Optimal Orbit Transfer of a Spacecraft with Fixed Length Tether

Abstract

Most control problems for tethered spacecraft have dealt only with dynamic interactions between the tether and subsatellite motion and the attitude motion of the base spacecraft, ignoring translational dynamics. In this paper, we focus on control of the translational motion of an orbiting tethered spacecraft. The motions of the base spacecraft, the tether and the subsatellite are assumed to occur in a fixed orbital plane. The tether is modeled as a massless, taut, inextensible cable that connects the base spacecraft and the subsatellite. The base spacecraft is assumed to be fully actuated by propulsive forces but there is no direct actuation of the tether or the subsatellite. Under these assumptions the equations of motion for a tethered spacecraft are derived, and linearized equations that characterize perturbations from a circular orbit are obtained. For a specific orbit transfer problem, we find an optimal solution that transfers the spacecraft from one circular orbit to another circular orbit while at tenuating the unactuated tether motion. A two-point boundary value problem is obtained and solved to determine a control that minimizes the propulsive control forces. A simulation example shows the effectiveness of the designed control scheme.