Concept design and underactuated attitude control of a drag sail with distributed discrete elements

To address the environmental uncertainties and manipulation challenges of traditional membrane sails for Low Earth Orbit (LEO) spacecraft, we propose the concept design and attitude control method for a drag sail with distributed discrete elements. This proposed system, composed of a 500-element blade array driven by simplified binary (0–1) control units, enhances the system’s robustness against partial blade failures and disturbances from intense solar activity. First, we establish a dynamic model based on free molecular flow theory. By systematically traversing the discrete control combinations of the blade elements, we reveal a distinct planar grid-like characteristic of the achievable moment set, which confirms the underactuated nature of the system. To address parametric perturbations caused by significant fluctuations in thermospheric density and crosswind disturbances, we design a Tube-based Model Predictive Control (TBMPC) scheme. The nonlinear control problem is transformed into two subproblems: pre-computing a nominal trajectory offline and regulating an error system online within a bounded tube. Numerical simulations demonstrate that the proposed system achieves three-axis attitude stabilization with a pointing error below 0.1° under complex space environments involving inertia uncertainty, thermospheric crosswinds, and sudden atmospheric density variations caused by solar activity. These results validate the effectiveness of the proposed system in complex LEO environments and indicate its feasibility for propellantless attitude control applications.