Three-dimensional optimal control of orbit transfer for an electrodynamic tethered subsatellite

A nonlinear optimal control scheme is presented for solving the orbit transfer problem of a tethered subsatellite system on an inclined orbit. The scheme accounts for the three-dimensional motions of the system as well as the complex state-control constraints. The nonlinear optimal control problem is solved by discretizing it first, based on the Gauss pseudospectral method, and then solving the resulting large-scale optimization problem via nonlinear programming. The presented scheme is used to find the optimal solutions for the transfer time, the system states, the tensional force and the electric current, and the effects of orbit inclination on the optimal solutions are also evaluated through a summary discussion. It is demonstrated through the case studies that the subsatellite can be maneuvered, under the mission-related constraints, from a nominal equilibrium position (below the mother satellite) to another equilibrium one (above the mother satellite) by changing only the tensional force and the electric current.