A collaborative trajectory planning method for multi-stage boosting vehicles

Regarding the investigation of a cluster of flight vehicles by using multi-stage solid rocket boosters， the research is implemented for the collaborative trajectory optimization. In order to facilitate the collaborative task during the re-entry phase and ensure the optimum energy performance of the cluster by eliminating individual state errors， a multi-layer collaborative trajectory optimization algorithm is proposed， which is based on the hp adaptive pseudo-spectral method. By designing different planning models in the top， middle and bottom layers， the algorithm achieves time-coordinated reentry. Firstly， a trajectory planning model is established， which is based on the flight characteristics of the booster phase， and sparse collocation points are used to determine the cluster's temporally coordinated interval. Then， the single-vehicle planning model is extended in dimension， and after introducing constraints on the rate of change of control variables， the hp adaptive pseudo-spectral method is applied to quick resolving for the desired terminal state. Finally， additional collocation points are incorporated for refined optimization. Simulation results demonstrate the effectiveness of the proposed method by enabling rapid and effective optimization of the flight vehicle cluster， which meets the requirements for collaborative trajectory planning.