The use of propellant to maintain the relative orientation of multiple spacecraft in a sparse aperture telescope such as NASA's Terrestrial Planet Finder (TPF) poses several issues. These include fuel depletion, optical contamination, plume impingement, thermal emission, and vibration excitation. An alternative is to eliminate the need for propellant, except for orbit transfer, and replace it with electromagnetic control. Relative separation, relative attitude, and inertial rotation of the array can all be controlled by creating electromagnetic dipoles on each spacecraft, in concert with reaction wheels, and varying their strengths and orientations. Whereas this does not require the existence of any naturally occurring magnetic fields, such as the Earth's, such fields can be exploited. Optimized designs are discussed for a generic system and a feasible design is shown to exist for a five-spacecraft, 75-m baseline TPF interferometer. NomenclatureA c = conductor cross-sectional area a = coil radius c = conductor current density c 0 = constant defined in Eq. (8) i = current J = mission efficiency metric l c = conductor length m coil = electromagnetic coil mass m em = electromagnetic mass m sa = solar array mass m sys = total system mass m tot = total spacecraft mass m 0 = core bus and payload mass n = number of coil turns P = power P w = solar array specific power p c = conductor resistivity R = resistance r = conductor radius s = array baselinë x = spacecraft acceleration γ = mass fraction of total electromagnetic mass η = amp turns µ 0 = permeability of free space ρ = coil density = relative mission efficiency ω = rotation rate

This paper elaborates on the theory and experiment of controlling tethered spacecraft formation without depending on thrusters. In dealing with such underactuated systems, much emphasis is placed on complete decentralization of the control and estimation algorithms in order to reduce the dimensionality and complication. The nonlinear equations of motions of multi-vehicle tethered spacecraft are derived by Lagrange's equations. Decentralization is then realized by the diagonalization technique and its stability is proven by contraction theory. The preliminary analysis predicts unstable dynamics depending on the direction of the tether motor. The controllability analysis indicates that both array resizing and spin-up are fully controllable only by the reaction wheels and the tether motor, thereby eliminating the need for thrusters. Based upon this analysis, gain-scheduling LQR controllers and nonlinear controllers by feedback linearization have been successfully implemented into the tethered SPHERES testbed, and tested at the NASA MSFCs flat floor facility using two and three SPHERES configurations. The relative sensing mechanism employing the ultrasound ranging system and the inertial gyro is also described.

The MIT Space Systems Laboratory (SSL) has developed a testbed for the testing of formation flight and autonomous docking algorithms in both 1-g and microgravity environments. The SPHERES testbed consists of multiple microsatellites, or Spheres, which can autonomously control their position and attitude. The testbed can be operated on an air table in a 1-g laboratory environment, in NASA's KC-135 reduced gravity research aircraft and inside the International Space Station (ISS). SPHERES launch to the ISS is currently manifested for May 19 2004 on Progress 14P. Various types of docking maneuvers, ranging from docking with a cooperative target to docking with a tumbling target, have been developed. The ultimate objective of this research is to integrate the different algorithms into one program that can assess the health status of the target vehicle, plan an optimal docking maneuver while accounting for the existing constraints and finally, execute that maneuver even in the presence of simulated failures. In this paper, results obtained to date on the ground based air table using the initial version of the program will be presented, as well as results obtained from microgravity experiments onboard the KC-135.

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