Gaussian Distribution–Based Control Vector Parameterization Method for Constrained Hypersonic Vehicle Reentry Trajectory Optimization

This study proposes a Gaussian-discretization control vector parametrization (CVP) algorithm to improve the reentry trajectory optimization accuracy of a hypersonic vehicle (HV) with a complex path and terminal state constraints. First, the reentry trajectory optimization problem (TOP) of the HV is established by analyzing the equations of motion and constraints. Second, a Gaussian distribution strategy is derived to obtain a suitable control parametrization time grid for improving control quality. By combining the handling strategies for path and terminal constraints, an efficient, non-uniform control parametrization trajectory optimization method is established, and the HV trajectory optimization algorithm framework is provided in detail. Lastly, the proposed algorithms are implemented on a widely studied common aero vehicle model. Numerical simulation tests are conducted on terminal-time-free and terminal-time-fixed TOPs to optimize the reentry downrange. Test results show that the proposed method has a stable solving ability with high satisfaction of terminal constraints. Simulation results reveal that the proposed method efficiently increases the downrange compared with other CVP methods under the tested scenario, thus showing the effectiveness of the proposed distribution strategy.