Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 419409, 13 pages http://dx.doi.org/10.1155/2013/419409 Research Article A New Concept for Atmospheric Reentry Optimal Guidance: An Inverse Problem Inspired Approach Davood Abbasi and Mahdi Mortazavi Aerospace Department, Center of Excellence in Computational Aerospace, Amirkabir University of Technology, P.O. Box 15875/4413, Teheran, Iran Correspondence should be addressed to Mahdi Mortazavi; mortazavi@aut.ac.ir Received 27 July 2012; Revised 29 April 2013; Accepted 21 May 2013 Academic Editor: Fatih Yaman Copyright © 2013 D. Abbasi and M. Mortazavi. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper presents a new concept for atmospheric reentry online optimal guidance and control using a method called MARE G&C that exploits the diferent time scale featured by reentry dynamics. Te new technique reaches a quasi-analytical solution and simplifed computations, even considering both lif-to-drag ratio and aerodynamic roll as control variables; in addition, the paper ofers a solution for the challenging path constraints issue, getting inspiration from the inverse problem methodology. Te fnal resulting algorithm seems suitable for onboard predictive guidance, a new need for future space missions. 1. Introduction Atmospheric reentry guidance and control (G&C) has been [1, 2] a signifcant and ongoing [3–6] research interest in the aerospace arena connected to several domains of engineering and science. Te reentry dynamic exhibits four main com- plicating features. (a) It is governed by a group of time- varying nonlinear diferential equations; (b) the states (tra- jectories) must satisfy some physical-operational constraints like heating rate, heat load, dynamic pressure, and maximum deceleration; (c) the controls have rational limits; and (d) parametric uncertainty is present. Te almost unique reentry features have made it a typical case study for engineers, mathematicians, and scientists who want to show the power of their solving theories or tech- niques. On the other hand, manned atmospheric reentry G&C is a common denominator of human space exploration, space station operations, and space tourism: all “industries of the future,” that are attracting growing investments from countries worldwide [3, 6]. Afer some earlier works on fnding simple reentry solu- tions, modern requirements made the reentry problem more difcult and only “fnding a solution” for its G&C is not suf- fcient. Nowadays, there is the need to optimize the reentry trajectory in “some sense” (maximizing downrange, reducing control use, etc.) and minimize, above all, the fnal landing point error relative to the previsions. Te other complications arise from the new guidance requirements. Te typical Apollo/Shuttle-era strategy (also called path following or drag-based strategy) [2] was the nominal trajectory guidance (the controller tries to reach a predetermined and ofine-designed trajectory represented in the drag-velocity plane). Although it had shown to be feasible in several missions (and so used in the ARD project by EU) [7], this method involves a great amount of prelaunch meas- urements (so great cost) and has little robustness against mis- sion variations and failures, disturbances, and of-design fight parameters. Terefore, predictive guidance (PG, the controller com- putes a new trajectory in advance based on the actual fight conditions) [8] has been considered; computing power and numerical algorithms now allow admissible guidance trajec- tories and control to be computed online, and this is the so- called path-generating strategy. PG methods are a more ver- satile tool than nominal trajectory guidance and are more fexible to disturbances, or entry conditions and vehicle parameter variations. Additionally, these techniques provide a systematic tool for instantaneously satisfying state and con- trol constraints in the online trajectory generation [9].