Density-based Pattern Control For Spacecraft Swarms Around Circular Orbits

Multi-agent system is promising in space applications, because of its high flexibility and robustness. This work considers controlling a large-scale spacecraft swarm to generate a specified spatial pattern. Due to the fact that a swarm has hundreds of spacecraft, traditional control techniques are incapable of achieving an effective performance. The density-based feedback control via velocity fields has been used to tackle the control difficulties with a large number of spacecraft. This method has two parts, namely, local density estimation and velocity field design. To achieve collision avoidance during spacecraft maneuvering, the classical density estimation is augmented by a repulsive term. The Q-guidance scheme is used to track the desired velocity and to compute the control acceleration for each spacecraft. In addition, the desired density is also addressed in this paper to obtain a wide convergence region. The new desired density construction method guarantees that each agent can reach the target area and it also supports injections of distant new agents. To apply the density-based feedback control to circular Earth orbit, the periodic solution of Clohessy-Wiltshire (CW) equation is transformed into a new coordinate system that permits a nullified steady state velocity. Numerical simulations demonstrate the validity of the methodology.