Position and Attitude Control of Deep-Space Spacecraft Formation Flying Via Virtual Structure and Θ-D Technique


Control of deep-space spacecraft formation flying is investigated in this paper using the virtual structure approach and the theta-D suboptimal control technique. The circular restricted three-body problem with the Sun and the Earth as the two primaries is utilized as a framework for study and a two-satellite formation flying scheme is considered. The virtual structure is stationkept in a nominal orbit around the L2 libration point. A maneuver mode of formation flying is then considered. Each spacecraft is required to maneuver to a new position and the formation line of sight is required to rotate to a desired orientation to acquire new science targets. During the rotation, the formation needs to be maintained and each spacecraft's attitude must align with the rotating formation orientation. The basic strategy is based on a “virtual structure” topology. A nonlinear model is developed that describes the relative formation dynamics. This highly nonlinear position and attitude control problem is solved by employing a recently developed nonlinear control approach, called the theta-D technique. This method is based on an approximate solution to the Hamilton-Jacobi-Bellman equation and yields a closed-form suboptimal feedback solution. The controller is designed such that the relative position error of the formation is maintained within 1 cm accuracy.


Mechanical and Aerospace Engineering


Goddard Space Flight Center

Keywords and Phrases

Spacecraft; Deep space; Space vehicles

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2007 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Jan 2007