This paper studies the distributed adaptive control of a team of underactuated flexible spacecraft under leader-follower architecture with the measurements of the rigid bodies only. By treating the flexible spacecraft as an underactuated Lagrange system, an adaptive control strategy is proposed with the feedback of the generalized coordinates, velocities and accelerations of the rigid bodies. Then an extended state observer is introduced to design a distributed adaptive controller without the measurement of the generalized accelerations

The vibration isolation system using a pair of oblique springs or a spring-rod mechanism as a negative stiffness mechanism exhibits a high-static low-dynamic stiffness characteristic and a nonlinear jump phenomenon when the system damping is light and the excitation amplitude is large. It is possible to remove the jump via adjusting the end trajectories of the above springs or rods. To realize this idea, the article presents a vibration isolation system with a cam–roller–spring–rod mechanism and gives the detailed numerical and experimental studies on the effects of the above mechanism on the vibration isolation performance. The comparative studies demonstrate that the vibration isolation system proposed works well and outperforms some other vibration isolation systems.