Optimal relative trajectory generation and tracking control of formation flying

The fuel consumption and tracking errors are two major concerns in the formation flying. Reasonably-designed reference trajectories and control algorithms can help to save fuel and minimize tracking errors. The full relative dynamics of the follower with respect to the leader and the tracking error dynamics are derived. Based on the unperturbed form of the full relative dynamics, the optimal trajectory generation problem is transformed into a nonlinear programming problem using LGR(Legendre-Gauss-Radau) method and thus can be solved numerically. An H_∞ control law with pole placement is developed to achieve reasonable tracking errors and fuel consumption. The controller can track the reference trajectories under Earth gravity perturbation, environmental disturbances and leader maneuver. Simulation results show the efficiency of the main results.