Sliding mode control for decentralized spacecraft formation flying using geometric mechanics

This paper presents a sliding mode control-based tracking control scheme for decentralized 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 Euclidean space. A virtual leader trajectory, in the form of natural attitude and translational (orbital) motion of a satellite, is generated off-line. 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 a spacecraft and the virtual leader is described in terms of exponential coordinates on SE(3). A sliding surface is defined using the exponential coordinates and velocity tracking errors. A Lyapunov analysis guarantees that the spacecraft asymptotically converge to their desired state. This tracking control scheme is combined with a collision avoidance input generated from artificial potentials for each spacecraft, which includes information of relative positions of other spacecraft within communications range. Asymptotic convergence to the desired trajectory with this combined control law is demonstrated using a Lyapunov analysis. Numerical simulations are performed to demonstrate the successful application of this tracking control scheme for a decentralized formation maneuver with collision avoidance in the presence of model uncertainty and unknown external disturbances.