Cooperative Orbital Control of Multiple Satellites via Consensus

In space systems consisting of a large number of satellites, coordinating orbits among satellites is necessary throughout the entire mission lifetime. Although previous works mainly focused on the boundedness of relative motion between satellites in the group, in this paper, an extra degree of freedom is also addressed in order to manipulate an arbitrary number of orbital elements, which is represented as coordinating a general orbital transfer and an in-space assembly. The underlying concept is using consensus theory to characterize the properties of the control objective as in a multiagent system. To that end, this paper assumes that the communication in the networked satellite system is represented as an undirected graph, and then implements the governing system dynamics in a control-affine form as described by the Gauss's variational equations. For the general orbital transfer problem, an edge-error-based controller is developed and proven asymptotically stable. Definitions of error functions are also investigated to understand the behavior of developed controllers. Several strategies for assembly control are discussed, namely, via changing of variables or in a two-phase control process based on the dynamical structure. Numerical simulations are performed to validate the analysis and demonstrate the results.