Hp-adaptive Pseudospectral Convex optimization for Rocket Powered Landing Trajectory Planning

Rocket powered landing trajectory planning is a typical non-convex and non-smooth optimization problem. To solve this problem, a convex optimization method based on hp-adaptive pseudospectral method is proposed. Combining the advantages of these two methods, the proposed method can quickly and accurately obtain the optimal trajectory. Firstly, the original non-convex optimal control problem is transformed into a convex optimal problem by lossless convexification and change of variables convexifying the non-convex thrust constraint and nonlinear dynamics respectively. Then, t Then, the hp adaptive pseudospectral method is used to discretize the time-continuous problem, in which the position of the discrete points can be adaptively adjusted to the control discontinuities according to the curvature of the state variable. Finally, the original non-convex problem can be transformed into a second-order cone programming problem, and the highly efficient interior point method can be used to quickly solve the problem. Numerical simulation results show that the proposed method can quickly solve the non-smooth trajectory optimization problem and accurately capture the control discontinuities.