Formation of a rotating ring-shaped three-body tethered nanosatellite system with limited control

The problem of forming a rotating ring-shaped tethered system consisting of three nanosatellites is considered. To analyze the dynamics of the tether system, a mathematical model is developed in the orbital coordinate system using the Lagrange method. Using the sliding mode control method, two control programs for the deployment of tethers are proposed, in which tether tensions and thrust forces created by low-thrust engines are used as controls. In the first control program, the control actions are directly limited by the permissible limits of tether tensions forces and thrust forces, and when designing the second control program, an auxiliary dynamic system is added into the control system, which introduces control corrections that take into account the saturation effect. The stability of motion of the tethered formation system for both control programs is investigated using the Lyapunov theory. The results of numerical simulations confirmed the possibility of using the proposed control programs for the formation of a rotating triangular tethered system in the form of a regular triangle in the presence of disturbances and with account of the given constraints.