Multi-objective optimisation of constellation deployment using low-thrust propulsion

Abstract

This work presents an analysis of the deployment of future constellations using a combination of low-thrust propulsion and natural dynamics. Different strategies to realise the transfer from the launcher injection orbit to the constellation operational orbit are investigated. The deployment of the constellation is formulated as a multi-objective optimisation problem that aims at minimising the maximum transfer ∆V , the launch cost and maximise at the same time the pay-off given by the service provided by the constellation. The paper will consider the case of a typical constellation with 27 satellites in Medium Earth Orbit and the use of only two launchers, one of which can carry a single satellite. It will be demonstrated that some strategies and deployment sequences are dominant and provide the best trade-off between peak transfer ∆V and monetary pay-off.

Many-objective robust trajectory optimisation under epistemic uncertainty and imprecision

“…Note that because of the Karhunen-Loève theorem, under suitable assumptions on the nature of the functions η i , ξ T,i and ξ I,i , the two expansions (10) and (11) converge in L 2 and uniformly in L to a zero-mean square-integrable stochastic process. However, since we are not interested in the short term variation, the lemmas on the derivation of the variation of the orbital parameters introduced 120 by Pierret [13] do not apply.…”

“…Model (10) is, however, not ideal to represent uncertainty in the thrust magnitude due to engine outage events because it would require a very high order expansion. Thus, when studying the optimal response to engine outage, we introduce the following piece-wise constant model:…”

“…In the work of Di Carlo et al [10], an epistemic uncertainty formulation was proposed, using Dempster-Shaffer theory of evidence. The belief in meeting a propellant mass threshold is optimised subject to a constraint in the belief in reaching the desired final state.…”

“…The minimisation of the expectation is a hard global optimisation problem, in the general case, while the search for an approximation to the Pareto set in high dimensions requires a high number of calls to both the objective and constraint functions. Thus, in order to make the many-objective optimisation tractable, we elaborate on the idea, proposed in [10], to use a surrogate model that directly maps the decision variables into the value of the lower expectation. This mapping completely bypasses the computation of the lower expectation during the search for the Pareto optimal set.…”

Robust Trajectory Optimisation of a TSTO Spaceplane Using Uncertainty-Based Atmospheric Models

“…It works for arbitrarily connected multi-phase problems with general dynamics, and ensures an even spread set of solutions within the Pareto-optimal set. The software has been successfully used for the trajectory and design optimisation of vertical and horizontal launch systems [10,11], deployment of constellations [12], interplanetary exploration missions [13] and the design of multi-debris removal missions.…”