Constrained multi-objective space trajectory optimisation under severe system and operational uncertainty

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In this paper we propose novel methods for the multi-objective optimisation of spacecraft low-thrust trajectories subject to severe uncertainty in system design and launcher parameters.
Uncertainty in system parameters and thrust profile is propagated through the spacecraft dynamics
to compute the lower expectation on the satisfaction of the terminal constraints on position and the optimal value of the propellant consumption. The lower expectation is the minimum expected value of a given quantity of interest with respect to a family of probability distributions that characterise the uncertainty in the system parameters.
In this paper we investigate a new efficient method for describing this family which scales well under an increase in the number of uncertain variables.
In our previous work we considered a very agnostic formulation assuming very little a priori information.
In this paper we consider the case in which mission designers have sufficient information to define some constraints on the probability associated to the system parameters. This information can come from previous missions or from on ground testing of components and subsystems.
We will show that when constraints on the input distributions are available, the family of distributions can be approximated as a sum of a relatively small number of kernels of positive functions, for which the lower expectation can be computed by solving a simple constrained linear system.
This process is fast and one can easily assess the sensitivity to the number of kernels and values of the input constraints.
Furthermore, in this work we will include in the computation of the lower expectation of the terminal
constraints also the effect of intermediate orbit determinations and the associated re-planning of the remaining leg of the trajectory, with a novel method that is analogous to differential dynamic programming.
Unlike our previous work in which we were computing the full lower probability function, in this paper we propose the use of the more easily understandable upper percentile, which corresponds to the threshold value that makes the lower expectation equal a pre-defined target value.
We will test our methodology on a multi-target asteroid exploration case study using small satellites.
Original languageEnglish
Publication statusPublished - 27 Oct 2021
Event72nd International Astronautical Congress - Dubai World Trade Centre, Dubai, United Arab Emirates
Duration: 25 Oct 202129 Oct 2021


Conference72nd International Astronautical Congress
Abbreviated titleIAC 2021
Country/TerritoryUnited Arab Emirates
Internet address


  • epistemic uncertainty
  • resilient satellite
  • robust Optimization
  • lower expectation
  • multi-objective optimization


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