Coulomb control of a triangular three-body satellite formation using nonlinear model predictive method

In this paper, a nonlinear model predictive controller for a three-body Coulomb satellite formation is designed. For a formation of three satellites flying freely in deep space, actively controlled Coulomb forces are used to stabilize the formation shape to a desired triangular configuration. The control problem is challenging because the system is nonlinear and nonaffine, and the system constraints need to be taken into account. The proposed solution to the control problem is a nonlinear model predictive controller ensuring stability and optimal control performance while satisfying system constraints. Perfect convergence to desired triangular shape is not physically achievable with Coulomb forces alone because the triangle is not a natural equilibrium solution. Numerical simulations illustrate the effectiveness of the proposed control strategy.