Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

Camilla Colombo, Massimiliano Vasile, Gianmarco Radice

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)
138 Downloads (Pure)


In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution.
Original languageEnglish
Pages (from-to)75-112
Number of pages37
JournalCelestial Mechanics and Dynamical Astronomy
Issue number75
Publication statusPublished - Nov 2009


  • numerical methods
  • n-body
  • asteroids
  • trajectory optimisation
  • optimisation methods
  • optimal control
  • low-thrust trajectories
  • near earth objects
  • differential dynamic programming
  • bellman principle
  • multi-body problem
  • multi-revolution trajectory


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