Deployment/retrieval optimization for flexible tethered satellite systems

A methodology for deployment/retrieval optimization of tethered satellite systems is presented. Previous research has focused on the case where the tether is modeled as an inelastic, straight rod for the determination of optimal system trajectories. However, the tether shape and string vibrations can often be very important, particularly when the deployment/retrieval speed changes rapidly, or when external forces such as aerodynamic drag or electrodynamic forces are present. An efficient mathematical model for flexible tethered systems is first derived, which treats the tether as composed of a system of lumped masses connected via inelastic links. A tension control law is presented based on a discretization of the tether length dynamics via Chebyshev polynomials. A scheme that minimizes the second derivative of length over the trajectory based on physically meaningful coefficients is presented. This is utilized in conjunction with evolutionary optimization methods to minimize the rigid body and flexible modes of the system during deployment/retrieval. It is shown that only a very small number of parameters are required to generate accurate trajectories. The results are compared to the case where the tether is modeled as a straight rod.