Distributed Collision Free Trajectory Optimization for the Reconfiguration of a Spacecraft Formation

In recent years there has been an increasing interest in formation flying with many lightweight spacecraft, as satellite missions can potentially become cheaper and more flexible. An example of such mission is the Silicon Wafer Integrated Femtosatellites mission, consisting of 100 to 1000 spacecraft with a mass of 0.1 kg. Due to modest control capabilities of the spacecraft and a higher risk of collisions, the requirements on trajectory optimization algorithms are increased. In this thesis a distributed trajectory optimization algorithm is developed which minimizes the required fuel for collision-free reconfiguration trajectories. First, the balance between cooperation in the formation and fuel consumption is investigated: with less cooperation the trajectory optimization algorithm can easily be distributed but the resulting fuel consumption is higher. The problem can also be distributed using dual methods, which can result in the same solution as a centralized algorithm. In literature both dual decomposition and the Alternating Direction Method of Multipliers (ADMM) in consensus form are proposed to solve this specific problem. In this thesis it is demonstrated that the Jacobian decomposition of the Augmented Lagrangian Method outperforms both dual decomposition and ADMM in terms of convergence rate. Furthermore it is shown that this algorithm does also converge in an asynchronous setting. Finally, the synchronous algorithms are significantly accelerated using Heavy Ball acceleration, the Fast Iterative Shrinkage-Threshold Algorithm and Anderson Acceleration.Mechanical Engineering | Systems and Contro