In-Plane Payload Capture with an Elastic Tether

The capture of payloads using tethers is a challenging task from a control point of view. In previous studies on coplanar capture, the precapture control design has been achieved by assuming that the tether is inextensible. However, the effect of tether longitudinal vibrations can cause errors in the position and velocity of the tether tip. Furthermore, the extra mass at the tip of the tether can induce longitudinal vibrations with significant amplitude that ultimately cause the tether to become slack. A guidance scheme based on optimal control methodology that can achieve rendezvous with a payload using a longitudinally flexible tether is demonstrated. Rather than treating the precapture and postcapture phases separately, an integrated control scheme is developed that successfully guides the tether to achieve rendezvous with a payload and then simultaneously damps the tether librations and longitudinal vibrations. Closed-loop performance of the system is demonstrated using a receding-horizon control strategy.