Asymptotic Tracking Control for Spacecraft Formation Flying with Decentralized Collision Avoidance

This paper presents a tracking control scheme for spacecraft formation flying with a decentralized collision-avoidance scheme, using 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 in three-dimensional Euclidean space. A virtual leader trajectory, in the form of attitude and orbital motion of a virtual satellite, is generated offline. Each spacecraft tracks a desired relative configuration with respect to the virtual leader in an 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 continuous-time feedback tracking control scheme is designed using these exponential coordinates and the relative velocities. A Lyapunov analysis guarantees that the spacecraft asymptotically converge to their desired state trajectories. This tracking control scheme is combined with a decentralized collision-avoidance control scheme 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 simulation results verify the successful application of this tracking control scheme to a formation maneuver with decentralized collision avoidance.