In this paper, an iterative convex programming method, Newton-Kantorovich/Pseudospectral-Convex Programming (N-K/PCP) approach, is presented to solve the onboard trajectory planning for the rocket-powered launch vehicle. Convex programming has been becoming a vehicle design subject with substantial research issues in the design of trajectory planning methods with deterministic convergence properties. However, due to the nonlinear dynamics, trajectory planning problems are always non-convex, and difficult to be solved by the convex programming approach directly. By transcribing the differential dynamic equations into nonlinear algebraic constraints with the Gauss pseudospectral discretization, and by convexifying these algebraic constraints and the non-convex constraints with the linearization technique and a lossless relaxation technique, this paper formulates the continuous-time infinite-dimensional trajectory planning problem as an finite-dimensional convex programming problem. At last, by iteratively solving the convex programming problem with the convex optimization method and successively updating the nominal solution with the N-K method, and the modeling error caused by the linearization can be well compensated, and the trajectory planning problem can be solved exactly. The convergence of the proposed iterative convex programming method is proved theoretically, and the effectiveness is demonstrated by numerical experiments and comparisons with other state-of-the-art methods.
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