High Performance Algorithms to Improve the Runtime Computation of Spacecraft Trajectories

Nitin Arora
Georgia Institute of Technology
Department of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 2013


   title={High Performance Algorithms to Improve the Runtime Computation of Spacecraft Trajectories},

   author={Arora, Nitin},



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Increasing space mission complexity coupled with challenging science requirements are driving the need for fast and robust space trajectory design and simulation tools. Current state-of-the art methods and techniques are often found to be lacking, particularly when problems are scaled to the future demands of mission design. This challenging problem is addressed in this thesis by 1) identifying a set of high impact building-block" astrodynamics algorithms, 2) systematically improving several current state-of-the art solution methods via theoretical and methodological improvements and 3) taking advantage of modern computational hardware and numerical techniques to provide significant improvements in speed and robustness. In this thesis, five high impact astrodynamics problems are identified and their algorithms are selected for improvement. The solutions to the selected problems have applications ranging from preliminary mission design to high-fidelity space trajectory design and simulation. The first problem identified is the multiple-revolution Lambert problem. Lambert’s problem is one of the most extensively studied problems in spaceflight mechanics and enjoys a large volume of research, spanning over several decades. In this thesis, a new formulation of the multiple revolution Lambert problem is presented. The formulation is based on a cosine transformation and uses rational functions for generating accurate initial guesses. Thanks to a new geometry based parameter, the resulting formulation is simplified and only requires one auxiliary function to handle the separate forms of the conic. Apart from enjoying 40% to 60% reduction in runtime over the current state-of-the art Gooding’s method, the new formulation also results in a robust and accurate implementation. High-fidelity perturbation models are one of the major speed bottlenecks encountered during spacecraft trajectory design and simulation. The current work attempts to improve the performance of two aspects of these perturbation models, namely, the high-fidelity geopotential evaluation and the accurate ephemeris computation. High-fidelity geopotentials are typically computed via spherical harmonics, which is slow and non-intuitive to implement efficiently. In this thesis a new model called Fetch is proposed. Fetch is designed to take advantage of all the previous methods in the literature, while finding innovative solutions to correct their respective problems. The model is based on a modification to the Junkins weighting function method and achieves up to three orders of magnitude in speedup over the conventional spherical harmonics approach. As a part of this thesis, the Fetch model is applied to interpolate the GRACE GGM03C gravity model. Four Fetch models with different spherical harmonic degrees and order are computed and archived. The next problem that deserves attention is the computation of accurate solar system body state and orientation data. The current work attempts to solve this problem by proposing a new ephemeris system called FIRE (Fast Interpolated Runtime Ephemeris). FIRE is custom designed for space trajectory applications that favor speed and smooth derivatives. It relies on spline interpolation and is based on a multi-level computation architecture. FIRE is demonstrated to be 50 to 70 times faster (compared to JPL’s SPICE system) for typical trajectory applications while still achieving high accuracy. The speed is gained in exchange for a modest memory burden, which is necessary for the interpolation coefficients. Shifting the focus to applications that require partial derivatives of a final state with respect to an initial state; the thesis also investigates the problem of fast sensitivity computation. Sensitivity information is used by many batch and sequential filtering applications, gradient based optimization algorithms, and is applied in a wide range of engineering fields. The current work focuses on efficiently parallelizing sensitivity computation across a single trajectory. A new hybrid parallelization strategy is proposed, utilizing the Central Processing Unit (CPU) and the Graphics Processing Unit (GPU) to achieve rapid sensitivity computation on a single workstation. For example, trajectory propagation with overlapped computations demonstrate that first order sensitivities are calculated almost for free when compared to the conventional CPU implementation. The proposed technique can be applied to various optimization methods like optimal control, parameter optimization and other gradient based techniques. The last chapter in this thesis aims to combine the two previously developed (Fetch and FIRE) perturbation models with a GPU based integration algorithm for simulating multiple high-fidelity space trajectories. The resulting tool provides unprecedented, multiplicative speedups over similar simulations on the CPU with performance gains of two to four orders in magnitude for various cases. The proposed tool is highly relevant to a variety of problems like space object conjunction analysis, covariance realism, particle filters and Monte-Carlo analyses.
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