Three-dimensional optimal deployment of a tethered subsatellite with an elastic tether

This paper presents the nonlinear optimal control for the deployment process of an elastically tethered subsatellite model, which involves not only the usually addressed in-plane motion, but also the out-of-plane motion. All the nonlinearities in the system model and the mission-related state-control constraints are taken into consideration. Instead of the commonly used state-space model, a second-order differential inclusion formulation is exploited in this paper to achieve a significant reduction of the number of system variables. The optimal control is solved by discretizing the optimal control problem first and then solving the resulting large-scale optimization problem. The case studies in the paper demonstrate well the performance of the proposed strategy.