Recovery trajectory optimization of the solar-powered stratospheric airship for the station-keeping mission

Recently, the station-keeping of the stratospheric airship is an attractive topic due to its application to provide long-endurance communication and surveillance services. The motion of the stratospheric airship is sensitive to the wind because of the characteristics of large volume and low airspeed. When the wind speed exceeds the maximum airspeed, the airship may float out of the given station-keeping region. In such a case, how to recover to the station-keeping site is a necessary problem to consider. In this paper, the recovery trajectory optimization of the stratospheric airship is discussed and the purpose is to find the economical recovery flight trajectory to the station-keeping site. The trajectory optimization model is established by considering the motion model of the stratospheric airship, the atmospheric model, the wind field model, the solar radiation model, and the thermal model. To represent the exploitation of solar energy during the flight, the solar radiation collection problem is modeled for the airship whose hull is approximated by the double-ellipsoid geometry. Then the recovery trajectory optimization problem is formulated with constraints consideration and three recovery flight scenarios are put forward. The trajectory optimization problem is transformed into the nonlinear programming problem (NLP) by the orthogonal collocation and can be solved by the off-the-shelf NLP solver. The accuracy of the solution is improved by a modified ph-adaptive mesh refinement method. Two study cases are carried out to make a profound study of the recovery flight problem. In the first case, the basic characteristics of the flight trajectories using different recovery flight scenarios are compared and analyzed. Then the influence of the solar position on the recovery trajectory is discussed in the second case, which also gives some insights on the flight characteristics of the solar-powered stratospheric airship. The results of this paper may provide some important references for the station-keeping application of the stratospheric airship.