Reduced cost mission design using surrogate models

Abstract

This paper uses surrogate models to reduce the computational cost associated with spacecraft mission design in three-body dynamical systems. Sampling-based least squares regression is used to project the system response onto a set of orthogonal bases, providing a representation of the ΔV required for rendezvous as a reduced-order surrogate model. Models are presented for mid-field rendezvous of spacecraft in orbits in the Earth–Moon circular restricted three-body problem, including a halo orbit about the Earth–Moon L2 libration point (EML-2) and a distant retrograde orbit (DRO) about the Moon. In each case, the initial position of the spacecraft, the time of flight, and the separation between the chaser and the target vehicles are all considered as design inputs. The results show that sample sizes on the order of 102 are sufficient to produce accurate surrogates, with RMS errors reaching 0.2m/s for the halo orbit and falling below 0.01m/s for the DRO. A single function call to the resulting surrogate is up to two orders of magnitude faster than computing the same solution using full fidelity propagators. The expansion coefficients solved for in the surrogates are then used to conduct a global sensitivity analysis of the ΔV on each of the input parameters, which identifies the separation between the spacecraft as the primary contributor to the ΔV cost. Finally, the models are demonstrated to be useful for cheap evaluation of the cost function in constrained optimization problems seeking to minimize the ΔV required for rendezvous. These surrogate models show significant advantages for mission design in three-body systems, in terms of both computational cost and capabilities, over traditional Monte Carlo methods.