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Asteroid Rendezvous Missions Using Indirect Methods of Optimal Control

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Item Summary

Title:Asteroid Rendezvous Missions Using Indirect Methods of Optimal Control
Authors:Patterson, Geoffrey
Date Issued:Aug 2015
Publisher:[Honolulu] : [University of Hawaii at Manoa], [August 2015]
Abstract:The main contribution of this dissertation is the development of techniques to overcome the difficulty in initializing algorithms based on indirect methods of optimal control and the Pontryagin maximum principle. Moreover, the developed techniques efficiently solve an enormous set of timeminimal and fuel-minimal spacecraft trajectory optimization problems, demonstrating the large scale applicability of the techniques as well as presenting a new approach to trajectory optimization. Using the techniques developed within, a main objective of this dissertation is to assess the feasibility of space missions to a new population of near Earth asteroids which temporarily orbit Earth, called minimoons. We design rendezvous missions to a database of over 16,000 simulated minimoons.
As a first approach, the time-minimization rendezvous problem is investigated. The Circular restricted three-body problem is used to model the gravitational effects of the Earth and Moon on the spacecraft. Continuation-based techniques which rely on the knowledge of an existing solution are used to initialize the algorithms. For a spacecraft with 1 Newton maximum thrust, our methods successfully compute locally time-minimal transfers to over 96% of the 16,923 simulated minimoons, with transfer times on the order of one month. For a sample of 250 minimoons, continuation techniques further reduce the maximum thrust as low as 0.1 Newtons with transfer times less than four months.
The time-minimal results give some understanding of a lower bound for the transfer times, but have high fuel requirements. To improve the results and investigate fuel constraints, the fuelminimization problem is investigated. The spacecraft is assumed to start on a Halo orbit around the Earth-Moon L2 Lagrangian point. The Circular Restricted Four-Body Problem is used to model the gravitational e ects of the Earth, Moon, and Sun, and the mass variation of the spacecraft is modeled. The structure of the control is xed to three boosts, and the transfer times are constrained to be less than six months. Again indirect methods are employed to identify fuel-minimal transfers, and a continuation-based \cloud" technique is developed to overcome the initialization di culty. For a spacecraft with 22 Newton maximum thrust and 230 second speci c impulse, our methods produce rendezvous missions with delta-v values under 500 meters per second for over 30% of the simulated asteroids, and for some transfers delta-v values less than 100 meters per second.
Most importantly, the work presented in this dissertation strongly suggests that minimoons are accessible via spacecraft at low cost and should continue to be investigated.
Description:Ph.D. University of Hawaii at Manoa 2015.
Includes bibliographical references.
Appears in Collections: Ph.D. - Mathematics

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