Nonlinear Control for Proximity Operations Based on Differential Algebra

A new algorithm based on differential algebra is proposed to obtain a high-order Taylor expansion of the state-dependent Riccati equation solution. The main advantage of this approach is that the suboptimal solution of a class of nonlinear optimal control problems, characterized by a quadratic cost function and an input-affine plant model, is obtained by a mere evaluation of a polynomial expression, reducing the computational effort due to a well-known algorithm for the state-dependent Riccati equation solution. A relative position tracking and attitude synchronization problem involving docking maneuvering operations between two Earth satellites is investigated. Particularly, two possible docking scenarios are simulated by using a specific platform designed by DLR, German Aerospace Center, Institute of Space Systems to emulate the satellite motion on ground. The experiments show the effectiveness of the proposed differential-algebra-based algorithm and the potential computational benefit when it runs on real hardware.