Efficient ascent trajectory optimization using convex models based on the Newton–Kantorovich/Pseudospectral approach

Abstract

This paper presents an iterative convex programming algorithm for the complex ascent trajectory planning problem. Due to the nonlinear dynamics and constraints, ascent trajectory planning problems are always difficult to be solved rapidly. With deterministic convergence, convex programming is becoming increasingly attractive to such problems. In this paper, first, path constraints (dynamic pressure, load and bending moment) are convexified by a change of variables and a reasonable approximation. Then, based on the Newton–Kantorovich/Pseudospectral (N–K/PS) approach, the dynamic equations are transcribed into linearized algebraic equality constraints with a given initial guess, and the ascent trajectory planning problem is formulated as a convex programming problem. At last, by iteratively solving the convex programming problem with readily available convex optimization methods and successively updating the initial guess with the Newton–Kantorovich iteration, the trajectory planning problem can be solved accurately and rapidly. The convergence of the proposed iterative convex programming method is proved theoretically, and numerical simulations show that the method proposed can potentially be implemented onboard a launch vehicle for real-time applications.