An Iterative Convex Programming Method for Rocket Landing Trajectory Optimization

Abstract

A rapid trajectory optimization method is proposed to solve the fuel-optimal Earth-landing problem of reusable rockets, in which the nonlinear aerodynamic drag force is non-negligible. To enable the online and autonomous operation ability, the method is designed based on convex optimization, which features rapid and deterministic convergence properties, and a homotopic-iterative strategy is proposed to convexify the nonlinear system dynamics of the rocket. In the proposed iterative algorithm, the problem is first solved based on the lossless convexification method while the drag force is considered to be zero. Then, during subsequent iterations, the drag profile is approximated by the last solution and homotopically added to the problem. Thus, the nonlinear drag is gradually included while the problem remains convex. Because the convexification of the nonlinear terms is not based on linearization, no reference trajectory or initial guess is needed, which greatly enhances the autonomy of the algorithm. Numerical experiments are provided to demonstrate the effectiveness, rapidness, and accuracy of the proposed algorithm.