Control Synthesis for an Underactuated Cable Suspended System Using Dynamic Decoupling

This article studies the dynamics and control of a novel underactuated system: a ball and plate system suspended by a team of quadrotors via cables. The plate is sought to be horizontally stabilized at a certain height, with the ball stabilized at the center of mass of the plate. The freely moving ball adds 2 degrees of underactuation to the system. The design proceeds through a decoupling of the quadrotors and the plate dynamics. Through a partial feedback linearization approach, the attitude of the plate and the translational height of the plate is initially controlled, while maintaining a bounded velocity along the $y$ and $x$ directions. These inputs are then synthesized through the quadrotors with a backstepping and timescale separation argument based on Tikhonov's theorem.