Low-thrust Transfers to Candidate Near-rectilinear Halo Orbits Facilitated by Invariant Manifolds
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Engineering topics
Publications and source records attributed to Junkins, John L..
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We have developed a new method for solving low-thrust fuel-optimal orbit transfer problems in the vicinity of a large body (planet or asteroid), considering a high-fidelity spherical harmonic gravity model. The algorithm is formulated via the indirect optimization method, leading to a two-point boundary value problem (TPBVP). We make use of a hyperbolic tangent smoothing law for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and thus promote convergence. The TPBVP is solved using the method of particular solutions (MPS) shooting method and Picard-Chebyshev numerical integration. Application of Picard-Chebyshev integration affords an avenue for increased efficiency that is not available with step-by-step integrators. We demonstrate that computing the particular solutions with only a low-fidelity force model greatly increases the efficiency of the algorithm while ultimately achieving near machine precision accuracy. A salient feature of the MPS is that it is parallelizable, and thus further speedups are available. It is also shown that, for near Earth orbits and over a small number of en-route revolutions around the Earth, only the zonal perturbation terms are required in the costate equations to obtain a solution that is accurate to machine precision and optimal to engineering precision. The proposed framework can be used for trajectory design around small asteroids and also for orbit debris rendezvous and removal tasks.
A method and apparatus is provide for receiving a first set of optical data from a first field of view and receiving a second set of optical data from a second field of view. A portion of the first set of optical data is communicated and a portion of the second set of optical data is reflected, both toward an optical combiner. The optical combiner then focuses the portions onto the image plane such that information at the image plane that is associated with the first and second fields of view is received by an optical detector and used to determine an attitude characteristic.
A new star pattern recognition method is developed using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding cataloged vector matrix in a reference frame. It is shown that singular values and right singular vectors are invariant with respect to coordinate transformation and robust under uncertainty. One advantage of singular value comparison is that a pairing process for individual measured and cataloged stars is not necessary, and the attitude estimation and pattern recognition process are not separated. An associated method for mission catalog design is introduced and simulation results are presented.
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.
Improved method for placement of eigenvalues and eigenvectors of closed-loop control system by use of either state or output feedback. Applied to reduced-order finite-element mathematical model of NASA's MAST truss beam structure. Model represents deployer/retractor assembly, inertial properties of Space Shuttle, and rigid platforms for allocation of sensors and actuators. Algorithm formulated in real arithmetic for efficient implementation. Choice of open-loop eigenvector matrix and its closest unitary matrix believed suitable for generating well-conditioned eigensystem with small control gains. Implication of this approach is that element of iterative search for "optimal" unitary matrix appears unnecessary in practice for many test problems.
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This paper seeks to provide a brief overview of the somewhat unfamiliar concept underlying system identification especially as it applies to large flexible space structures. Having elaborated on the concept, the authors provide a detailed description of the identification process including model development, its experimental validation and final certification. This discussion is followed by a classification of the different identification methods and a brief evaluation of the potential of existing methodology to address special circumstances of large flexible space structures. The paper concludes by making a few recommendations that are deemed necessary to meet the enormous challenges posed by the deployment or erection of large space structures.
The Task Committee on Methods for Identification of Large Structures in Space was founded in Jul. 1984. The charter of the committee was to prepare a state-of-the-art report on methods of system identification applicable to large space structures (LSS). Funding to support preparation of the report was received in Aug. 1985 from the Air Force Rocket Propulsion Laboratory (now the Air Force Astronautics Laboratory), in the form of a contract to the ASCE. The report was completed, and published by AFRPL in Sep. 1986. The Task Committee consisted of ten members, including ASCE and AFRPL representatives. The membership represented Government, Industry, and Universities, and consisted of electrical, mechanical, and civil engineers, with backgrounds in Structural Dynamics, Optimization, and Controls. An effort was made to use consistent terminology and notation throughout the report which would be compatible with the terminology used in both the structures and controls communities.
An improved method is developed for eigenvalues and eigenvectors placement of a closed-loop control system using either state or output feedback. The method basically consists of three steps. First, the singular value of QR decomposition is used to generate an orthonormal basis that spans admissible eigenvector space corresponding to each assigned eigenvalue. Secondly, given a unitary matrix, the eigenvector set which best approximates the given matrix in the least-square sense and still satisfy eigenvalue cosntraints is determined. Thirdly, a unitary matrix is sought to minimize the error between the unitary matrix and the assignable eigenvector matrix. For use as the desired eigenvector set, two matrices, namely, the open-loop eigenvector matrix and its closest unitary matrix are proposed. The latter matrix generally encourages both minimum conditioning and control gains. In addition, the algorithm is formulated in real arithmetic for efficient implementation. To illustrate the basic concepts, numerical examples are included.
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