Infinite-horizon control for retrieving a tethered subsatellite via an elastic tether

This paper presents a nonlinear optimal control scheme for the retrieval of an elastically tethered subsatellite model. The scheme accounts for in-plane and out-of-plane motions. The control design is formulated over an infinite horizon by using a domain-transformation technique and all the nonlinearities in the system model are taken into consideration. Two Legendre pseudospectral algorithms are explored to find an optimal trajectory that guides the subsatellite from an initial position far from the spaceship into a final position close to the spaceship. The first approach involves direct transcription and nonlinear programming, and the second one is based on the method of quasi linearization and matrix algebra. The case studies in the paper well demonstrate the effectiveness and dominant real-time merits of the proposed strategies.