Time-energy optimal landing on planetary bodies via theory of functional connections

Andrea D'Ambrosio, Enrico Schiassi, Hunter Johnston, Fabio Curti, Daniele Mortari, Roberto Furfaro

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)4198-4220
Number of pages23
JournalAdvances in Space Research
Issue number12
StatePublished - Jun 15 2022


  • Asteroids and large planetary bodies
  • Optimal landing trajectories
  • Real-time optimization
  • Theory of functional connections

ASJC Scopus subject areas

  • Aerospace Engineering
  • Astronomy and Astrophysics
  • Geophysics
  • Atmospheric Science
  • Space and Planetary Science
  • Earth and Planetary Sciences(all)


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