Optimal control of nanosatellite fast deorbit using electrodynamic tether

This paper proposes a piecewise two-phased optimal control scheme for fast nanosatellite deorbit by a short electrodynamic tether. The first phase concerns the open-loop control trajectory optimization, where the optimal control problem is formulated only for the tether libration motion by assuming the slow-varying orbital elements of the electrodynamic tether system as constant within a discretized interval. The second phase deals with the closed-loop optimal control for tracking the derived optimal reference trajectory subject to multiple major orbital perturbations. The finite receding horizon control method is used in the optimal trajectory tracking. Both optimal control problems are solved by a direct collocation method based on the Hermite-Simpson method using discretization schemes with coincident nodes. The resulting nonlinear programming problem significantly reduces the problem size and improves the computational efficiency. Numerical results for fast nanosatellite deorbit by an electrodynamic tether in both equatorial and highly inclined orbits show the proposed method achieves high control accuracy and efficiency.