Trajectory optimization for collaborative recovery of parafoil systems using unmanned vessel

Traditional trajectory optimization methods for the parafoil system set fixed-point landing as the objective. However, in recent payload fairing recovery missions, the recovery system comprising two parafoils is collaboratively recovered by a mobile vehicle, posing new challenges to the current trajectory optimization technique. In order to recover two parafoil systems autonomously with an unmanned surface vessel, this paper presents a trajectory optimization framework composed of three following component processes consecutively. Firstly, a feasibility judgment algorithm based on reachable boundary estimation is designed to determine the possibility of recovering two parafoil systems. Secondly, the decoupled-then-simultaneous strategy is proposed to enhance the convergence of solving the collaborative recovery problem. Thirdly, the finite-element collocation approach is utilized to convert the formulated trajectory optimization problems into nonlinear programming (NLP) problems, which are solved by a highly efficient NLP solver. Simulation results show that the proposed trajectory optimization framework can efficiently generate the optimal trajectory for recovering two parafoil systems with a vessel.