Ascent Trajectory Optimization with Nonlinearity-Kept Convexification

Ascent trajectory optimization in the atmospheric phase is challenging since nonlinear aerodynamic forces and strict path constraints exist. Traditional convex optimization approaches mostly rely on linearization to convexify the problem, but their convergence is sensitive to user-provided initial state and control profiles. In this article, we decompose the problem into three subproblems for optimizing the flight-path angle, the heading angle, and the speed. The first two subproblems are convexified mainly by successive approximation while the theoretical analysis is conducted to equivalently transform the third subproblem into an initial value problem. The proposed approach can keep most nonlinearity of the original problem. This brings a unique benefit in that an iterative algorithm for solving the subproblems can quickly converge in a few iterations even when rough initial state and control profiles are provided and no trust region is used. Additionally, linking constraints with the exoatmospheric phase are properly formulated and convexified so that an integrated iterative algorithm can be developed to obtain an ascent trajectory from lift-off to orbit. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed approach.