Tag Archives: Optimization and Control

Using multiobjective optimization to reconstruct interferometric data (I) [IMA]

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http://arxiv.org/abs/2304.12107


Imaging in radioastronomy is an ill-posed inverse problem. Particularly the Event Horizon Telescope (EHT) Collaboration faces two big limitations for the existing methods when imaging the active galactic nuclei (AGN): large and expensive surveys solving the problem with different optimization parameters must be done, and only one local minima for each instance is returned. With our novel nonconvex, multiobjective optimization modeling approach, we aim to overcome these limitations. To this end we used a multiobjective version of the genetic algorithm (GA): the Multiobjective Evolutionary Algorithm Based on Decomposition, or MOEA/D. GA strategies explore the objective function by evolutionary operations to find the different local minima, and to avoid getting trapped in saddle points. First, we have tested our algorithm (MOEA/D) using synthetic data based on the 2017 Event Horizon Telescope (EHT) array and a possible EHT + next-generation EHT (ngEHT) configuration. We successfully recover a fully evolved Pareto front of non-dominated solutions for these examples. The Pareto front divides into clusters of image morphologies representing the full set of locally optimal solutions. We discuss approaches to find the most natural guess among these solutions and demonstrate its performance on synthetic data. Finally, we apply MOEA/D to observations of the black hole shadow in Messier 87 (M87) with the EHT data in 2017. MOEA/D is very flexible, faster than any other Bayesian method and explores more solutions than Regularized Maximum Likelihood methods (RML). We have done two papers to present this new algorithm: the first explains the basic idea behind multi-objective optimization and MOEA/D and it is used to recover static images, while in the second paper we extend the algorithm to allow dynamic and (static and dynamic) polarimetric reconstructions.

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H. Müller, A. Mus and A. Lobanov
Tue, 25 Apr 23
31/72

Comments: accepted for publication in A&A, both first authors have contributed equally to this work

Research on FAST Active Reflector Adjustment Algorithm Based on Computer Simulation [CL]

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http://arxiv.org/abs/2204.05495


Based on the background of the 2021 Higher Education Club Cup National College Students Mathematical Contest in Modeling A, according to the relevant data of the China Sky Eye (FAST) radio telescope, the main cable nodes and actuators are adjusted and controlled by mathematical modeling and computer simulation methods to realize the active reflector. The adjustment of the shape enables it to better receive the signal of the external celestial body and improve the utilization rate of the reflector, so as to achieve a higher receiving ratio of the feed cabin. In this paper, a point set mapping algorithm based on the rotation matrix of the spatial coordinate axis is proposed, that is, the mapping matrix is obtained by mathematical derivation, and the linear interpolation algorithm based on the original spherical surface and the ideal paraboloid to solve the working paraboloid is obtained. When the interpolation ratio is adjusted to 89% to satisfy the optimal solution under realistic constraints. Then, a three-dimensional spatial signal reflection model based on spatial linear invariance is proposed. Each reflective panel is used as an evaluation index. For each reflective surface, the 0-1 variable of signal accessibility on the feeder is defined. The signal is mapped to the plane where the feeder is located, which reduces a lot of computational difficulty. Finally, it is found that the panel of the feed cabin that can receive the reflected signal accounts for 19.3%. Compared with the original spherical reflection model, the working paraboloid model established in this paper has a The signal ratio has increased by 224%.

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T. Shi, S. Tao and H. Wang
Wed, 13 Apr 22
58/73

Comments: 21 pages, 11 figures

Bayesian Shape Reconstruction and Optimal Guidance for Autonomous Landing on Asteroids [EPA]

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http://arxiv.org/abs/2203.06485


Construction of the precise shape of an asteroid is critical for spacecraft operations as the gravitational potential is determined by spatial mass distribution. The typical approach to shape determination requires a prolonged mapping phase of the mission over which extensive measurements are collected and transmitted for Earth-based processing. This paper presents a set of approaches to explore an unknown asteroid with onboard calculations, and to land on its surface area selected in an optimal fashion. The main motivation is to avoid the extended period of mapping or preliminary ground observations that are commonly required in spacecraft missions around asteroids. First, range measurements from the spacecraft to the surface are used to incrementally correct an initial shape estimate according to the Bayesian framework. Then, an optimal guidance scheme is proposed to control the vantage point of the range sensor to construct a complete 3D model of the asteroid shape. This shape model is then used in a nonlinear controller to track a desired trajectory about the asteroid. Finally, a multi resolution approach is presented to construct a higher fidelity shape representation in a specified location while avoiding the inherent burdens of a uniformly high resolution mesh. This approach enables for an accurate shape determination around a potential landing site. We demonstrate this approach using several radar shape models of asteroids and provide a full dynamical simulation about asteroid 4769 Castalia.

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S. Kulumani and T. Lee
Tue, 15 Mar 22
48/108

Comments: J Astronaut Sci (2022)

Feasible Low-thrust Trajectory Identification via a Deep Neural Network Classifier [CL]

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http://arxiv.org/abs/2202.04962


In recent years, deep learning techniques have been introduced into the field of trajectory optimization to improve convergence and speed. Training such models requires large trajectory datasets. However, the convergence of low thrust (LT) optimizations is unpredictable before the optimization process ends. For randomly initialized low thrust transfer data generation, most of the computation power will be wasted on optimizing infeasible low thrust transfers, which leads to an inefficient data generation process. This work proposes a deep neural network (DNN) classifier to accurately identify feasible LT transfer prior to the optimization process. The DNN-classifier achieves an overall accuracy of 97.9%, which has the best performance among the tested algorithms. The accurate low-thrust trajectory feasibility identification can avoid optimization on undesired samples, so that the majority of the optimized samples are LT trajectories that converge. This technique enables efficient dataset generation for different mission scenarios with different spacecraft configurations.

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R. Xie and A. Dempster
Fri, 11 Feb 22
32/71

Comments: 18 Pages; 10 figures; Presented at 2021 AAS/AIAA Astrodynamics Specialist Conference, Big Sky, Virtual

Design of optimal low-thrust manoeuvres for remote sensing multi-satellite formation flying in low Earth orbit [IMA]

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http://arxiv.org/abs/2202.03998


This paper presents a strategy for optimal manoeuvre design of multi-satellite formation flying in low Earth orbit environment, with the aim of providing a tool for mission operation design. The proposed methodology for formation flying manoeuvres foresees a continuous low-thrust control profile, to enable the operational phases. The design is performed starting from the dynamic representation described in the relative orbital elements, including the main orbital perturbations effects. It also exploits an interface with the classical radial-transversal-normal description to include the maximum delta-v limitation and the safety condition requirements. The methodology is applied to a remote sensing mission study, Formation Flying L-band Aperture Synthesis, for land and ocean application, such as a potential high-resolution Soil Moisture and Ocean Salinity (SMOS) follow-on mission, as part of a European Space Agency mission concept study. Moreover, the results are applicable to a wide range of low Earth orbit missions, exploiting a distributed system, and in particular to Formation Flying L-band Aperture Synthesis (FFLAS) as a follow-on concept to SMOS.

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F. Scala, G. Gaias, C. Colombo, et. al.
Wed, 9 Feb 22
26/48

Comments: 19 pages

Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization [CL]

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http://arxiv.org/abs/2201.11137


We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish its key properties analytically and numerically. The prototype is a discretization of Born-Infeld dynamics, with a squared relativistic speed limit depending on the objective function. This class of frictionless, energy-conserving optimizers proceeds unobstructed until slowing naturally near the minimal loss, which dominates the phase space volume of the system. Building from studies of chaotic systems such as dynamical billiards, we formulate a specific algorithm with good performance on machine learning and PDE-solving tasks, including generalization. It cannot stop at a high local minimum and cannot overshoot the global minimum, yielding an advantage in non-convex loss functions, and proceeds faster than GD+momentum in shallow valleys.

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G. Luca and E. Silverstein
Fri, 28 Jan 22
17/64

Comments: 9 pages + Appendix, 8 figures. Code available online

Optimal Design of Coatings for Mirrors of Gravitational Wave Detectors: Analytic Turbo Solution via Herpin Equivalent Layers [CL]

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http://arxiv.org/abs/2112.04393


In this paper, an analytical solution to the problem of optimal dielectric coating design of mirrors for gravitational wave detectors is found. The technique used to solve this problem is based on Herpin’s equivalent layers, which provide a simple, constructive, and analytical solution. The performance of the Herpin-type design exceeds that of the periodic design and is almost equal to the performance of the numerical, non-constructive optimized design obtained by brute force. Note that the existence of explicit analytic constructive solutions of a constrained optimization problem is not guaranteed in general, when such a solution is found, we speak of turbo optimal solutions.

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V. Pierro, V. Fiumara and F. Chiadini
Thu, 9 Dec 21
3/63

Comments: accepted for publication in “Gravitational Wave Observatory: The Realm of Applied Science” special issue of Applied Science

COSMIC: fast closed-form identification from large-scale data for LTV systems [CL]

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http://arxiv.org/abs/2112.04355


We introduce a closed-form method for identification of discrete-time linear time-variant systems from data, formulating the learning problem as a regularized least squares problem where the regularizer favors smooth solutions within a trajectory. We develop a closed-form algorithm with guarantees of optimality and with a complexity that increases linearly with the number of instants considered per trajectory. The COSMIC algorithm achieves the desired result even in the presence of large volumes of data. Our method solved the problem using two orders of magnitude less computational power than a general purpose convex solver and was about 3 times faster than a Stochastic Block Coordinate Descent especially designed method. Computational times of our method remained in the order of magnitude of the second even for 10k and 100k time instants, where the general purpose solver crashed. To prove its applicability to real world systems, we test with spring-mass-damper system and use the estimated model to find the optimal control path. Our algorithm was applied to both a Low Fidelity and Functional Engineering Simulators for the Comet Interceptor mission, that requires precise pointing of the on-board cameras in a fast dynamics environment. Thus, this paper provides a fast alternative to classical system identification techniques for linear time-variant systems, while proving to be a solid base for applications in the Space industry and a step forward to the incorporation of algorithms that leverage data in such a safety-critical environment.

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M. Carvalho, C. Soares, P. Lourenço, et. al.
Thu, 9 Dec 21
12/63

Comments: N/A

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions [CL]

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http://arxiv.org/abs/2111.03275


In this paper, we develop a novel data-driven method for Deformable Mirror (DM) control. The developed method updates both the DM model and DM control actions that produce desired mirror surface shapes. The novel method explicitly takes into account actuator constraints and couples a feedback control algorithm with an algorithm for recursive estimation of DM influence function models. In addition to this, we explore the possibility of using Walsh basis functions for DM control. By expressing the desired and observed mirror surface shapes as sums of Walsh pattern matrices, we formulate the control problem in the 2D Walsh basis domain. We thoroughly experimentally verify the developed approach on a 140-actuator MEMS DM, developed by Boston Micromachines. Our results show that the novel method produces the root-mean-square surface error in the $14-40$ nanometer range. These results can additionally be improved by tuning the control and estimation parameters. The developed approach is also applicable to other DM types, such as for example, segmented DMs.

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A. Haber and T. Bifano
Mon, 8 Nov 21
56/69

Comments: 25 pages, 11 figures

Lunaport: Math, Mechanics & Transport [IMA]

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http://arxiv.org/abs/2107.14423


Issues for transport facilities on the lunar surface related to science, engineering, architecture, and human-factors are discussed. Logistic decisions made in the next decade may be crucial to financial success. In addition to outlining some of the problems and their relations with math and computation, the paper provides useful resources for decision-makers, scientists, and engineers.

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P. Kainen
Mon, 2 Aug 21
42/82

Comments: 45 pages, submitted to Symmetry, for Special Issue on Symmetry in Mechanical and Transport Engineering, Transport Logistics, and Mathematical Design of Efficient Transport Facilities

Analysis of 3GM Callisto Gravity Experiment of the JUICE Mission [EPA]

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http://arxiv.org/abs/2101.03401


The ESA’s JUICE mission will provide a thorough investigation of the Jupiter system and the Galilean moons during its nominal tour, comprising flybys of Europa and Callisto, and an orbital phase about Ganymede at the end of the mission. The 3GM experiment will exploit accurate Doppler and range measurements to determine the moons’ orbits and gravity fields (both static and tidal) and infer their interior structure. This paper presents the attainable accuracies of the Callisto geodesy experiment and addresses the effect of different flybys mean anomaly distribution and geometry on the estimation of the tidal Love number k2.

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M. Benedetto, P. Cappuccio, S. Molli, et. al.
Tue, 12 Jan 21
23/90

Comments: 2020 AAS/AIAA Astrodynamics Specialist Conference, Virtual Lake Tahoe

Analytical framework for space debris collision avoidance maneuver design [IMA]

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http://arxiv.org/abs/2012.12651


An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss’ planetary equations and relative motion equations are used to map maneuvers at a given time to displacements at the predicted close approach. The model is then extended to map changes in state between two times, allowing one to propagate covariance matrices. The analytical formulation reduces the optimization problem to an eigenproblem, both for maximum deviation and minimum collision probability. Two maximum deviation cases, total deviation and impact parameter, are compared for a large set of spacecraft-debris conjunction geometries derived from European Space Agency’s Meteoroid and Space Debris Terrestrial Environment Reference (MASTER-2009) model. Moreover, the maximum impact parameter and minimum collision probability maneuvers are compared assuming covariances known at the maneuver time, to evaluate the net effect of lead time in collision probability. In all cases, solutions are analyzed in the b-plane to leverage its natural separation of phasing and geometry change effects. Both uncertainties and maximum deviation grow along the time axis for long lead times, limiting the reduction in collision probability.

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J. Gonzalo, C. Colombo and P. Lizia
Thu, 24 Dec 20
11/73

Comments: 44 pages, 24 figures. Author’s accepted manuscript for a paper published in Journal of Guidance, Control, and Dynamics

Minimum-Time Earth-to-Mars Interplanetary Orbit Transfer Using Adaptive Gaussian Quadrature Collocation [CL]

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http://arxiv.org/abs/2012.04116


The problem of minimum-time, low-thrust, Earth-to-Mars interplanetary orbital trajectory optimization is considered. The minimum-time orbital transfer problem is modeled as a four-phase optimal control problem where the four phases correspond to planetary alignment, Earth escape, heliocentric transfer, and Mars capture. The four-phase optimal control problem is then solved using an adaptive Gaussian quadrature collocation method. The following three models are used in the study: (1) circular planetary motion; (2) elliptic planetary motion; and (3) elliptic planetary motion with gravity perturbations. Results for all three cases are provided, and one particular case is studied in detail to show the key features of the optimal solutions. It was found that the minimum times for cases (1), (2), and (3) are, respectively, 215 d, 196 d, and 198 d with departure dates, respectively, of 1 July 2020, 30 June 2020, and 28 June 2020. Finally, the problem formulation developed in this study is compared against prior work on an Earth-to-Mars interplanetary orbit transfer where it is found that the results of this research show significant improvement in transfer time relative to the prior work.

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B. Holden, S. He and A. Rao
Wed, 9 Dec 20
24/80

Comments: 29 pages, 10 figures

Impact Probability Under Aleatory And Epistemic Uncertainties [EPA]

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http://arxiv.org/abs/2011.13632


We present an approach to estimate an upper bound for the impact probability of a potentially hazardous asteroid when part of the force model depends on unknown parameters whose statistical distribution needs to be assumed. As case study we consider Apophis’ risk assessment for the 2036 and 2068 keyholes based on information available as of 2013. Within the framework of epistemic uncertainties, under the independence and non-correlation assumption, we assign parametric families of distributions to the physical properties of Apophis that define the Yarkovsky perturbation and in turn the future orbital evolution of the asteroid. We find ${\rm IP}\leq 5\times 10^{-5}$ for the 2036 keyhole and ${\rm IP}\leq 1.6\times 10^{-5}$ for the 2068 keyhole. These upper bounds are largely conservative choices due to the rather wide range of statistical distributions that we explored.

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C. Tardioli, D. Farnocchia, M. Vasile, et. al.
Mon, 30 Nov 20
80/117

Comments: N/A

Introducing MISS, a new tool for collision avoidance analysis and design [IMA]

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http://arxiv.org/abs/2010.08379


The core aspects and latest developments of Manoeuvre Intelligence for Space Safety (MISS), a new software tool for collision avoidance analysis and design, are presented. The tool leverages analytical and semi-analytical methods for the efficient modelling of the orbit modifications due to different control strategies, such as impulsive or low-thrust manoeuvres, and maps them into displacements at the nominal close approach using relative motion equations. B-plane representations are then used to separate the phasing-related and geometry-related components of the displacement. Both maximum miss distance and minimum collision probability collision avoidance manoeuvres are considered. The tool also allows for the computation of state transition matrices and propagation of uncertainties. Several test cases are provided to assess the capabilities and performance of the tool.

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J. Gonzalo, C. Colombo and P. Lizia
Mon, 19 Oct 20
35/44

Comments: 11 pages, 7 figures. Preprint of article published in Journal of Space Safety Engineering

Simple ΔV Approximation for Optimization of Debris-to-Debris Transfers [IMA]

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http://arxiv.org/abs/2004.02225


A method for the rapid estimation of transfer costs for the removal of debris in low Earth orbit is proposed. Debris objects among a population with similar inclination values are considered. The proposed approximate analysis can provide estimations of actual Deltav between any debris object pair as a function of time; these estimations allow for the rapid evaluation of the costs of large sequences of targets to be removed. The effect of Earth’s oblateness perturbation (J2) is exploited to reduce transfer costs. The debris removal problem of the 9th edition of the Global Trajectory Optimization Competition is used to evaluate the estimation accuracy; Deltav estimations of the transfers between objects pairs are verified by comparing them with the GTOC9 solution proposed by the winning team from JPL. The comparison of the results demonstrates the very good accuracy of the simple approximation. Key words: Space debris; approximation; trajectory optimization; J2 perturbation

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H. Shen and L. Casalino
Tue, 7 Apr 20
32/72

Comments: N/A

Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation [IMA]

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http://arxiv.org/abs/2003.13804


Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as Least-Squares fitting or Markov-Chain Monte-Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters together with their corresponding uncertainties and correlations is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential data assimilation method, the Ensemble Square Root Filter, to thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be $295 \pm 18$ $\mathrm{J\,m^{-2}\,K^{-1}\,s^{-1/2}}$, while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12 $\mathrm{W\,m^{-1}\,K^{-1}}$ and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure and thus, results are more accurate than previously derived parameters.

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M. Hamm, I. Pelivan, M. Grott, et. al.
Wed, 1 Apr 20
28/83

Comments: N/A

Reduction of Saturn Orbit Insertion Impulse using Deep-Space Low Thrust [EPA]

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http://arxiv.org/abs/2001.04357


Orbit insertion at Saturn requires a large impulsive manoeuver due to the velocity difference between the spacecraft and the planet. This paper presents a strategy to reduce dramatically the hyperbolic excess speed at Saturn by means of deep-space electric propulsion. The interplanetary trajectory includes a gravity assist at Jupiter, combined with low-thrust maneuvers. The thrust arc from Earth to Jupiter lowers the launch energy requirement, while an ad hoc steering law applied after the Jupiter flyby reduces the hyperbolic excess speed upon arrival at Saturn. This lowers the orbit insertion impulse to the point where capture is possible even with a gravity assist with Titan. The control-law algorithm, the benefits to the mass budget and the main technological aspects are presented and discussed. The simple steering law is compared with a trajectory optimizer to evaluate the quality of the results and possibilities for improvement.

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E. Fantino, R. Flores, J. Pelaez, et. al.
Tue, 14 Jan 20
15/72

Comments: N/A

Adaptive Proximal Gradient Method for Constrained Matrix Factorization [CL]

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http://arxiv.org/abs/1910.10094


The Proximal Gradient Method (PGM) is a robust and efficient way to minimize the sum of a smooth convex function $f$ and a non-differentiable convex function $r$. It determines the sizes of gradient steps according to the Lipschitz constant of the gradient of $f$. For many problems in data analysis, the Lipschitz constants are expensive or impossible to compute analytically because they depend on details of the experimental setup and the noise properties of the data. Adaptive optimization methods like AdaGrad choose step sizes according to on-the-fly estimates of the Hessian of $f$. As quasi-Newton methods, they generally outperform first-order gradient methods like PGM and adjust step sizes iteratively and with low computational cost. We propose an iterative proximal quasi-Newton algorithm, AdaProx, that utilizes the adaptive schemes of Adam and its variants (AMSGrad, AdamX, PAdam) and works for arbitrary proxable penalty functions $r$. In test cases for Constrained Matrix Factorization we demonstrate the advantages of AdaProx in fidelity and performance over PGM, especially when factorization components are poorly balanced. The python implementation of the algorithm presented here is available as an open-source package at https://github.com/pmelchior/proxmin

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P. Melchior, R. Joseph and F. Moolekamp
Wed, 23 Oct 19
53/64

Comments: 12 pages, 5 figures; submitted to Optimization & Engineering

Spacecraft design optimisation for demise and survivability [CL]

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http://arxiv.org/abs/1910.05091


Among the mitigation measures introduced to cope with the space debris issue there is the de-orbiting of decommissioned satellites. Guidelines for re-entering objects call for a ground casualty risk no higher than 0.0001. To comply with this requirement, satellites can be designed through a design-for-demise philosophy. Still, a spacecraft designed to demise has to survive the debris-populated space environment for many years. The demisability and the survivability of a satellite can both be influenced by a set of common design choices such as the material selection, the geometry definition, and the position of the components. Within this context, two models have been developed to analyse the demise and the survivability of satellites. Given the competing nature of the demisability and the survivability, a multi-objective optimisation framework was developed, with the aim to identify trade-off solutions for the preliminary design of satellites. As the problem is nonlinear and involves the combination of continuous and discrete variables, classical derivative based approaches are unsuited and a genetic algorithm was selected instead. The genetic algorithm uses the developed demisability and survivability criteria as the fitness functions of the multi-objective algorithm. The paper presents a test case, which considers the preliminary optimisation of tanks in terms of material, geometry, location, and number of tanks for a representative Earth observation mission. The configuration of the external structure of the spacecraft is fixed. Tanks were selected because they are sensitive to both design requirements: they represent critical components in the demise process and impact damage can cause the loss of the mission because of leaking and ruptures. The results present the possible trade off solutions, constituting the Pareto front obtained from the multi-objective optimisation.

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M. Trisolini, H. Lewis and C. Colombo
Mon, 14 Oct 19
40/69

Comments: Paper accepted for publication in Aerospace Science and Technology

GTOC X: Solution Approach of Team Sapienza-PoliTo [CL]

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http://arxiv.org/abs/1909.11984


This paper summarizes the solution approach and the numerical methods developed by the joint team Sapienza University of Rome and Politecnico di Torino (Team Sapienza-PoliTo) in the context of the 10th Global Trajectory Optimization Competition. The proposed method is based on a preliminary partition of the galaxy into several small zones of interest, where partial settlement trees are developed, in order to match a (theoretical) optimal star distribution. A multi-settler stochastic Beam Best-First Search, that exploits a guided multi-star multi-vessel transition logic, is proposed for solving a coverage problem, where the number of stars to capture and their distribution within a zone is assigned. The star-to-star transfers were then optimized through an indirect procedure. A number of refinements, involving settle time re-optimization, explosion, and pruning, were also investigated. The submitted 1013-star solution, as well as an enhanced 1200-point rework, are presented.

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A. Zavoli, L. Federici, B. Benedikter, et. al.
Fri, 27 Sep 19
22/64

Comments: 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME

A Stochastic LBFGS Algorithm for Radio Interferometric Calibration [IMA]

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http://arxiv.org/abs/1904.05619


We present a stochastic, limited-memory Broyden Fletcher Goldfarb Shanno (LBFGS) algorithm that is suitable for handling very large amounts of data. A direct application of this algorithm is radio interferometric calibration of raw data at fine time and frequency resolution. Almost all existing radio interferometric calibration algorithms assume that it is possible to fit the dataset being calibrated into memory. Therefore, the raw data is averaged in time and frequency to reduce its size by many orders of magnitude before calibration is performed. However, this averaging is detrimental for the detection of some signals of interest that have narrow bandwidth and time duration such as fast radio bursts (FRBs). Using the proposed algorithm, it is possible to calibrate data at such a fine resolution that they cannot be entirely loaded into memory, thus preserving such signals. As an additional demonstration, we use the proposed algorithm for training deep neural networks and compare the performance against the mainstream first order optimization algorithms that are used in deep learning.

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S. Yatawatta, L. Clercq, H. Spreeuw, et. al.
Fri, 12 Apr 19
39/62

Comments: N/A

Multi-Revolution Low-Thrust Trajectory Optimization Using Symplectic Methods [CL]

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http://arxiv.org/abs/1901.02881


Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy low-thrust multi-revolution orbit transfer problem. First, the optimal orbit transfer problem is posed as a constrained nonlinear optimal control problem. Then, the constrained nonlinear optimal control problem is converted into an equivalent linear quadratic form near a reference solution. The reference solution is updated iteratively by solving a sequence of linear-quadratic optimal control sub-problems, until convergence. Each sub-problem is solved via a symplectic method in discrete form. To facilitate the convergence of the algorithm, the spacecraft dynamics are expressed via modified equinoctial elements. Interpolating the non-singular equinoctial orbital elements and the spacecraft mass between the initial point and end point is proven beneficial to accelerate the convergence process. Numerical examples reveal that the proposed method displays high accuracy and efficiency.

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Z. E and D. Guzzetti
Fri, 11 Jan 19
7/45

Comments: N/A

Scheduling multiple agile Earth observation satellites with multiple observations [IMA]

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http://arxiv.org/abs/1812.00203


The Earth observation satellites (EOSs) are specially designed to collect images according to user requirements. The agile EOSs (AEOS), with stronger attitude maneuverability, greatly improve the observation capability, while increasing the complexity in scheduling. We address a multiple AEOSs scheduling with multiple observations for the first time}, where the objective function aims to maximize the entire observation profit over a fixed horizon. The profit attained by multiple observations for each target is nonlinear to the number of observations. We model the multiple AEOSs scheduling as a specific interval scheduling problem with each satellite orbit respected as machine. Then A column generation based framework is developed to solve this problem, in which we deal with the pricing problems with a label-setting algorithm. Extensive simulations are conducted on the basis of a China’s AEOS constellation, and the results indicate the optimality gap is less than 3% on average, which validates the performance of the scheduling solution obtained by the proposed framework. We also compare the framework in the conventional EOS scheduling.

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C. Han, X. Wang, G. Song, et. al.
Tue, 4 Dec 18
25/78

Comments: N/A

Novel Sparse Recovery Algorithms for 3D Debris Localization using Rotating Point Spread Function Imagery [CL]

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http://arxiv.org/abs/1809.10541


An optical imager that exploits off-center image rotation to encode both the lateral and depth coordinates of point sources in a single snapshot can perform 3D localization and tracking of space debris. When actively illuminated, unresolved space debris, which can be regarded as a swarm of point sources, can scatter a fraction of laser irradiance back into the imaging sensor. Determining the source locations and fluxes is a large-scale sparse 3D inverse problem, for which we have developed efficient and effective algorithms based on sparse recovery using non-convex optimization. Numerical simulations illustrate the efficiency and stability of the algorithms.

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C. Wang, R. Plemmons, S. Prasad, et. al.
Fri, 28 Sep 18
27/52

Comments: 16 pages. arXiv admin note: substantial text overlap with arXiv:1804.04000

Parameter-space study of kinetic-impactor mission design [EPA]

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http://arxiv.org/abs/1706.02096


While almost all potentially hazardous asteroids (PHAs) with a size larger than one kilometre have been discovered, it is well-known that the vast majority of the smaller ones are in fact yet to be found. There is therefore an excellent motivation to consider at once all possible Earth-crossing orbits, and to undertake a systematic study of mitigation missions for the entire parameter space of orbital elements. It is shown that the whole parameter space can be reduced, without loss of generality, to only three relevant dimensionless parameters: the eccentricity and inclination of the asteroid orbit, and the asteroid true anomaly at impact. Ballistic kinetic-impactor mitigation missions are studied for the entire parameter space, considering critical feasibility constraints such as the launcher performance and the illumination conditions at deflection. Different classes of optimal solutions are found to exist and can be directly linked to asteroid orbital properties. The aim of this work is to help identify an appropriate response to the potential threat of a collision of a near-Earth object with our planet, to provide a preliminary mission design, and to determine in which parts of parameter space difficulties may arise. (abridged)

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A. Payez and J. Schoenmaekers
Thu, 8 Jun 17
26/69

Comments: Contributed to the proceedings of the 5th Planetary Defense Conference (PDC 2017), Tokyo, May 15th-19th 2017. 10 pages

Probabilistic Cross-Identification in Crowded Fields as an Assignment Problem [IMA]

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http://arxiv.org/abs/1609.03065


One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood partitioning to the fundamental assignment problem of discrete mathematics and efficiently solve the two-way catalog-level matching in the realm of combinatorial optimization using the so-called Hungarian algorithm. We introduce the method, demonstrate its performance in a mock universe where the true associations are known, and discuss the applicability of the new procedure to large surveys.

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T. Budavari and A. Basu
Tue, 13 Sep 16
55/91

Comments: 6 pages, 4 figures, accepted for publication in the Astronomical Journal

Optimal Orderings of k-subsets for Star Identification [CL]

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http://arxiv.org/abs/1607.04552


Finding the optimal ordering of k-subsets with respect to an objective function is known to be an extremely challenging problem. In this paper we introduce a new objective for this task, rooted in the problem of star identification on spacecrafts: subsets of detected spikes are to be generated in an ordering that minimizes time to detection of a valid star constellation. We carry out an extensive analysis of the combinatorial optimization problem, and propose multiple algorithmic solutions, offering different quality-complexity trade-offs. Three main approaches are investigated: exhaustive search (branch and prune), goal-driven (greedy scene elimination, minimally intersecting subsets), and stateless algorithms which implicitly seek to satisfy the problem’s goals (pattern shifting, base unrank). In practical terms, these last algorithms are found to provide satisfactory approximations to the ideal performance levels, at small computational costs.

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J. Mueller, C. Sanchez-Sanchez, L. Simoes, et. al.
Mon, 18 Jul 16
25/50

Comments: N/A

Galaxy Redshifts from Discrete Optimization of Correlation Functions [IMA]

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http://arxiv.org/abs/1604.00652


We propose a new method of constraining the redshifts of individual extragalactic sources based on their celestial coordinates. Techniques from integer linear programming are utilized to optimize simultaneously for the angular two-point cross- and autocorrelation functions. Our novel formalism introduced here not only transforms the otherwise hopelessly expensive, brute-force combinatorial search into a linear system with integer constraints but is also readily implementable in off-the-shelf solvers. We adopt Gurobi and use Python to dynamically build the cost function. The preliminary results on simulated data show great promise for future applications to sky surveys by complementing and enhancing photometric redshift estimators. Our approach is the first use of linear programming in astronomy.

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B. Lee, T. Budavari and A. Basu
Tue, 5 Apr 16
59/67

Comments: 10 pages with 4 figures, submitted to The Astrophysical Journal (3/14/16)

Systematic Low-Thrust Trajectory Optimization for a Multi-Rendezvous Mission using Adjoint Scaling [IMA]

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http://arxiv.org/abs/1603.02352


A deep-space exploration mission with low-thrust propulsion to rendezvous with multiple asteroids is investigated. Indirect methods, based on the optimal control theory, are implemented to optimize the fuel consumption. The application of indirect methods for optimizing low-thrust trajectories between two asteroids is briefly given. An effective method is proposed to provide initial guesses for transfers between close near-circular near-coplanar orbits. The conditions for optimality of a multi-asteroid rendezvous mission are determined. The intuitive method of splitting the trajectories into several legs that are solved sequentially is applied first. Then the results are patched together by a scaling method to provide a tentative guess for optimizing the whole trajectory. Numerical examples of optimizing three probe exploration sequences that contain a dozen asteroids each demonstrate the validity and efficiency of these methods.

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F. Jiang and G. Tang
Wed, 9 Mar 16
56/71

Comments: N/A

Multiscale functions, Scale dynamics and Applications to partial differential equations [CL]

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http://arxiv.org/abs/1509.01048


Modeling phenomena from experimental data, always begin with a \emph{choice of hypothesis} on the observed dynamics such as \emph{determinism}, \emph{randomness}, \emph{derivability} etc. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following : \emph{“With a finite set of data concerning a phenomenon, can we recover its underlying nature ?} From this problem, we introduce in this paper the definition of \emph{multi-scale functions}, \emph{scale calculus} and \emph{scale dynamics} based on the \emph{time-scale calculus} (see \cite{bohn}). These definitions will be illustrated on the \emph{multi-scale Okamoto’s functions}. The introduced formalism explains why there exists different continuous models associated to an equation with different \emph{scale regimes} whereas the equation is \emph{scale invariant}. A typical example of such an equation, is the \emph{Euler-Lagrange equation} and particularly the \emph{Newton’s equation} which will be discussed. Notably, we obtain a \emph{non-linear diffusion equation} via the \emph{scale Newton’s equation} and also the \emph{non-linear Schr\”odinger equation} via the \emph{scale Newton’s equation}. Under special assumptions, we recover the classical \emph{diffusion} equation and the \emph{Schr\”odinger equation}.

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J. Cresson and F. Pierret
Fri, 4 Sep 15
34/58

Comments: N/A

Mission Analysis For the Ion Beam Deflection of Fictitious Asteroid 2015PDC [CL]

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http://arxiv.org/abs/1504.02854


A realistic mission scenario for the deflection of fictitious asteroid 2015PDC is investigated that makes use of the ion beam shepherd concept as primary deflection technique. The article deals with the design of a low thrust rendezvous trajectory to the asteroid, the estimation of the propagated covariance ellipsoid and the outcome of a slow-push deflection starting from three worst case scenarios (impacts in New Delhi, Dhaka and Teheran). Displacing the impact point towards very low populated areas, as opposed to full deflection, is found to be the simplest and most effective mitigation approach. Mission design, technical and political aspects are discussed.

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C. Bombardelli, D. Amato and J. Cano
Tue, 14 Apr 15
87/87

Comments: 19 pages, 19 figures, presented at the 2015 Planetary Defence Conference

Earth–Mars Transfers with Ballistic Capture [EPA]

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http://arxiv.org/abs/1410.8856


We construct a new type of transfer from the Earth to Mars, which ends in ballistic capture. This results in a substantial savings in capture $\Delta v$ from that of a classical Hohmann transfer under certain conditions. This is accomplished by first becoming captured at Mars, very distant from the planet, and then from there, following a ballistic capture transfer to a desired altitude within a ballistic capture set. This is achieved by manipulating the stable sets, or sets of initial conditions whose orbits satisfy a simple definition of stability. This transfer type may be of interest for Mars missions because of lower capture $\Delta v$, moderate flight time, and flexibility of launch period from the Earth.

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F. Topputo and E. Belbruno
Mon, 3 Nov 14
31/40

Comments: N/A

Multiple Space Debris Collecting Mission — Optimal Mission Planning [CL]

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http://arxiv.org/abs/1404.1446


This paper addresses the problem of planning successive Space Debris Collecting missions so that they can be achieved at minimal cost by a generic vehicle. The problem mixes combinatorial optimization to select and order the debris among a list of candidates, and continuous optimization to fix the rendezvous dates and to define the minimum fuel orbital maneuvers. The solution method proposed consists in three stages. Firstly the orbital transfer problem is simplified by considering a generic transfer strategy suited either to a high thrust or a low thrust vehicle. A response surface modelling is built by solving the reduced problem for all pairs of debris and for discretized dates, and storing the results in cost matrices. Secondly a simulated annealing algorithm is applied to find the optimal mission planning. The cost function is assessed by interpolation on the response surface based on the cost matrices. This allows the convergence of the simulated algorithm in a limited computation time, yielding an optimal mission planning. Thirdly the successive missions are re-optimized in terms of transfer maneuvers and dates without changing the debris order. These continuous control problems yield a refined solution with the performance requirement for designing the future Space Debris Collecting vehicle. The method is applicable for large list of debris and for various assumptions regarding the cleaning program (number of missions, number of debris per mission, total duration, deorbitation scenario, high or low thrust vehicle). It is exemplified on an application case with 3 missions to plan, each mission visiting 5 SSO debris to be selected in a list of 21 candidates.

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M. Cerf
Tue, 8 Apr 14
19/71

Integer-ambiguity resolution in astronomy and geodesy [CL]

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http://arxiv.org/abs/1312.4920


Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning, and in global navigation satellite systems. In this paper, we analyse the theoretical aspects of the matter and propose new methods for solving those NLP problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.

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Wed, 18 Dec 13
26/70