Trajectory optimization for RLV in TAEM phase using adaptive Gauss pseudospectral method

Dear editor, With the development of space technology, the trajectory optimization for reusable launch vehicle (RLV) in terminal area energy management (TAEM) phase has aroused increasing attention among researchers because of its nonlinearity and complex path constraints. TAEM phase starts from the terminal entry point (TEP) with an altitude of 30 km and velocity of 3 Ma, and ends at the approach and landing interface (ALI) with an altitude of 3 km and velocity of 0.5 Ma [1]. For trajectory optimization in the TAEM phase, major studies have referred to the geometric trajectory generation scheme. An off-line trajectory planner including ground-track planner and vertical-trajectory planning methodology was developed in [1]. In [2], a reference trajectory of the TAEM phase is generated through iterative solution of a parameter optimization problem in the presence of large variations of initial states. An energy-tube concept was introduced in the terminal area trajectory optimization, and a crosssection of the energy tube is defined by the altitude and velocity information in [3]. An advantage of this method is that it provides sufficient capabilities to deal with off-nominal conditions when energy dissipation is required. Mu et al. [4] designed TAEM trajectory by iterating the motion equations at each node of altitude. Guo et al. [5] proposed a fast algorithm where the Gauss pseudospectral method (GPM) and model predictive control are combined. In this study, we consider the coupling between the longitudinal motion and the lateral motion of an RLV, path constraints, and terminal constraint to design the 3-DOF optimal TAEM trajectory through the adaptive Gauss pseudospectral method (AGPM). The combination of adaptive scheme and the GPM can improve the accuracy and rapidity of trajectory optimization effectively. Further, the trajectory obtained by our scheme is the basic of the TAEM real-time trajectory. Problem statement. Based on the 3-DOF translational equations used for trajectory optimization in the TAEM phase mentioned in [5], the objective of TAEM trajectory optimization is to minimize a cost function (1) (In this work, the cost function we chose is to minimize the terminal time) by using the AGPM when considering the constraints involving the heating rate constraint (2), dynamic pressure constraint (3), load constraint (4) and terminal condition (5) (x represents the state mentioned in [6] and tf is the terminal time). minJ = tf , (1)