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TECHNICAL PAPERS

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

[+] Author and Article Information
Ming Xin1

Department of Aerospace Engineering, Mississippi State University, Mississippi State, MS 39759xin@ae.msstate.edu

S. N. Balakrishnan

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, MO 65401bala@umr.edu

H. J. Pernicka

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, MO 65401pernicka@umr.edu

1

Corrresponding author.

J. Dyn. Sys., Meas., Control 129(5), 689-698 (Mar 16, 2007) (10 pages) doi:10.1115/1.2764509 History: Received May 27, 2006; Revised March 16, 2007

## Abstract

Control of deep-space spacecraft formation flying is investigated in this paper using the virtual structure approach and the $θ-D$ 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 $θ-D$ 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 $1cm$ accuracy.

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## Figures

Figure 1

Basic geometry of the CR3BP

Figure 2

Nominal Lissajous orbit about the Sun-Earth L2 libration point

Figure 3

Virtual structure geometry

Figure 4

Formation maneuver geometry

Figure 5

Relative position errors of the first spacecraft

Figure 6

Attitude errors of the first spacecraft

Figure 7

Angular rate response of the first spacecraft

Figure 8

Control force and torque response of the first spacecraft

Figure 9

Control force response of the first spacecraft in 1day

Figure 10

Position error of the second spacecraft

Figure 11

Attitude error of the second spacecraft

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