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The purpose of this paper is to propose a hybrid optimization approach with high level of solving precision and efficiency for endo-atmospheric ascent trajectory planning of launch vehicles.

Based on the indirect method of optimal control problems, the optimal endo-atmospheric ascent problem with path constraints and final condition constraints is transformed into a Hamiltonian two point boundary value problem (TPBVP). An advanced Gauss pseudo-spectral method is applied to change the Hamiltonian TPBVP into a system of nonlinear algebraic equations, which is solved by a modified Newton method. To guarantee the convergence of the solution, analytical initial guess technology and homotopy technology are also introduced. At last, simulation tests are made.

The hybrid approach for optimal endo-atmospheric ascent trajectory planning has both fast convergence rate and high solution precision. The simulation results indicate that not only the proposed method is feasible but also it is better than the indirect method, which is a most popular approach for solving the optimal endo-atmospheric ascent problem. Given the same degree of solution accuracy, the new method consumes quite less time on the CPU than that of the indirect method.

The new optimization approach has high level of both solution accuracy and efficiency. It can be used in rapid trajectory designing, on-line trajectory planning and closed-loop guidance of launch vehicles. Also, the proposed Gauss pseudo-spectral method in this paper is a new and efficient method for solving general TPBVPs.

The paper provides a new hybrid optimization method for rapid endo-atmospheric ascent trajectory planning of launch vehicles.