Matrix Methods for Optimal Manifesting of Multinode Space Exploration Systems

Abstract

This paper presents matrix-based methods for determining optimal cargo manifests for space exploration. An exploration system is defined as a sequence of in-space and on-surface transports between multiple nodes coupled with demands for resources. The goal is to maximize value and robustness of exploration while satisfying logistical demands and physical constraints at all times. To reduce problem complexity, demands are abstracted to a single class of resources, and one metric (e.g., mass or volume) governs capacity limits. Matrices represent cargo carried by transports, cargo used to satisfy demands, and cargo transferred to other transports. A system of equations enforces flow conservation, demand satisfaction, and capacity constraints. Exploration system feasibility is evaluated by determining if a solution exists to a linear program or network-flow problem. Manifests are optimized subject to an objective function using linear or nonlinear programming techniques. In addition to modeling the manifesting problem, a few metrics such as the transport criticality index are formulated to enable analysis and interpretation. The proposed matrix manifest modeling methods are demonstrated with a notional lunar exploration system composed of 32 transports, including eight cargo and nine crewed landings at an outpost at the lunar south pole and several surface excursions to Malapert Crater and Schrödinger Basin. It is found that carry-along and prepositioning logistics strategies yield different manifesting solutions in which transport criticality varies. For the lunar scenario, transport criticality is larger for a prepositioning strategy (mean value of 3.02), as compared with an alternative carry-along case (mean value of 1.99).