Abstract Retrieval of tethered satellite systems is an unstable process. Several complex control methods have been proposed to stabilize this process. Recently, a simple, heuristic bang–bang control algorithm was found to be effective at significantly reducing libration angles by introducing short periods of extension during the retraction phase. In this paper, an analytical method is derived for the determination of effective retraction/extension speeds for bang–bang length rate control. The performance of the derived control profiles is validated by comparison to optimized two-switch bang–bang profiles. Additionally, particle swarm optimization is leveraged to optimize switch times and tether length rates for control profiles with increased numbers of switches. It is verified that the analytical methodology for control speed selection can be employed to define both extension/retraction and retraction-only controls. It is determined that speeds of retraction and extension contribute greatly to the libration motion of the tethers, and that proper speed selection is especially critical when the tethered satellite system is near its equilibrium state. Accurate switch timing is also found to be particularly important, as slight variations can significantly affect the tether libration response. While an increased number of switches is found to improve the tether response and to reduce the retraction time, the achievable benefits may not be sufficient to justify the increased complexity.

Highlights • Length-rate control is proposed for libration reduction during retrieval. • A method for effective length-rate selection in bang–bang control is derived. • The analytical method approximates well optimal length-rates in bang–bang control. • Two switches are sufficient to reduce oscillations, with or without extension. • Particle swarm optimization is used to investigate multi-switch bang–bang control.