Rocket landing guidance based on second-order Picard-Chebyshev-Newton type algorithm

Abstract

This paper proposes a rocket substage vertical landing guidance method based on the second-order Picard-Chebyshev-Newton type algorithm. Firstly, the continuous-time dynamic equation is discretized based on the natural second-order Picard iteration formulation and the Chebyshev polynomial. Secondly, the landing problem that considers terminal constraints is transformed into a nonlinear least-squares problem with respect to the terminal constraint function and solved with the Gauss-Newton method. In addition, the projection method is introduced to the iteration process of the Gauss-Newton method to realize the inequality constraints of the thrust. Finally, the closed-loop strategy for rocket substage vertical landing guidance is proposed and the numerical simulations of the rocket vertical landing stage are carried out. The simulation results demonstrate that compared with the sequential convex optimization algorithm, the proposed algorithm has higher computational efficiency.