Belinda G. Marchand

Control Strategies for Formation Flight in the Vicinity of the Libration Points

The concept of formation flight of multiple spacecraft offers many promising possibilities, both for space exploration and the associated technology development. Past studies on formation flight have focused primarily on Earth-orbiting clusters. However, space-based observatory and interferometry missions, such as the proposed Terrestrial Planet Finder and the Micro Arc-second X-ray Imaging Mission, reflect plans for formation flight in multibody regimes, particularly in the vicinity of the sun-Earth/moon libration points. two specific tasks are accomplished in this study. First, in a dynamically sensitive regime such as that near the libration points, baseline propulsive requirements are established. A decentralized control strategy based on existing linear and nonlinear control techniques is employed and the results are presented through a series of sample mission configurations. Note that the control problem is formulated to facilitate future tradeoff studies in the libration point environment. The analysis is presented within the context of both the circular restricted three-body problem and the more complete ephemeris model. Once baseline costs are available, the second task is the introduction of potential constraints. These constraints may affect not only the formation control strategies but also the conceptual design of the mission, and their influence on the cost is evaluated.

Improved Corrections Process for Constrained Trajectory Design in the n-Body Problem

The general objective is the development of efficient techniques for preliminary design of trajectory arcs in nonlinear autonomous dynamic systems in which the desired solution is subject to algebraic interior and/or exterior constraints. For application to then-body problem, trajectoriesmust satisfy specific requirements, e.g., periodicity in terms of the states, interior or boundary constraints, and specified coverage. Thus, a strategy is formulated in a sequence of increasingly complex steps: 1) a trajectory isfirstmodeled as a series of arcs (analytical or numerical) and general trajectory characteristics and timing requirements are established; 2) the specific constraints and associated partials are formulated; 3) a corrections process ensures position and velocity continuity while satisfying the constraints; and finally, 4) the solution is transitioned to a full model employing ephemerides. Though the examples pertain to spacecraft mission design, the methodology is generally applicable to autonomous systems subject to algebraic constraints. For spacecraft mission design applications, an immediate advantage of this approach, particularly for the identification of periodic orbits, is that the startup solution need not exhibit any symmetry to achieve the objectives.

Natural and non-natural spacecraft formations near the L1 and L2 libration points in the Sun–Earth/Moon ephemeris system

Space-based observatory and interferometry missions, such as Terrestrial Planet Finder (TPF), Stellar Imager, and MAXIM, have sparked great interest in multi-spacecraft formation flight in the vicinity of the Sun–Earth/Moon (SEM) libration points. The initial phase of this research considered the formation keeping problem from the perspective of continuous control as applied to non-natural formations. In the present study, closer inspection of the flow corresponding to the stable and centre manifolds near the reference orbit, reveals some interesting natural relative motions as well as some discrete control strategies for deployment. In addition, some implementation issues associated with discrete formation keeping of natural versus non-natural configurations are addressed in the present study.

Formation Control of the MAXIM L2 Libration Orbit Mission

The Micro-Arcsecond X-ray Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imager mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 micro-arcsecond imaging. Currently the mission architecture comprises 25 spacecraft, 24 as optics modules and one as the detector, which will form sparse sub-apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. To achieve these mission goals, the formation is required to cooperatively point at desired targets. Once pointed, the individual elements of the MAXIM formation must remain stable, maintaining their relative positions and attitudes below a critical threshold. These pointing and formation stability requirements impact the control and design of the formation. In this paper, we provide analysis of control efforts that are dependent upon the stability and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions to minimize the control efforts and we address continuous control via input feedback linearization (IFL). Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

Design of the Onboard Autonomous Targeting Algorithm for the Trans-Earth Phase of Orion

This paper discusses the adaptation and implementation of a modifled two-level corrections process as the onboard targeting algorithm for the Trans-Earth Injection phase of the Crew Exploration Vehicle. Unlike earlier Apollo missions to the Moon, Project Orion intends to land near the polar regions, a task that can lead to a substantial plane change maneuver prior to Earth return. To reduce the fuel expenditure associated with this plane change, a three-maneuver sequence is employed during the return phase. First, the initial maneuver raises apolune at departure. The subsequent maneuver executes a plane change. The third and flnal maneuver places the spacecraft on its flnal approach to Earth while targeting the entry state for precision landing. An autonomous onboard targeting algorithm is sought in the event of loss of communication with the ground. This last scenario presents a very unique challenge, one never required of any Apollo vehicle. The Apollo missions also beneflted from ∞exible entry requirements in contrast to Orion. Precision targeting in multi-body regimes has only been previously demonstrated in unmanned sample return missions, like Genesis. The two-level corrector formulation presented here ensures the entry constraints are met without violating the available fuel budget.

An Autonomous Onboard Targeting Algorithm Using Finite Thrust Maneuvers

In earlier investigations, the adaptation and implementation of a modified two-level corrections process as the onboard targeting algorithm for the Trans-Earth Injection phase of Orion is presented. The objective of that targeting algorithm is to generate the times of ignition and magnitudes of the required maneuvers such that the desired state at entry interface is achieved. In an actual onboard flight software implementation, these times of ignition and maneuvers are relayed onto Flight Control for command and execution. Although this process works well when the burn durations or burn arcs are small, this might not be the case during a contingency situation when lower thrust engines are employed to perform the maneuvers. Therefore, a new version of the modified two-level corrections process is formulated to handle the case of finite burn arcs. This paper presents the development and formulation of that finite burn modified two-level corrections process which can again be used as an onboard targeting algorithm for the Trans-Earth Injection phase of Orion. Additionally, performance results and a comparison between the two methods are presented. The finite burn two-level corrector formulation presented here ensures the entry constraints at entry interface are still met without violating the available fuel budget, while still accounting for much longer burn times in its design.

Onboard Autonomous Targeting for the Trans-Earth Phase of Orion

The present investigation focuses on one aspect of the autonomous targeting process used onboard during the Orion trans-Earth injection phase, specifically, a fast and robust algorithm that identifies a feasible return trajectory, one that meets the entry constraints without exceeding the fuel available. Unlike earlier Apollo missions, Orion seeks to land near the polar regions of the moon. Thus, a substantial plane change maneuver is required before returning to Earth. To reduce the fuel expenditure associated with this plane change, a three-maneuver sequence is employed during the return phase. An autonomous onboard targeting process for precision entry (one that incorporates multiple coordinated trans-Earth maneuvers) is sought in the event of loss of communication with the ground. The latter scenario presents a very unique challenge: one never before required of any Apollo vehicle. The Apollo missions also benefited from flexible entry requirements in contrast to Orion. Precision targeting in multibody regimes has only been previously demonstrated in unmanned sample return missions such as Genesis. The formulation presented here ensures that the entry constraints are met without violating the available fuel budget.

Above the Horizon Satellite Coverage with Dual-Altitude Band Constraints

The optimal satellite coverage problem traditionally refers to maximizing the visibility of targets against an Earth background. In this study, the focus shifts to satellite coverage of targets against a space background within a dualaltitude band defined by an upper and a lower target altitude. Furthermore, because objects against an Earth background are outside the region of interest, the coverage area to be maximized exists above the local horizon and, naturally, within a prespecified sensor range. The present analysis is restricted to satellites on circular orbits to simplify the mathematical development of the objective function. In the course of this development, geometrical arguments are employed to identify an analytical expression for the resulting coverage area. A graphical analysis tool, developed during the course of this study, is employed to develop new insight into how the coverage area is affected by changes in the mutual intersection of these reference surfaces. The result of the study is an objective function that can be employed in an optimization process in the search for optimal satellite constellations that maximize coverage of the area of interest.

Constellation Design for Space-Based Space Situational Awareness Applications: An Analytical Approach

The growing number of resident space objects in Earth orbit has made effective monitoring a formidable task. Supplementing the capabilities of ground-based sensor networks with on-orbit sensing platforms would dramatically enhance the ability of such systems to detect, track, identify, and characterize resident space objects. To facilitate constellation design that promotes these goals, an optimization approach is selected, which inherently requires a predefined mathematical representation of a cost index or measure of merit. Such representations are often analytically available, but when considering optimal constellation design for space-based space situational awareness applications, a closed-form expression for the cost index is only available under certain assumptions. The present study focuses on a subset of cases that admit exact representations. In this case, geometrical arguments are employed to establish an analytical formulation for the coverage area provided as well as for certain coverage mult...

Hybrid optimal control for HIV multi-drug therapies: a finite set control transcription approach.

In this study, the treatment of Human Immunodeficiency Virus (HIV) infection is investigated through an optimal structured treatment interruption (STI) schedule of two classes of antiretroviral drugs, mainly, reverse transcriptase inhibitors and protease inhibitors. An STI treatment strategy may be beneficial in lowering the risk of HIV mutating to drug-resistant strains, and could provide patients with respite from toxic side effects of HAART. A shorter treatment period is considered compared to previous studies and the solution to the HIV STI problem is obtained via the Finite Set Control Transcription (FSCT) formulation. The FSCT formulation offers a unique approach for handling multiple independent decision variables simultaneously, and, as is shown by the results of this study, is well-suited for an effective treatment of the optimal STI problem. The results obtained in the present investigation demonstrate that immune boosting and subsequent natural suppression of the viral load are possible even when a reduced STI therapy treatment duration is in consideration.