Abstract
This paper considers the problem of relative motion control involved in a leader-follower formation keeping mission. More specifically, center of mass dynamics of two Earth orbiting satellite is modeled, including the nonlinearity due to Earth oblateness. Next, the differential algebra is exploited to compute an high order Taylor expansion of the State-Dependent Riccati Equation (SDRE) solution. This new approach reduces the computational cost of the online Algebraic Riccati Equation solution required by SDRE algorithm; in fact, the differential algebraic formulation gives a polynomial representation which can be directly evaluated for SDRE solutions or exploited to define an initial first guess for iterative SDRE algorithms.