基于hp伪谱同伦凸优化的火箭垂直回收在线轨迹规划方法

For the trajectory optimization problem of reusable launch vehicle vertical recovery, an online trajectory planning algorithm with optimal terminal time estimation strategy is proposed based on the hp-pseudospectral homotopic convex optimization method. Firstly, considering the non-convexity of the state constraints and process constraints, the lossless convexification is used to deal with the thrust magnitudes constraint. Then, the aerodynamic and non-convex mass constraint are transformed into linear time-varying profile by combing the homotopic approach and fixed point iteration ideas to complete the problem convexification. The control problem is further discretized based on the hp flipped Radau pseudospectral method, and is transformed into a parameter optimization problem, which is then solved by the primal-dual interior point method. Finally, in order to further reduce fuel consumption and improve economic efficiency, considering the problem that the optimal terminal time is difficult to be determined online, a fast estimation strategy for the optimal terminal time is designed by combining analytical derivation and quadratic interpolation method. The simulation results show that the designed trajectory optimization algorithm has fast speed of optimal terminal time estimation, excellent convergence performance, high accuracy and computational efficiency, and has the potential for online application.