A comparison among classical and SDRE techniques in formation flying orbital control

A key point in formation flying mission design is represented by the accuracy and the cost of maintaining the requested orbital configuration. In fact, the relative geometry among spacecraft should be kept within tight limits in order to accomplish payload missions. At the same time, this effort requires to accommodate onboard the relevant amount of propellant, which should be correctly evaluated. The quest for optimal control strategy faces the non linear nature of the orbital dynamics, furthermore affected by perturbations that can be only modeled and therefore not perfectly known. As a result, traditional optimal strategies as the Linear Quadratic Controller (LQR), which design can be achieved under the hypothesis of simplified (as an example linearized) dynamics, not always meet the objective. Innovative approaches, like the State Dependent Riccati Equation (SDRE) technique, allow to better take into account, at an increasing level of approximations, the real dynamics. The paper presents extensive results of the simulations carried out for two different problems in formation flying control: the maintaining of a desired relative geometry and the acquisition of a requested configuration. A relevant point, also with respect to currently available literature, is the fact that the considered reference orbits have an eccentricity different from zero.