Abstract
In this paper, we propose a unified approach to solve the time-energy optimal landing problem on planetary bodies (e.g. planets, moons, and asteroids). In particular, the indirect optimization method, based on the derivation of the first order necessary conditions from the Hamiltonian, is exploited and the Two-Point Boundary Value Problem arising from the application of the Pontryagin Minimum Principle is solved using the Theory of Functional Connections. The optimal landing trajectories are accurately computed with a computational time on the order of 10–100 ms, using a MATLAB implementation. The speed and accuracy of the proposed method makes it suitable for real time applications. The algorithm is applied and validated for the landing on large (Mars and Moon) and small (asteroids Gaspra and Bennu) planetary bodies.
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