Christopher W. T. Roscoe

Formation Establishment and Reconfiguration Using Differential Elements in J2-Perturbed Orbits

A practical algorithm is developed for on-board planning of n-impulse fuel-optimal maneuvers for establishment and reconfiguration of spacecraft formations. The method is valid in circular and elliptic orbits and includes first-order secular J2 effects. The dynamics are expressed in terms of differential mean orbital elements, and relations are provided to allow the formation designer to transform these into intuitive geometric quantities for visualization and analysis. The maneuver targeting problem is formulated as an optimal control problem in both continuous and discrete time. The continuous-time formulation cannot be solved directly in an efficientmanner, and the discrete-time formulation, which has an analytical solution, does not directly yield the optimal thrust times. Therefore, a practical algorithm is designed by iteratively solving the discrete-time formulation while using the continuous-time necessary conditions to refine the thrust times until they converge to the optimal values. Simulation results are shown for a variety of reconfiguration maneuvers and reference orbits, including simulations with and without navigation errors for the NASA CubeSat Proximity Operations Demonstration mission.

Optimal Formation Design for Magnetospheric Multiscale Mission Using Differential Orbital Elements

The Magnetospheric Multiscale Mission requires a formation of four satellites in a nearly regular tetrahedron throughout a region of interest defined near the apogee of a highly eccentric reference orbit. Previous papers have addressed the design of formations in orbits of high eccentricity to maximize a quality factor in a region of interest, including the use of differential mean orbital elements as design variables. In this paper, a robust optimization method is presented to improve formation performance in the presence of formation initialization errors. Several design methods are analyzed by applying differential semimajor axis errors, which have a strong effect on the long-term stability of spacecraft formations. It is shown that large formations can satisfy mission requirements for a longer time than smaller formations, when the same magnitude of errors are considered, and generally exhibit less variation in quality factors due to these errors. The robust optimization method is applied to these smaller formations and produces results that are much more stable when semimajor axis errors are included, at a cost of some performance in the nominal error-free case. The results are verified using the NASA General Mission Analysis Tool and are shown to be reasonably accurate, except in predicting very long-term behavior. A physical analysis of the geometry of several magnetospheric multiscale formation designs is provided, and eight distinct optimal tetrahedron orientations are identified (two configurations, in which the chief satellite can be placed at any of the four vertices).

Formation establishment and reconfiguration using differential elements in J2-perturbed orbits

A practical algorithm is developed for on-board planning of n-impulse fuel-optimal maneuvers for establishment and reconfiguration of spacecraft formations. The method is valid in circular and elliptic orbits and includes first-order secular J 2 effects. The dynamics are expressed in terms of differential mean orbital elements, and relations are provided to allow the formation designer to transform these into intuitive geometric quantities for visualization and analysis. The maneuver targeting problem is formulated as an optimal control problem in both continuous and discrete time. The continuous-time formulation cannot be solved directly in an efficientmanner, and the discrete-time formulation, which has an analytical solution, does not directly yield the optimal thrust times. Therefore, a practical algorithm is designed by iteratively solving the discrete-time formulation while using the continuous-time necessary conditions to refine the thrust times until they converge to the optimal values. Simulation results are shown for a variety of reconfiguration maneuvers and reference orbits, including simulations with and without navigation errors for the NASA CubeSat Proximity Operations Demonstration mission.

Application Of Multi-Hypothesis Sequential Monte Carlo For Breakup Analysis With The Comparison Of Two Probabilistic Admissible Region Techniques

As more objects are launched into space, the potential for breakup events and space object collisions is ever increasing. These events create large clouds of debris that are extremely hazardous to space operations. Providing timely, accurate, and statistically meaningful Space Situational Awareness (SSA) data is crucial in order to protect assets and operations in space. The space object tracking problem, in general, is nonlinear in both state dynamics and observations, making it ill-suited to linear filtering techniques such as the Kalman filter. Additionally, given the multi-object, multi-scenario nature of the problem, space situational awareness requires multi-hypothesis tracking and management that is combinatorially challenging in nature. In practice, it is often seen that assumptions of underlying linearity and/or Gaussianity are used to provide tractable solutions to the multiple space object tracking problem. However, these assumptions are, at times, detrimental to tracking data and provide statistically inconsistent solutions. This paper details a tractable solution to the multiple space object tracking problem applicable to space object breakup events. Within this solution, simplifying assumptions of the underlying probability density function are relaxed and heuristic methods for hypothesis management are avoided. This is done by implementing Sequential Monte Carlo (SMC) methods for both nonlinear filtering as well as hypothesis management. This goal of this paper is to detail the solution and use it as a platform to discuss computational limitations that hinder proper analysis of large breakup events.