Attitude Maneuver of Dual Rigid Bodies Spacecraft Using hp-Adaptive Pseudo-spectral Method

Abstract

The spatial attitude optimal control problem of a spacecraft system with dual rigid bodies interconnected by a frictionless universal joint is considered. Based on the conservation of angular momentum, the dynamical model of the system is deduced using Quaternion. For there exists non-square matrix in the dynamical equation caused by the representation of Quaternion, the first-order derivative of the scalar section in Quaternion is employed to serve as a pseudo-control input for the system. Then the motion planning problem of the system can be discretized into a nonlinear programming problem based on hp-adaptive Radau pseudo-spectral method. Comparing with the previous works, the hp-adaptive method and the pseudo-control input is combined together to deal with the potential non-square matrix. Also as a contrast to the use of pseudo-control input employed in hp-adaptive method, another method (the Radau pseudo-spectral method) and the theory of pseudo-inverse matrix is adopted. The effectiveness of hp-adaptive method on the system expressed by pseudo-control input and the rationality of the Radau pseudo-spectral method on the system expressed by pseudo-inverse matrix is demonstrated and verified perfectly through numerical simulation.