Multi-Phase Trajectory Optimization of Vehicle Based on hp-Adaptive Pseudospectral Method

In order to solve the trajectory optimization problem of a boost-glide vehicle with multi-phase and multi-constraint, a longitudinal motion model and a multi-phase trajectory optimization model were built based on the constraint consideration of velocity, switch point of trajectory phase and the parameter of trajectory end. Hp-adaptive-based Legendre-Gauss-Radau points were used to transcribe the optimization problem to a finite-dimensional nonlinear programming problem, and maximal downrange optimization trajectory was obtained. An improved optimization strategy was proposed based on dynamic programming theory to decide the switch points of free phases, due to the difficulty with the multi-phase trajectory optimization arithmetic. Compared with the hp-adaptive pseudospectral method, the improved strategy can get almost the same optimization trajectory and a smaller finite-dimensional approximation. Numerical simulation results show that the boost-glide vehicle trajectory optimization problem can be solved, and the results are better than the gliding trajectory with the maximum lift-to-drag ratio.