Unified Performance Control of Spacecraft Attitude Tracking With Relaxed Quaternion Conditions

For quaternion-based spacecraft attitude tracking control, most existing prescribed performance control (PPC) schemes require that the scalar part of the error quaternion remain non-zero during the attitude maneuvering, meaning that only local operational range is allowed, which is too restrictive from practical point of view. Differently, by imposing a novel performance constraint, a piecewise virtual control law without singular term is designed, which is singular in most of the existing control schemes if the scalar part of the error quaternion is equal to zero, thus naturally obviating the classical assumption and resting in a global solution. Moreover, the unified prescribed performance constraints are imposed on both the attitude error and virtual angular velocity error. With such design, the performance boundary is uniform with respect to initial error, which implies that off-line computation of performance boundary for initial error can be avoided. Particularly, the initial value of the virtual angular velocity error is difficult to obtain off-line. In addition, by utilizing neural network approximation method, the Nussbaum gain technique and a positive integrable function, the proposed control is able to achieve asymptotic attitude tracking in the presence of inertia uncertainties, external disturbances and actuators fault, as rigorously authenticated by Lyapunov stability theory. A numerical example is provided to verify the effectiveness of proposed control scheme.