Spacecraft Formation Flying Control Using Mean Orbit Elements

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Spacecraft Formation Flying Control Using Mean Orbit Elements 1 Hanspeter Schaub,' Srinivas R. Vadali/ John L. Junkins,' and Kyle T. Alfrfend'' Abstract Two nonlinear feedback control laws are presented for reestablishing a desired 1 2 invariant relative orbit. Since it is convenient to describe the relative orbit of a deputy with respect to a chief satellite in terms of mean orbit element differences, and because the conditions for a relative orbit being 1 2 invariant are expressed in terms of mean orbit elements, the first control law feeds back errors in terms of mean orbit elements. Dealing with mean orbit elements has the advantage that short period oscillations are not perceived as tracking errors; rather, only the long term tracking errors are compensated for. The second control law feeds back traditional Cartesian position and velocity tracking errors. For both of the control laws, the desired orbit is computed using mean orbit elements. A numerical study compares and contrasts the two feedback laws.

Introduction In recent years the challenging concept of spacecraft formation flying has been studied by various authors [1-6]. These spacecraft may be in a simple along-track string formation or a more dynamic formation where several deputy spacecraft orbit relative to a chief reference spacecraft. With these formations, the purpose is to increase the baseline of scientific instruments placed on the spacecraft. These instruments could form a radio-telescope or surface-mapping radar array. One method to find natural relative orbits about a reference spacecraft is to use the Clohessy-Wiltshire (CW) equations [7]. Here a circular reference orbit and spherical Earth model is assumed and the equations of motion of the orbiting spacecraft are linearized relative to the rotating frame of the reference spacecraft. These 'Presented at the Astrodynamics Specialist Conference in Girdwood, Alaska, Aug. 16-18, 1999, Paper No. AAS 99-310. 2Research Engineer, Sandia National Laboratories, Albuquerque, NM 87185, AAS Member. 3P rofessor of Aerospace Engineering, Aerospace Engineering Department, Texas A&M University, College Station TX 77843, Member AAS. "George J. Eppright Distinguished Chair Professor of Aerospace Engineering, Aerospace Engineering Department, Texas A&M University, College Station TX 77843, Fellow AAS. 5Professor and Head of Aerospace Engineering Department, Texas A&M University, College Station TX 77843, Fellow AAS.

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equations of motion are sometimes also referred to as the Hill-Clohessy-Wiltshire equations [8]. Reference [3] successfully demonstrates that these linear equations of motion can be used to establish a large family of relative orbits which require a small amount of fuel of maintain. However, the drawback of this method is that the resulting "natural" orbits ignore the nonlinear effects in that the method doesn't take into account the effects of higher order gravitational perturbations. Further, the results are generally limited to the special case

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