High precision rapid trajectory optimization algorithm for launch vehicle landing

Aiming to solve the precision landing problem of vertical takeoff-vertical landing reusable rockets, a high accuracy rapid trajectory optimization algorithm is proposed. The non-convex and nonlinear problem is transformed into convex problem through a proper combination of convexification techniques and pseudospectral discretization, so the fast and deterministic convergence properties of convex optimization theory as well as the high discretization accuracy of pseudospectral methods can be taken advantage of. In terms of optimization accuracy, a high-fidelity optimization model is built, and the effects of the design of ignition and terminal time on the optimality of the trajectory are analyzed. The flip-Radau pseudospectral discretization is adopted, and its unique time domain mapping is utilized to transform the ignition and terminal time into special control variables, so the accuracy and optimality of the trajectory are improved. For rapidness, in order to solve the non-convex problem by convex optimization methods, an improved successive convexification algorithm is proposed based on a novel online trust-region update strategy, thus the number of iterations is decreased and the convergence property is enhanced. The effectiveness of the proposed algorithm is demonstrated by numerical experiments. With high accuracy results and a high computing speed, the algorithm has the potential to develop into an online optimal guidance method.