Optimal control of orbit transfer for a tethered subsatellite system

This article presents a nonlinear optimal control scheme for the orbit transfer problem of a tethered subsatellite model in the orbit plane. The scheme takes into consideration the complex state-control constraints and elasticity of tether. A combination of the Gauss pseudospectral method and costate mapping theorem is exploited in this work to find an optimal trajectory that guides the subsatellite from one nominal equilibrium position to another by changing the tensional force of the tether. The nonlinear optimal control problem is solved by first discretizing it and then solving the resulting large-scale optimization problem via nonlinear programming. The optimal control force and transfer trajectory are solved through a case study. Interestingly, the controlled trajectory of the transfer process is geometrically symmetric about the midpoint of the time interval. Finally, the optimality of the solutions is also validated through a brief analysis of costate information.