Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight by Oscillation Synchronization

Abstract

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.

Hybrid fuzzy sliding mode control for motorised space tether spin-up when coupled with axial and torsional oscillation

“…A strategy for the control of the librations of a tethered satellite system in elliptic orbits using tether length control, which drives the system to controlled periodic libration trajectories was suggested by Williams in 2006(Williams 2006a, 2006bWilliams et al 2006). In 2007 and 2008, Chung, Slotine and Miller (Chung et al 2007;) proposed a series of papers to describe a fully decentralised linear and nonlinear control law for spinning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics.…”