This paper presents a comprehensive treatment to the optimal atmospheric ascent problem of launch vehicles subject to path constraints and final condition constraints. The development is particularly tailored for the purpose of eventual realization of closed-loop endo-atmospheric ascent guidance. We demonstrate that the classical finite difference method for two-point boundary-value problems is well suited for solving the optimal ascent problem on-board. The performance and execution of the guidance algorithm are assessed with a series of open-loop and closed-loop tests using the vehicle data of a reusable launch vehicle. The test results render strong supporting evidence to the belief that closed-loop optimal endo-atmospheric ascent guidance is now feasible.
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