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  • 1
    Publication Date: 2018-06-06
    Description: In this work we present a method to solve the impulsive minimum fuel maneuver problem for a distributed set of spacecraft. We develop the method assuming a fully non-linear dynamics model and parameterize the problem to allow the method to be applicable to any flight regime. Furthermore, the approach is not limited by the inter-spacecraft separation distances and is applicable to both small formations as well as constellations. We assume that the desired relative motion is driven by mission requirements and has been determined a-priori. The goal of this work is to develop a technique to achieve the desired relative motion in a minimum fuel manner. To permit applicability to multiple flight regimes, we have chosen to parameterize the cost function in terms of the maneuver times expressed in a useful time system and the maneuver locations expressed in their Cartesian vector representations. We also include as an independent variable the initial reference orbit to solve for the optimal injection orbit to minimize and equalize the fuel expenditure of distributed sets of spacecraft with large inter-spacecraft separations. In this work we derive the derivatives of the cost and constraints with respect to all of the independent variables.
    Keywords: Astrodynamics
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  • 2
    Publication Date: 2019-07-17
    Description: The Magnetospheric Imaging Constellation (MagIC) is a NASA space science concept to study the Earth's Magnetosphere. The concept proposes to apply tomography techniques using an array of spacecraft to obtain three dimensional images of the Earth's magnetosphere. This paper presents an optimal orbit design to ensure that the constellation is in the desired region of the magnetosphere for maximum time. The solution is found using a steepest descent optimization algorithm that takes into account perturbations from the non-spherical Earth, drag, Sun, Moon and other significant bodies. The solution also satisfies constraints on maximum eclipse duration and geometry constraints to allow an adequate GPS navigation solution. We present three solutions depending upon the epoch of the primary science: vernal equinox, summer solstice, and a third midway between the vernal equinox and summer solstice. Orbit insertion is also considered. All spacecraft are assumed to be launched on a single vehicle into a nominal orbit and the (Delta)V's to achieve the nominal orbit are presented. After insertion into the nominal orbit, each spacecraft undergoes a phasing maneuver to place it in the appropriate position with respect to the rest of the constellation. We present a minimum fuel approach to maneuver each spacecraft from the nominal orbit into the desired final orbit.
    Keywords: Astrodynamics
    Type: 16th International Symposium on Space Flight Dynamics; Pasadena, CA; United States
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  • 3
    Publication Date: 2019-07-17
    Description: Leonardo-BRDF is a NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the orbit dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal two-burn initialization scheme is presented with the required delta-V to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated delta-V's are calculated to maintain the formation in the presence of perturbations.
    Keywords: Astrodynamics
    Type: 2001 Flight Mechanics Symposium; 131; NASA/CP-2001-209986
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  • 4
    Publication Date: 2019-07-10
    Description: The problem of minimum-fuel formation reconfiguration for the Magnetospheric Multi-Scale (MMS) mission is studied. This reconfiguration trajectory optimization problem can be posed as a nonlinear optimal control problem. In this research, this optimal control problem is solved using a spectral collocation method called the Gauss pseudospectral method. The objective of this research is to provide highly accurate minimum-fuel solutions to the MMS formation reconfiguration problem and to gain insight into the underlying structure of fuel-optimal trajectories.
    Keywords: Astrodynamics
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  • 5
    Publication Date: 2019-07-10
    Description: This paper presents a robust and efficient approach for relative navigation and attitude estimation of spacecraft flying in formation. This approach uses measurements from a new optical sensor that provides a line of sight vector from the master spacecraft to the secondary satellite. The overall system provides a novel, reliable, and autonomous relative navigation and attitude determination system, employing relatively simple electronic circuits with modest digital signal processing requirements and is fully independent of any external systems. Experimental calibration results are presented, which are used to achieve accurate line of sight measurements. State estimation for formation flying is achieved through an optimal observer design. Also, because the rotational and translational motions are coupled through the observation vectors, three approaches are suggested to separate both signals just for stability analysis. Simulation and experimental results indicate that the combined sensor/estimator approach provides accurate relative position and attitude estimates.
    Keywords: Astrodynamics
    Type: 2001 Flight Mechanics Symposium; 115-129; NASA/CP-2001-209986
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