Nonlinear Control for Proximity Operations Based on Differential Algebra

Abstract

A new algorithm based on differential algebra (DA) is proposed to obtain a high order Taylor expansion of State-Dependent Riccati Equation (SDRE) solution. The main advantage of this approach is that the sub-optimal solution of a class of non-linear optimal control problem, 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 well-known algorithm for the SDRE solution. Relative position tracking and attitude synchronization problem involving in docking maneuvering operations between two Earth satellites is investigated. Particularly, two possible docking scenarios are simulated by using a specific platform designed by DLR (Deutsches Zentrum für Luft- und Raumfahrt) Institute of Space Systems to emulate the satellite motion on ground. The experiments show the effectiveness of proposed DA-based algorithm and the potential computational benefit when it runs on a real hardware.