Exploration of the region near the sun-earth collinear libration points for the control of large formations

Aurelie Heritier, Purdue University

Abstract

Spacecraft formations possess many applications in the future of space exploration. During the last decade, due to the detection of a large number of extrasolar planets, new studies on formation flying in multi-body regimes have emerged to support searches for Earth-like planets in other solar systems. The L2 Sun-Earth libration point region has been a popular destination in creating an architecture for astronomical missions. It is a relatively cold environment, far from the disturbances of the Sun and, therefore, ideal for astronomical instruments. However, controlling multiple spacecraft in a multi-body environment is challenging and a good understanding of the natural dynamics in this regime is essential. The current investigation explores the dynamical environment near the L2 Sun-Earth libration point to aid in the control of formations of spacecraft. By exploiting the natural dynamics in the circular restricted three-body model (CR3BP), natural regions are determined that are particularly suitable for maintaining formations of spacecraft. The natural dynamics at small distances from a given reference trajectory are initially investigated for the placement of small formations of spacecraft. Some regions with low relative drift represent suitable locations to maintain small formations and are derived analytically using variational equations. Spacecraft located in such regions avoid large variations in their mutual distances while maintaining the orientation of the formation. These regions represent quadric surfaces, and the type of quadric surfaces, either ellipsoids or elliptic cylinders, depends on the eigenstructure reflecting the phase space along the given reference trajectory. The natural flow at large distances from a given reference trajectory is explored next to characterize regions that are suitable to maintain large formations, i.e., when the mutual distances between the spacecraft reaches tens of thousands of kilometers. Spheres of points at various locations along the reference orbit are constructed to classify the space, and regions of low natural drift on the spheres are numerically identified when the distance between two vehicles is large. These low drift regions are examined in detail, and a correspondance with the quadric surfaces that are derived for small formations is established. In particular, the orientation of these low drift zones along a given reference orbit are investigated as some parameters vary, such as the size of the formation as well as the reference orbit. Using the low natural drift regions, control strategies are then developed for large formations. Traditional controllers, such as impulsive maneuvers and linear quadratic regulators (LQR), are employed to quantify the level of control that is required to maintain large formations along specific directions in the CR3BP. Designs of new controllers are also investigated to produce some set of desired relative motions between two spacecraft placed at large mutual distances. In a potential formation option investigated in this analysis, a deputy vehicle maintains a fixed circular motion in a plane relative to a chief spacecraft moving along its reference trajectory. Finally, the effectiveness of using the low natural drift regions as derived for large formations is tested for the New Worlds Observer mission concept. This scenario involves a large telescope-occulter formation for star observations, to detect and characterize habitable terrestrial exoplanets. The low drift zones are employed to reduce the control effort to maintain a large telescope-occulter formation during the observation of inertially-fixed target stars. In particular, the occulter is maintained via a linear quadratic regulator during star observations. Given a set of inertially-fixed target stars, an automatic star sequence design process is proposed with observation and reconfiguration phases using the low drift regions. This design creates star sequences that lead to relatively small overall maneuver costs for this particular mission concept.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace engineering

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