Analytical and numerical investigations on spacecraft formation control by using electrostatic forces

• This paper focuses on the electrostatic control for spacecraft formation flying.
• A Lyapunov based control strategy is presented and analyzed analytically.
• Two different virtual links selection strategies are presented.
• An optimal charge distribution strategy is presented
• Numerical results prove the suitability of the approach to a 4-spacecraft formation.

The paper investigates some analytical and numerical aspects of the formation control exploited by means of inter-spacecraft electrostatic actions. The analysis is based on the evaluation and check of the stability issues by using a sequence of purposely defined Lyapunov functions. The same Lyapunov approach can also define a specific under-actuate control strategy for controlling selected “virtual links” of the formation. Two different selection criteria for these links are then discussed, showing the implications on the control chain. An optimal charge distribution strategy, which assigns univocally the charges to all the spacecraft starting from the charge products computed by the control, is also presented and discussed. Numerical simulations prove the suitability of the proposed approach to a formation of 4 satellites.