Robust adaptive gain nonsingular fast terminal sliding mode control for spacecraft formation flying

This paper deals with an adaptive gain nonsingular terminal sliding mode control (TSMC) approach for the tracking control of spacecraft formation flying (SFF) in a leader-follower based framework. A nonlinear terminal sliding surface has been proposed in the present case for fast and finite time convergence of the trajectories, with feasible fuel cost. Moreover, it is free from singularity problem, which is inherent in conventional TSMC. A fast reaching law has been utilized to further improve the speed of convergence. To deal with the disturbances and uncertainties in the physical system, the parameters of the reaching law are updated using a novel adaptive tuning algorithm, derived based on Lyapunov stability theory. The hyperbolic tangent function based fast reaching law, with adaptively updated gains, can reduce the chattering inherent in conventional TSMC. The proposed strategy has been validated using numerical simulations, based on nonlinear SFF dynamics, with external disturbances and added random noise. The reference trajectories are generated using linearized Hill-Clohessy-Wiltshire (HCW) equations.