Spacecraft Coupled Tracking Maneuver Using Sliding Mode Control with Input Saturation

Abstract

This paper presents a sliding mode control scheme on for autonomous spacecraft formation flying via a virtual leader state trajectory. The configuration space for a spacecraft is the Lie group SE(3), which is the set of positions and orientations of the rigid spacecraft in three-dimensional (3D) Euclidean space. A virtual leader trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is generated offline. Each spacecraft tracks a desired relative configuration with respect to the virtual leader in a decentralized and autonomous manner to achieve the desired formation. The relative configuration between each spacecraft and the virtual leader is described in terms of exponential coordinates on SE(3). A new feedback control scheme is proposed for coupled translational and rotational maneuver using a new sliding surface, which is defined as the exponential coordinates and velocity tracking errors such that the sliding surface converges to zero without explicit reference states, unlike conventional control schemes where explicit reference states are used. The asymptotic convergence of the sliding surface and tracking errors are guaranteed, in the presence of unknown external disturbances and uncertain system parameters, and an auxiliary signal is generated to deal with control saturation. The convergence and stability of the closed-loop system are proven within a Lyapunov framework. Finally, numerical simulations are presented to validate the developed control scheme.