Fast Terminal Sliding Mode Control of Underactuated Spacecraft Formation Reconfiguration

Abstract

Fast nonsingular terminal sliding mode controllers (FNTSMCs) are proposed for underactuated spacecraft formation reconfiguration without either the radial or the in-track thrust. A nonlinear dynamic model of underactuated spacecraft formation is developed, which is then linearized about circular reference orbits. Based on the linearized model, the system controllability is analyzed for either underactuated case. Due to the loss of control in a certain direction, the disturbances consisting of the linearization errors and external perturbations do not enter the system from the same channels as those of the control inputs, and therefore turn into unmatched disturbances. To achieve underactuated formation reconfiguration in the presence of unmatched disturbances, underactuated FNTSMCs are designed to indirectly render the system states convergent to the neighborhood of equilibrium by using the inherent coupling of these system states. Modified FNTSMCs are also presented to enhance the system performance in case of a sharp increase in the control inputs when the system states are away from the sliding surfaces. Meanwhile, the terminal convergent region of each system state is presented. The overall stability of the closed-loop system is guaranteed by a Lyapunov-based approach. Theoretical analyses are validated by numerical simulations that formation reconfiguration could still be achieved by the proposed controllers even with the loss of radial or in-track control.