Multi-Scenario Trajectory Optimization for Vertical Takeoff and Vertical Landing Vehicles Using the Gauss Pseudospectral Method

Abstract

Vertical takeoff and vertical landing (VTVL) vehicles, based on throttling liquid rocket engines, are attracting increasing attention for their validation of guidance and control techniques during landing. However, validation requires the vehicle to fly in a special trajectory with multiple constraints. Propellant consumption should be carefully calculated for the purpose of carrying more experimental devices during the flight, which makes conducting minimum-propellant trajectory optimization a necessity. This study focuses on the optimization of VTVL vehicles based on a throttling liquid rocket engine. Three flight scenarios applicable to this vehicle are proposed, namely, VTVL vehicles without horizontal movement, VTVL vehicles with horizontal movement, and vertical takeoff and autonomous landing with horizontal movement. Trajectory optimization using the Gauss pseudospectral method (GPM) was conducted during the abovementioned flight scenarios. The results show that the GPM provides excellent solutions for trajectory optimization in the different scenarios. In VTVL vehicles with horizontal movement, vertical takeoff, and autonomous landing with horizontal movement scenarios, the thrust appears in a similar bang–bang control. Meanwhile, in VTVL vehicles without a horizontal movement scenario, the thrust appears like a segmented bang–bang control, which we call regulative bang–bang control. Moreover, by introducing the thrust derivative into the optimization objective using a weighted method, thrust fluctuation can be restrained. To ensure the compatibility of switching the flight among the three scenarios, the carried propellant mass should be decided based on the third flight scenario.