Optimal control problem for a fixed-time spatial spacecraft turn

Аuthors

Levsky M. V.

Khrunichev State Research and Production Space Center, 18, Novozavodskaya St., Moscow, 121087, Russia

e-mail: niiks@knrunichev.com

Abstract

Optimal control problem is discussed as applies to a fixed-time spatial spacecraft turn. A functional is minimized interpreting as a propellant consumption. An analytical solution is derived for the stated problem. The optimal solution belongs to a class oj two-impulse control. Under this control spacecraft turns along the so called free motion trajectory. The initial control problem is reduced to solution of three problems including acceleration of the spacecraft needed to reach the necessary angular momentum, uncontrolled rotation of the spacecraft, and damping of angular velocity. The complete solution of the reorientation problem in the closed form is given for dynamically symmetric spacecraft. This solution allows us to use the control method in practice. Simulation results are presented to demonstrate practical realizability of the suggested control algorithm.

Keywords:

spacecraft, motion control, quaternion, Pontryagin maximum principle, functional, controlling function, dynamics, optimal motion