Dynamics and Control of Tethered Formation Flight Spacecraft Using the SPHERES Testbed

Abstract

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.

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