optimization algorithm Search algorithm Mars Missions

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Tan Root for Battin's lambert Recipe

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2015年第9期38卷 1826-1826页

作者： Allen, Randal Wenzel, Russel Lone Star Anal 4555 Excel PkwySuite 500 Addison TX 75001 USA Raytheon Co Aurora CO 80011 USA

A function has been developed that bypasses Battin's infinite continued fraction evaluations for the universal lambert problem. The ATANR(x) function requires three mathematical functions that are already intrinsic to most computer languages, and frees the user from having to evaluate the equivalent infinite continued fractions. As such, the universal lambert equation is refined somewhat to make the solution more readily implemented as a mathematical subroutine. The computational accuracy for the ATANR(x) is well within the expected square root of machine precision over the vast majority of the domain. One can expand the partition's width near the local discontinuity and evaluate the appropriate function using the first two partial convergents of the true representation to approximate their behavior.

关键词： lambert algorithm MATLAB Astrodynamics

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