Multiple Spacecraft Formation Control with Θ-D Method


Formation control of multiple spacecraft flying in deep space about the L2 libration point is investigated. Dynamics of the spacecraft is formulated as a circular restricted three-body problem with Sun and Earth as the two primaries. A virtual structure (VS) concept is used as a framework for multiple spacecraft formation in which the centre of the virtual rigid body is assumed to follow a nominal orbit around the L2 libration point. Control is applied to each individual spacecraft so as to keep a constant relative distance from the centre of the vs. The relative formation dynamics is nonlinear and control of this system is carried out using a relatively new suboptimal control technique called as theta-D technique. The theta-D method provides approximate analytical solution to the Hamilton-Jacobi-Bellman equation. As it is a feedback control and in a closed form, it is implementable. Simulation results demonstrate that this controller is able to provide millimeter level formation flying accuracy.


Mechanical and Aerospace Engineering

Keywords and Phrases

Multiple Spacecraft Formation Control; Relative Formation Dynamics; Theta-D Method; Virtual Structure Concept

Document Type

Article - Journal

Document Version


File Type





© 2007 the Institution of Engineering and Technology (The IET), All rights reserved.

Publication Date

01 Jan 2007