Nonlinear Control of Formation Flying with State Constraints

The feasibility of a nonlinear state-dependent Riccati equation (SDRE) control design for relative position control of satellite formations is demonstrated. The design can include options for collision avoidance. Although there is no formal proof of the asymptotic stability of the closed-loop system, the necessary conditions for stability are verified and the test cases presented show indeed stable dynamics. Adoption of the SDRE technique requires a minimal effort to set up the state-dependent coefficient form however, once this is defined, it is rather easy to design the controller and tune its performances. The design method proposed can be extended to a higher number of satellites for the formation-keeping control, whereas a direct extension of the collision avoidance is feasible only if there is a guarantee that only one pair of satellites at a time are at risk of collision.