Evaluation of control strategies for spacecraft electrostatic formation keeping

The adoption of electrostatic (Coulomb) forces to acquire and maintain the relative configuration in a spacecraft formation is a topic of significant current research interest. Recent technological advances allow the independent charging of each platform enabling the control of their relative position by means of attractive and repulsive forces. This technique could offer high precision, high equivalent specific impulse, and long operational life time. In real space applications, the effectiveness of the electrostatic force should be limited by the plasma shielding effect. The commanded separation among the spacecraft is ruled by the Debye length parameter, which is larger at higher orbital altitudes. MEOs and GEOs are therefore the preferred scenarios for this control technique. Open-loop electrostatically controlled formations should be dynamically unstable, and a feedback control law is needed to stabilize their motion. Indeed, this paper proposes a comparison among possible different strategies to implement this technique. Due to the non-linearity of the governing equations of motion, the problem needs to be suitably formulated to allow the application of some traditional control laws. The classical proportional derivative technique, as well the optimal LQR approach are considered, together with a Lyapunov-based strategy. The more recent State Dependent Riccati Equation (SDRE) control approach, especially interesting for non-linear system, is also applied. The findings of numerical simulations relevant to a small spacecraft cluster in GEO are discussed in depth.