<div> <div> <div> <p>A control methodology to design and establish spacecraft formations is presented. The intuitive design of complex spacecraft formation geometry is achieved by utilizing two different sets of relative orbital elements derived from a linearization of the dynamics. These sets provide strong insights into the shape, size, and orientation of the relative trajectory and facilitate the design of relative orbits in addition to relative positions. An artificial potential function (APF) composed of an attractive potential for goal seeking and a repulsive potential for obstacle avoidance is constructed. The derivation of a control law from this APF results in a computationally efficient algorithm able to fully control the relative position and velocity of the spacecraft and therefore to establish spacecraft formations. The autonomous selection of some of the design parameters of the model based on fuel minimization considerations is described. An assessment of the formation establishment accuracy is conducted for different orbital perturbation as well as various degrees of thrust errors and state uncertainties. Then, the performance of the control algorithm is demonstrated with the numerical simulation of four different scenarios. The first scenario is the design and establishment of a 10-spacecraft triangular lattice, followed by the establishment of a 37-spacecraft formation composed of two hexagonal lattices on two different relative planes. The control method is used to illustrate proximity operations with the visual inspection of an on-orbit structure in the third scenario. Finally, a formation composed of four spacecraft arranged in a tetrahedron is presented.<br></p> </div> </div> </div>