Attitude synchronization of multiple spacecraft with cone avoidance constraints

In this paper, consensus theory and optimization theory are combined for distributed attitude control of a team of communicating spacecraft. By using the Laplacian matrix of the communication graph and a semidefinite program, a synthesis of a time varying optimal stochastic matrix P is done. This matrix P, is used to drive given initial attitudes of the spacecraft to a consensus attitude. The concept of quadratically constrained attitude control (Q-CAC) is then employed to generate an optimal collision-free attitude trajectory along the consensus attitude trajectory. This solution technique is used to simulate coordinated attitude rendezvous, and attitude formation acquisition of multiple spacecraft, in the presence of dynamic obstacles. A Lyapunov-based stability analysis, together with the simulation results are also provided, to demonstrate the effectiveness of the approach.