Flatness-based trajectory optimization for spacecraft proximity relative motion in elliptic orbits

Abstract

This paper presents a novel computational framework integrating differential flatness and improved pseudospectral method for spacecraft proximity maneuver trajectory optimization. Based on the flatness property of the relative motion model, the trajectory optimization problem is formulated in the flat output space, eliminating the differential constraints and decreasing the dimension of design variables. The flat output optimization problem is ultimately transformed into a nonlinear programming problem via the improved Chebyshev pseudospectral method, which is modified by conformal map and barycentric rational interpolation techniques to enhance the numerical accuracy for the high-order derivatives of flat outputs. Numerical simulation reveals the feasibility and validity of the proposed computational framework.