Adaptive fixed-time relative position tracking and attitude synchronization control for non-cooperative target spacecraft fly-around mission

In this paper, the problem of adaptive fixed-time tracking control for non-cooperative target spacecraft fly-around mission in the presence of the parameter uncertainties and external disturbances is investigated. Firstly, a novel and effective 6 DOF relative motion dynamic model constructed by relative position motion model expressed in the LOS frame and attitude dynamic model described by Modified Rodriguez parameters (MRPs) is firstly established. Subsequently, a new modified nonsingular fast terminal sliding mode (MNFTSM) with bounded convergence time in regardless of the initial states is designed, which not only can circumvent the singularity problem effectively, but also has the advantages of FTSM. By employing MNFTSM and adaptive techniques, two continuous adaptive fixed-time nonsingular fast terminal sliding mode (AFNFTSM) control laws are proposed, which can eliminate the chattering phenomenon and do not require precise knowledge of the mass, inertia matrix. Rigorous proofs show that both of two AFNFTSM control laws can guarantee that the relative position and attitude errors can converge to the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.