Many-objective robust trajectory optimisation under epistemic uncertainty and imprecision

This paper proposes a method to generate trajectories that are optimal with respect to multiple objectives and robust against epistemic uncertainty. Epistemic uncertainty is modelled with probability boxes and trajectories are optimised with respect to the lower expectations on cost functions and constraint satisfaction. The paper proposes an approach to the calculation of the lower expectation using Bernstein polynomials, and an efficient many-objective optimisation of the trajectories. A surrogate model of the lower expectation is combined with a dimensionality reduction technique to contain the computational cost and make the optimisation under epistemic uncertainty tractable. This approach is applied to the design of a rendezvous mission to Apophis with a spacecraft equipped with a low thrust engine. The paper presents both the case in which the thrust and specific impulse are affected by a time dependent uncertainty and the case in which the engine is affected by an outage that reduces the level of thrust at a random time along the trajectory.