Abstract: The NASA DART and ESA Hera missions to binary asteroid 65803 Didymos have generated a lot of interest in the study of spacecraft dynamics in the vicinity of binary asteroids. The combination of the effect of the irregular shape and the rotation of the primary bodies makes them not only non-linear, but also non-autonomous systems. This study uses a technique to design reference trajectories in the context of a mission to a binary asteroid system using a fourth-order gravitational potential model for the two primary bodies. The rotation of the primary bodies, their elliptical mutual motion and the solar radiation pressure are also considered in the model, which makes this study unique. It then compares the control effort required when these reference trajectories are used with that required when reference trajectories are built with simpler models. The goal is to examine how the choice of the model used to compute reference trajectories influences the control effort required to keep the spacecraft close to them. PubDate: 2021-03-04

Abstract: Two-line elements are widely used for space operations to predict orbits with a moderate accuracy for 2-3 days. Local optimization methods can estimate a TLE as long as there exists an initial estimate, whereas global optimization methods are computationally intensive, and estimating a large number of them is prohibitive. In this paper, the feasibility of predicting the initial estimates within the radius of convergence of the actual TLEs using machine learning methods is investigated. First, a Monte-Carlo approach to estimate a TLE, when there is no initial estimate that is within the radius of convergence of the actual TLE, is introduced. The proposed Monte-Carlo method is leveraged for demonstrating the behavior of the fitting error between the realistic trajectory and the trajectory propagated by SGP4 theory during the TLE estimation processes and evaluating the unbiased performance of the proposed machine learning models. Second, gradient boosting decision trees and fully-connected neural networks are trained to map the orbital evolution of space objects to the associated TLEs using 9.5 million publicly available TLEs from the US space catalog. The desired precision in the mapping to estimate a TLE is achieved for one of the three test cases, which is a low area-to-mass ratio space object. PubDate: 2021-02-09

Abstract: This study proposes a near-optimal, impulsive control method for overflying ground targets. A set of impulses, which adjusts the satellite ground trajectory to enable the overflight, is derived. The proposed impulsive solution is expressed in closed-form which only consists of orbital revolution numbers and target overflight errors. It allows not only simplifying the search for a minimum delta-v solution but also facilitating its extension to the multiple-target overflight problem. It is also provided in this paper an insight connecting the overflight problem to a relative orbit transfer problem controlling a phase angle or mean anomaly. Numerical examples for single-, two-, and three-target overflight verify that the controlled trajectory with the proposed impulsive solution successfully overflies the designated targets within a prescribed time. It is also demonstrated that the total delta-v required for the proposed method is near-optimal based on the performance comparison with a numerical optimization-based method which employs a very large set of initial guesses. PubDate: 2021-02-02

Abstract: With the advent of the Deep Space Atomic Clock, operationally accurate and reliable one-way radiometric data sent from a radio beacon (i.e., a DSN antenna or other spacecraft) and collected using a spacecraft’s radio receiver enables the development and use of autonomous radio navigation. This work examines the fusion of radiometric data with optical data (i.e. OpNav) to yield robust and accurate trajectory solutions that include selected model reductions and computationally efficient navigation algorithms that can be readily adopted for onboard, autonomous navigation. The methodology is characterized using a representative high-fidelity simulation of deep space cruise, approach, and delivery to Mars. The results show that the combination of the two data types yields solutions that are almost an order of magnitude more accurate than those obtained using each data type by itself. Furthermore, the combined data solutions readily meet representative entry navigation requirements (in this case at Mars). PubDate: 2021-01-22 DOI: 10.1007/s40295-020-00244-x

Abstract: Low-thrust, optimal strategies are investigated for making a smooth landing on a uniformly rotating, homogeneous rectangular parallelepiped while avoiding the sharp corners during the approach. The individual effects of principal spherical harmonic coefficients on the stability against impact are determined numerically. An iterative predictor-corrector algorithm is utilized to find a direct and retrograde family of equatorial orbits. Stability analysis of equatorial orbits confirms the fact that retrograde orbits are less prone to disturbances than direct orbits. For an optimal landing, each approach trajectory begins from a stable equatorial orbit, and terminates at a prescribed landing point. The optimality conditions are given by Euler-Lagrange equations, and the associated two-point boundary value problem is solved by a collocation method with additional path constraints, and its results are compared with those of a direct nonlinear programming search technique. It is observed that a smaller energy expenditure is required for a landing made further away from the initial location such that sufficient time is allowed for the spacecraft to remain in an unforced orbital trajectory for a majority of the trajectory. A sample inclined orbit is also studied for a possible non-planar optimal approach in the body-fixed frame, and further investigated for various landing locations. PubDate: 2020-12-02 DOI: 10.1007/s40295-020-00243-y

Abstract: Deep Space Gateway is a NASA program planned to support deep space human exploration and prove new technologies needed to achieve it. One Gateway requirement is the ability to operate in the absence of communications with the Deep Space Network (DSN) for a period of at least three weeks. In this paper, three types of onboard sensors (a camera for optical navigation, a GPS receiver, and X-ray navigation) are considered to enhance its autonomy and reduce the reliance on DSN. A trade study is conducted to explore alternatives on how to achieve autonomy and how to reduce DSN dependency while satisfying navigation performance requirements. Using linear covariance analysis, error budgets, and sensitivity analysis, the performance of navigation systems using combinations of DSN with the aforementioned onboard sensors is shown. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00224-1

Abstract: Lunar gravity assist is a means to boost the energy and C3 of an escape trajectory. Trajectories with two lunar gravity assists are considered and analyzed. Two approaches are applied and tested for the design of missions aimed at Near-Earth asteroids. In the first method, indirect optimization of the heliocentric leg is combined to an approximate analytical treatment of the geocentric phase for short escape trajectories. In the second method, the results of pre-computed maps of escape C3 are employed for the design of longer Sun-perturbed escape sequences combined with direct optimization of the heliocentric leg. Features are compared and suggestions about a combined use of the approaches are presented. The techniques are efficiently applied to the design of a mission to a near-Earth asteroid. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00229-w

Abstract: Distributed Spacecraft Missions present challenges for current trajectory optimization capabilities. When tasked with the global optimization of interplanetary Multi-Vehicle Mission (MVM) trajectories specifically, state-of-the-art techniques are hindered by their need to treat the MVM as multiple decoupled trajectory optimization subproblems. This shortfall blunts their ability to utilize inter-spacecraft coordination constraints and may lead to suboptimal solutions to the coupled MVM problem. Only a handful of platforms capable of fully-automated multi-objective interplanetary global trajectory optimization exist for single-vehicle missions (SVMs), but none can perform this task for interplanetary MVMs. We present a fully-automated technique that frames interplanetary MVMs as Multi-Objective, Multi-Agent, Hybrid Optimal Control Problems (MOMA HOCP). This framework is introduced with three novel coordination constraints to explore different coupled decision spaces. The technique is applied to explore the preliminary design of a dual-manifest mission to the Ice Giants: Uranus, and Neptune, which has been shown to be infeasible using only a single spacecraft anytime between 2020 and 2070. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00215-2

Abstract: This paper proposes a method for calculating the periodic orbits in the Circular Restricted Three-Body Problem. The solution is based on the continuation method with a parameter. The parameter is the angular velocity of rotation of the attracting masses around their barycenter. Analytical periodic solutions of the problem of two fixed attracting masses serve as generating solutions. Seven possible generating solutions are described. Numerical examples of the initial conditions are given for the Earth–Moon system, making it possible to calculate the described orbits and their graphic illustrations. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00222-3

Abstract: This paper investigates a novel adaptive attitude controller design for rigid microsatellite based on feedback linearization approach, in which an accurate attitude pointing is required within a strict power limitation for space environment. The control strategy is performed to guarantee the stability of the satellite attitude under the effect of uncertain actuator parameters such as torque magnitude error and misalignment. The controller estimates the total torque fault through an observer in order to provide a reliable attitude control during the satellite manoeuvre. The stability of the closed-loop dynamic of the designed control law is proven via Lyapunov analysis. Finally, a comparative study with the well-known controllers from the literature is examined through numerical simulations to demonstrate the feasibility and effectiveness of the proposed control method. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00227-y

Abstract: Solving minimum-time low-thrust orbital transfer problems in the three-body problem by indirect methods is an extremely difficult task, which is mainly due to the small convergence domain of the optimal solution and the highly nonlinear nature associated with the three-body problem. Homotopy methods, the principle of which is to embed a given problem into a family of problems parameterized by a homotopic parameter, have been utilized to address this difficulty. However, it is not guaranteed that the optimal solution of the original problem can be obtained by most of the existing homotopy methods. In this paper, a new bounding homotopy method is proposed, by which the continuous homotopy path can be constructed and the optimal solution of the original problem is guaranteed to be found. In the parameter bounding homotopy method, an initialized problem with much higher thrust is constructed and a state-of-the-art parameter bounding homotopy approach is utilized to connect separated homotopy branches outside the predefined domain of the homotopic parameter. Furthermore, multiple optimal solutions of the original problem can be obtained if the homotopic approach continues after the first solution, among which the best solution can be figured out. Finally, numerical solutions of minimum-time low-thrust orbital transfers from GEO to Moon orbit and from GTO to halo orbit in the circular restricted three-body problem are provided to demonstrate the effectiveness of the homotopy method. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00213-4

Abstract: Many current applications of maneuver design to astrodynamics consider a deterministic case, where statistics or uncertainty is left unquantified. When including constraints based on the probability of collision, any solution must be robust to the uncertainty of the system. This paper considers the methodology of separated representations for orbit uncertainty propagation and its subsequent application to a reliability design formulation of the maneuver design problem. Separated representations is a polynomial surrogate method that has been shown to be both efficient at propagating uncertainty when considering high stochastic dimension and accurate over long propagation times. This efficiency is leveraged to improve tractability when solving the reliability design problem using optimization under uncertainty. Two sequential, potential collisions are considered in the results of this paper, with one object able to maneuver. The optimization problem therefore seeks to avoid both collisions. The probability of each collision is estimated via large numbers of samples propagated via the separated representation. The accuracy of the surrogates is compared to that of a Monte Carlo reference, and the variability of the estimated probabilities of collision is analyzed. PubDate: 2020-12-01 DOI: 10.1007/s40295-020-00218-z

Abstract: Thermal control paints are widely used in spacecraft industry to protect the spacecraft/satellite surfaces from the deleterious effects of the space environment. Dynamic reflectivity of spacecraft materials must be taken into account for improved space situational awareness (SSA). Additionally, a thorough characterization of each spacecraft material’s optical properties while on orbit can be used for designing of spacecraft surfaces for optimal thermal properties throughout a mission lifetime. This work presents the initial experimental results on performance of different organic and inorganic thermal control paints manufactured by AZ Technology exposed to various fluences of high energy (90 keV) electrons, designed to simulate a portion of the geosynchronous Earth orbit (GEO) space environment. In-vacuo reflectance spectroscopy was utilized to qualify and quantify radiation induced changes of optical properties in the studied coupons of thermal control paints. PubDate: 2020-11-21 DOI: 10.1007/s40295-020-00241-0

Abstract: In this work, the Taylor series based technique, Analytic Continuation is implemented to develop a method for the computation of the gravity and drag perturbed State Transition Matrix (STM) incorporating adaptive time steps and expansion order. Analytic Continuation has been developed for the two-body problem based on two scalar variables f and gp and their higher order time derivatives using Leibniz rule. The method has been proven to be very precise and efficient in trajectory propagation. The method is expanded to include the computation of the STM for the perturbed two-body problem. Leibniz product rule is used to compute the partials for the recursive formulas and an arbitrary order Taylor series is used to compute the STM. Four types of orbits, LEO, MEO, GTO and HEO, are presented and the simulations are run for 10 orbit periods. The accuracy of the STM is evaluated via RMS error for the unperturbed cases, symplectic check for the gravity perturbed cases and error propagation for the gravity and drag perturbed orbits. The results are compared against analytical and high order numerical solvers (ODE45, ODE113 and ODE87) in terms of accuracy. The results show that the method maintains double-precision accuracy for all test cases and 1-2 orders of magnitude improvement in linear prediction results compared to ODE87. The present approach is simple, adaptive and can readily be expanded to compute the full spherical harmonics gravity perturbations as well as the higher order state transition tensors. PubDate: 2020-11-16 DOI: 10.1007/s40295-020-00238-9

Abstract: Conjunction assessment of space objects in Low Earth Orbit (LEO) generally uses information collected by ground-based space surveillance sensors. These sensors track both the primary object (normally an active satellite) and the secondary object (typically space debris). The tracking data is used to update both objects’ orbits for collision risk assessment. The primary satellite’s involvement in this process is that of a satellite in jeopardy - the primary satellite does not usually contribute tracking data on the secondary as they are typically unequipped to do so. In this paper, an examination how an at-risk LEO primary satellite could obtain optical tracking data on a secondary object prior to the Time of Closest Approach (TCA) and assess its own collision risk without the need for additional ground-based space surveillance data is performed. This analysis was made possible by using in-situ optical measurements of space objects conjuncting with the Canadian NEOSSat Space Situational Awareness R&D microsatellite. By taking advantage of the near “constant-bearing, decreasing range” observing geometry formed during a LEO conjunction, NEOSSat can collect astrometric and photometric measurements of the secondary object in the time prior to TCA, or in the multiple half-orbits preceding TCA. This paper begins by describing the in-situ phenomenology of optically observed conjunctions in terms of the observing approach, geometry and detected astrometric and photometric characteristics. It was found that conjuncting objects are detectable to magnitude 16 and astrometric observations can be used for position covariances in the computation of probability of collision. Illustrative examples are provided. In orbits prior to TCA, in-track positioning error is improved by a factor of two or more by processing space-based observations on a filtered position estimate of the secondary. However, cross-track positioning knowledge is negligibly improved due to the inherent astrometric measurement precision of the NEOSSat sensor and the oblique observing geometry during conjunction observations. A short analysis of object detectability where star trackers could be used to perform similar observations finds that larger payload-sized objects would generally be detectable. However, smaller debris objects would require higher sensitivity from the star tracker if employed for optical conjunction derisk observations. PubDate: 2020-11-11 DOI: 10.1007/s40295-020-00236-x

Abstract: This paper combines the nonlinear Udwadia-Kalaba control approach with the Assumed Mode Method to model flexible structures and derives an attitude controller for a spacecraft. The study case of this paper is a satellite with four flexible cantilever beams attached to a rigid central hub. Two main topics are covered in this paper. The first one is the formulation of the equation of motion and the second one is the nonlinear controller design. The combination of these two techniques is able to provide a controller that damps the vibration of a flexible structure while achieving the desired rigid-motion state. PubDate: 2020-10-23 DOI: 10.1007/s40295-020-00234-z

Abstract: A deep learning approach is presented to detect safe landing locations using LIDAR scans of the Lunar surface. Semantic Segmentation is used to classify hazardous and safe locations from a LIDAR scan during the landing phase. Digital Elevation Maps from the Lunar Reconnaissance Orbiter mission are used to generate the training, validation, and testing dataset. The ground truth is generated using geometric techniques by evaluating the surface roughness, slope, and other hazard avoidance specifications. In order to train a robust model, artificially generated training data is augmented to the training dataset. A UNet-like neural network structure learns a lower dimensional representation of LIDAR scan to retain essential information regarding safety of the landing locations. A softmax activation layer at the bottom of the network ensures that the network outputs a probability of a safe landing spot. The network is also trained with a cost function that prioritizes the false safes to achieve a sub 1% false safes value. The results presented show the effectiveness of the technique for hazard detection. Future work on electing one landing spot based on proximity to the intended landing spot and the size of safety region around it is motivated. PubDate: 2020-10-21 DOI: 10.1007/s40295-020-00239-8

Abstract: We present the general concept of a telescope with optics and detectors mounted on two separate spacecrafts, in orbit around the telescope’s target (scopocentric or target-centric orbit), and using propulsion to maintain the Target-Optics-Detector alignment and Optics-Detector distance. Specifically, we study the case of such a telescope with the Sun as the target, orbiting at \(\sim \) 1 AU. We present a simple differential acceleration budget for maintaining Target-Optics-Detector alignment and Optics-Detector distance, backed by simulations of the orbital dynamics, including solar radiation pressure and influence of the planets. Of prime interest are heliocentric orbits (such as Earth-trailing/leading orbits or Distant Retrograde Orbits), where thrust requirement to maintain formation is primarily in a single direction (either sunward or anti-sunward), can be quite minuscule (a few m/s/year), and preferably met by constant-thrust engines such as solar electric propulsion or even by solar sailing via simple extendable and/or orientable flaps or rudders. PubDate: 2020-09-22 DOI: 10.1007/s40295-020-00231-2

Abstract: Observations of resident space objects generated by sensors are the primary method of maintaining knowledge of the object states. With the increasing number of objects, efficient sensor allocation is becoming integral. This requires the coordination of multiple sensors with different capabilities in an optimized manner. While the optimization is greatly simplified if instantaneous communication between the sensors can be assumed and immediate processing is available, this is not a realistic setup. Information exchange and processing induces time delays that are longer than the time available to plan and start the sensor tasking step, without unnecessarily idling the sensor. In this paper, a method is introduced to form efficient sensor tasking in a multi-sensor system, without immediate communication between the sensors and observation processing, in the following called feedback. The coordination is exemplified using two sensors, with different fields of view in a follow-up scenario of objects in the geosynchronous region. The efficiency of the method is evaluated using the two line element catalog. PubDate: 2020-09-09 DOI: 10.1007/s40295-020-00232-1