This paper proposes a robust control allocation for the capture control of the space inertial sensor’s test mass under overcritical conditions. Uncertainty factors of the test mass control system under the overcritical condition are analyzed first, and a 6-DOF test mass dynamics model with system uncertainty is established. Subsequently, a time-varying weight function is designed to coordinate the allocation of 6-DOF generalized forces. Moreover, a robust control allocation method is proposed to distribute the commanded forces and torques into individual electrodes in an optimal manner, which takes into account the system uncertainties. This method transforms the robust control allocation problem into a second-order cone optimization problem, and its dual problem is introduced to simplify the computational complexity and improve the solving efficiency. Numerical simulation results are presented to illustrate and highlight the fine performance benefits obtained using the proposed robust control allocation method, which improves capture efficiency, increases the security margin and reduces allocation errors.

A distributed six-degree-of-freedom (6-DOF) cooperative control for multiple spacecraft formation is investigated considering parametric uncertainties, external disturbances, and time-varying communication delays. Unit dual quaternions are used to describe the kinematics and dynamics models of the 6-DOF relative motion of the spacecraft. A distributed coordinated controller based on dual quaternions with time-varying communication delays is proposed. The unknown mass and inertia, as well as unknown disturbances, are then taken into account. An adaptive coordinated control law is developed by combining the coordinated control algorithm with an adaptive algorithm to compensate for parametric uncertainties and external disturbances. The Lyapunov method is used to prove that the tracking errors converge globally asymptotically. Numerical simulations show that the proposed method can realize cooperative control of attitude and orbit for the multi-spacecraft formation.

In order to meet the position and attitude requirements of spacecrafts and test masses for gravitational-wave detection missions, the attitude-orbit coordination control of multiple spacecrafts and test masses is studied. A distributed coordination control law for spacecraft formation based on dual quaternion is proposed. By describing the relationship between spacecrafts and test masses in the desired states, the coordination control problem is converted into a consistent-tracking control problem in which each spacecraft or test mass tracks its desired states. An accurate attitude-orbit relative dynamics model of the spacecraft and the test masses is proposed based on dual quaternions. A cooperative feedback control law based on a consistency algorithm is designed to achieve the consistent attitude tracking of multiple rigid bodies (spacecraft and test mass) and maintain the specific formation configuration. Moreover, the communication delays of the system are taken into account. The distributed coordination control law ensures almost global asymptotic convergence of the relative position and attitude error in the presence of communication delays. The simulation results demonstrate the effectiveness of the proposed control method, which meets the formation-configuration requirements for gravitational-wave detection missions.