Deployment of tethered three-body system in elliptic orbit under low-thrust

An energy-based tether deployment control algorithm is proposed for a three-body system in elliptic orbit with maneuvering thrust. This methodology considers both orbital eccentricity and thrust to accurately predict post-deployment tether libration angles. Next, a performance function is introduced to pre-design the system behavior. Virtual loads and a pseudo-potential energy function are then incorporated to enhance transient and steady-state performance. Virtual loads significantly increase the interaction between the actuated tether length subsystem and the unactuated libration component. The stability of the system is rigorously proven mathematically. Finally, numerical simulations verified the effectiveness of the proposed control algorithm.