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Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight

This paper describes a fully decentralized nonlinear control law for spinning tethered formation flight, based on 
exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated 
by oscillation synchronization in biological systems, we use contraction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of spacecraft, as well as the three inline configuration. The convergence result is global and exponential. Numerical simulations and experimental results using the SPHERES testbed validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics.