Space trajectory optimisation in the interplanetary environment

The identification of the minimum, delta-v, up to the 4th revolution, with the π- and k-lines

Since Battin’s theorisation, different techniques were proposed to improve the gravity assisted trajectory design from the simpler combinatorial resolution. In particular, the Tisserand chart, to group ballistic flyby by their energy levels, the Tisserand-Poicaré graph to study low-energy flybys and the Keplerian map to model the orbital variation due to close encounters with a kick function.

The trend of the delta-v iso-lines over the solutions for tangential manoeuvres at departure from Earth (in blue) and at arrival at Mars (in green) with the color scaled on the eccentricity

The aim of this specific research activity is to improve the understanding of third body effects and leverage and control the dynamics of its natural perturbations to reduce mission cost and create new opportunities for space exploration. In parallel, the enhanced knowledge is used to implement control techniques which exploits the inherent dynamical structure of the problem.

Research outcomes

  • Energy-related objective/constraint functions for the optimisation of trajectories in the three body problem dynamics
  • Analytical explanation of the pork-chop
  • Extension of the pork-chop to multi-revolution orbit
  • Conic-syzygy function for fast preliminary design of multi-gravity assisted trajectories

Scientific production

  • D. Menzio, C. Colombo, “The combined Lambert-Tisserand method applied to the single flyby problem,” 68th International Astronautical Congress, Adelaide, Australia, 25-29 September 2017.
  • D. Menzio, C. Colombo, “An analysis of the pork-chop plot for direct, multirevolution and fly-by missions,” Advances in the Astronautical Sciences, Vol. 165, pp. 1739–1753, 2018. Proceedings of the 4th IAA Conference on Dynamics and Control of Space Systems (DYCOSS), Changsha, China, 21-23 May 2018.
  • D. Menzio, C. Colombo, “Adapted syzygy functions for the preliminary design of multi gravity assists trajectories,” 69th International Astronautical Congress, Bremen, Germany, 1-5 October 2018.