An on-orbit drag-free control technique for spaceborne gravitational wave detection missions was discussed. Based on the analysis and design of a possible future geocentric orbit detection mission, the relative motion dynamics and coupling characteristics between the spacecraft and mass blocks of an on-orbit drag-free system with with two test masses were modeled. At the same time, the performance index and perturbation of the drag-free system in the mission were preliminarily analyzed, and a relative translational control law based on frequency domain H_∞ optimal control theory was designed. Numerical simulation results show that when the test masses of the two-test-mass on-orbit drag-free system are arranged according to the breathing angle of laser rangefinder, without a fixed tracking point strategy and without suspension control input along the non-sensitive axis, the spacecraft can achieve tracking of the reference point while meeting the frequency domain performance index of the system. At the same time, the time domain displacement of each test mass can be controlled to the micron level, thus obtaining the pure gravitational reference required by the mission.

To enhance the air–water adaptability of the aerial-aquatic vehicles (AAVs), an improved tandem twin-rotor AAV design is proposed based on the characteristics and application requirements of air–water cross-domain movement. Computational fluid dynamics (CFD) software was used to simulate the underwater cruising state and dynamic water entry process of the tandem twin-rotor AAV. Results indicate that the underwater cruise resistance of the improved tandem twin-rotor AAV is relatively small. Among them, the two sets of tandem air power systems account for a relatively large proportion of the underwater drag, about 29.8%, while the drag reduction achieved by improving the head shape is around 15.4%. The head shape, water entry angle and speed have a great influence on the water entry trajectory and attitude of the tandem twin-rotor AAV. Following improvement, the tandem twin-rotor AAV demonstrates an enhancement in reducing the deviation of the water entry trajectory, mitigating water surface ricochet and enhancement of water entry depth to a certain extent. The inclination angle should be in the range of 20–30° to alleviate unfavorable outcomes, including prolonged water entry time caused by water surface ricochet at lower entry angles, while concurrently mitigating the heightened impact pressure resulting from steeper entry angles. Higher entry velocities lead to greater impact pressures, necessitating careful consideration of water entry depth and impact pressure to prevent adverse effects on structural integrity.

The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft. The test mass must be released to the cage center of the inertial sensor accurately and quickly. This paper proposes a minimum-time capture control method for the test mass release phase of drag-free spacecraft. An analytical solution of optimal control is derived based on Pontryagin’s minimum principle and the linearized dynamics model of the test mass during the release phase. The parameters of the analytical solution are initially guessed with an approximate linear solution of the test mass dynamics model and are slightly modified by using differential correction. Compared with the exact numerical solution by the hp-adaptive pseudospectral method, the analytical solution is proved to be minimum-time. Numerical simulation shows that the proposed control method quickly captures the test mass to the cage center of the inertial sensor. The capture time to stabilization is only half that of the traditional controller.

This paper aims to propose a switching rule to improve the efficiency and stability of the mode switching process for the drag-free satellite. The switching rules will ensure the stability of the different controllers during the switching process. Unlike traditional satellite switching control, the inner loop and the outer loop of the drag-free satellite are strongly coupled. The drag-free satellite not only needs to consider the controller design in the inner loop but also the controller design of the outer loop. In the outer loop, a Proportion Integration Differentiation control method is adopted to design the controller. In the inner loop, considering the release error effect of the test mass, a nonlinear sliding-mode control is employed as a controller before the mode switch. The H∞ mixed-sensitivity controller, to improve the robustness of the system and solve the problem of controller saturation, is designed after the mode switch. In the stability analysis of the switching system, the piecewise continuous Lyapunov function method is adopted. The region of attraction, which is used as the switching rule, is calculated based on the sum of squares. The obtained results demonstrate that the proposed switching rule satisfies the control accuracy and system stability.