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.

Automated summary

This paper proposes a method to generate trajectories that are optimal with respect to multiple objectives and robust against epistemic uncertainty. The method models epistemic uncertainty with probability boxes and optimizes trajectories based on lower expectations on cost functions and constraint satisfaction. The paper introduces the calculation of lower expectation using Bernstein polynomials and an efficient many-objective optimization method. It also combines a surrogate model of lower expectation with dimensionality reduction technique to control the computational cost. The proposed approach is applied to the design of a rendezvous mission and considers uncertainties in thrust and engine outage in the trajectory.