Model Predictive Control of Collinear Coulomb Spacecraft Formations

A model predictive control scheme to stabilize desired configurations of collinear Coulomb spacecraft formations is derived in this paper. The nonlinearities of the dynamics with respect to the input make this problem difficult to solve, computationally. It is shown that the nonlinearities in the input lead to a finite horizon optimization problem which is a nonconvex quadratically-constrained quadratic program (QCQP). A convex relaxation of the nonconvex QCQP is therefore derived which can be solved quickly using a convex optimization solver. A simulation of a four spacecraft formation is provided which demonstrates why optimizing over a prediction horizon is a prudent approach to Coulomb spacecraft formation control.