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Entire Flight Trajectory Design for Temporary Reconnaissance Mission* Trans. Japan Soc. Aero. Space Sci. Vol. 60, No. 3, pp. 137–151, 2017 Entire Flight Trajectory Design for Temporary Reconnaissance Mission* Mingpei LIN and Ming XU† School of Astronautics, Beihang University, Beijing 100191, China A highly maneuverable and reusable spaceplane, which is remarkable for its ability to send payloads and data back to Earth in the volatile environment, is attached with high priority in responsive reconnaissance missions. In view of the fact that a classical nonlinear optimization algorithm is mostly restricted in discovering the optimum solution of a multi-stage trajectory-design problem, a two-level optimization algorithm is established to enhance the convergence of the solution. By means of dividing the entire trajectory into ascending, on-orbit, deorbit, and reentry segments, respective optimizations of the four segments above compose the sublevels of the optimization scheme and are associated elaborately one after another by transmitting the terminal value of a former segment to its following segment. A genetic algorithm, which is employed in the top level of this scheme, will incorporate the intermediate solution and state quantities from sublevels as the fitness function of the GA and generate the new optimized value for the first segment in each sublevel during each iteration. This two-level iteration will be operated under given constraints and will eventually acquire the optimum trajec- tory with a maximum target coverage time. Furthermore, a Monte Carlo simulation is conducted to observe the robustness of the optimized solution. Key Words: Entire Trajectory Optimization, Reconnaissance Mission, Two-level Decomposition Algorithm, Monte Carlo Simulation Nomenclature ·: bank angle r: geocentric radius J: cost function h: altitude f: flattening of the Earth V: velocity a: semi-major axis £: flight path angle i: inclination ½: rotation rate of the Earth e: eccentricity μ: atmospheric density +: right ascension of ascending node q: dynamic pressure ¬: pitchover coefficient of the rocket Q_ : heat rate t: time na: axial load P: thrust nL: normal load D: drag N0: thrust-weight rate L: lift ¯: half-field angle of satellite CD: drag coefficient ¢: solar angle of satellite CL: lift coefficient Isp: specific impulse Aref : reference area ³: mission design parameters m: mass Subscripts g: gravity 0: initial ®: gravitational coefficient of the Earth f: final ­: energy ratio constant j: the j-th time ¤: pitch angle in ascent phase out: leaving the footprint ’_: rate of pitch angle in ascent phase in: entering the footprint º: geocentric latitude u: upper bounds ª: longitude l: lower bounds ¸: right ascension ¤: declination 1. Introduction ¿: central angle ¼: heading angle The frontiers of contemporary space technology have be- ¡: angle of attack come decisively more advanced as the result of the growing demands from space-faring nations. The United States put © 2017 The Japan Society for Aeronautical and Space Sciences + forward the plan for operationally responsive space (abbr. Received 1 April 2016; final revision received 21 December 2016; accepted for publication 30 December 2016. ORS) in 2007 to strengthen its capabilities to utilize space †Corresponding author, [email protected] resources and achieve national security objectives.1) Soon 137 Trans. Japan Soc. Aero. Space Sci., Vol. 60, No. 3, 2017 afterwards, the proposal of ORS was widely adopted by neuver time, reentry time) and control variables (attack an- other nations and the gradual maturity of responsive space gle, bank angle, etc.) makes this optimization problem thorny technology ensued.2) Responsive reconnaissance, one of as well. In addition, the long time span of a reconnaissance the most crucial responsive space technologies, has been mission along with nonlinear characteristics of dynamical deeply researched to meet the requirement for spacecraft to systems results in a large-scale iterative computation, which observe specific ground targets and send data back to termi- poses a considerable challenge to the robustness of the de- nals simultaneously once a mission is dispatched.3–5) Five signed algorithm. typical potential responsive orbits, including Cobra Orbits, In this paper, to maximize the total coverage time (abbr. Magic Orbits, LEO Sun-synchronous Orbits, LEO Fast Ac- TCT) for a specific ground target within a limited time span, cess Orbits (abbr. FAO) and LEO Repeat Coverage Orbits which is one of the most significant indicators in a temporary (abbr. RCO), were introduced by Wertz3) and their perfor- reconnaissance mission, a two-level optimization algorithm mances in space responsive missions of telecommunication is established to design the entire flight trajectory and en- and high-resolution surveillance were evaluated respectively. hance the convergence of the solution. By means of dividing Nevertheless, he did not propose any detailed missions utiliz- the entire trajectory into the ascending segment, on-orbit seg- ing the orbits mentioned above. Omarabdelkhalik and ment, deorbit segment, and reentry segment, the respective Mortari6) and Kim et al.7) discussed the trajectory design optimizations of the four segments above compose the sub- within a given time frame to cover a particular ground target level of the optimization scheme. On one hand, each segment under two different conditions: with maneuver and without has its distinctive performance functions, constraints, and maneuver. But their study was focused on a long-term recon- control variables and will be optimized respectively by dif- naissance mission and a constellation design involving mul- ferent optimization algorithms. On the other hand, the four tiple satellites. In 2014, a study from Co and Black8) showed segments are associated elaborately one after another by a single low-Earth satellite equipped with electric propulsion transmitting the terminal states of a former segment to its fol- can overfly any target inside its coverage area within 1.8% of lowing segment. The genetic algorithm, which is employed its propellant budget. This research finding indicates that it in the top level of this scheme, will incorporate the intermedi- could be cost-efficient to retask a satellite for a new applica- ate solutions and state parameters from the sublevels as the tion if the satellite could be able to perform 40–50 orbital ma- fitness function of the GA and generate the new optimized neuvers during its mission life. value (orbital semi-major axis, inclination, orbit maneuver However, little work offered an appropriate solution to the time) for the first segment in the sublevel during each itera- problem in which a fully reusable or partially reusable launch tion. The two-level iteration will be operating under given vehicle (abbr. RLV) is responsible for an operationally re- constraints and eventually acquire the optimum trajectory sponsive mission. Scholz et al.9) provided an overview of with the maximum target coverage time. Furthermore, a an architecture analysis and several Space Operation Ve- Monte Carlo simulation is conducted to observe the robust- hicles (abbr. SOV) that have the potential to satisfy the re- ness of the optimized solution of the entire problem. sponsive space objectives. They pointed out the importance of using RLVs to provide the capability of delivering respon- 2. Problem Statement for a Temporary Reconnaissance sive payloads to strengthen existing intelligence, surveillance Mission and reconnaissance assets and to establish space superiority within the first 10 days of a conflict. In fact, RLVs such as 2.1. Temporary reconnaissance mission X-37B10) or XS-111) are especially appropriate for the imple- The spaceplane model employed in this study resembles mentation of responsive missions due to their low cost and the X-37B, which is a vertical-takeoff, horizontal-landing, strong spatial maneuverability. Encouraged by the theory winged-body and rocketed-powered single-stage vehicle. It of employing an RLV for a responsive reconnaissance mis- is assumed that the spaceplane, which is equipped with an sion, and to further expand this idea, the entire flight trajec- optical sensor and has powerful orbit maneuver capability, tory design of a reusable spaceplane for a temporary recon- is launched by the Long March 2F carrier rocket (LM-2F) naissance mission is studied in this paper. from the launch site of Jiuquan. Operating in low Earth orbit The entire trajectory of a spaceplane for a temporary re- (LEO), the spaceplane will run the reconnaissance mission of connaissance mission, which starts from a launching site a given target on the ground once receiving a responsive and terminates at a landing position, is normally divided into space assignment. After the spaceplane completes the mis- an ascending segment, on-orbit segment, deorbit segment, sion it will execute a deorbit impulsive maneuver, reenter and reentry segment. Scarcely has the idea of entire trajectory the atmosphere, and horizontally land on the ground within optimization been explored in the past due to the fact that a given time. For this problem, we try to select appropriate each segment of the whole trajectory can be optimized rou- orbit parameters and the time of orbit maneuvers to maxi- tinely with various standard nonlinear algorithms based on mize the coverage time over a local target of interest (N the theories of different disciplines,12–17) while a single opti- 30.58/ E104.07) during 10 days within all constraints, in- mization method can hardly find a convergent solution for cluding the carrying capacity of the launch vehicle, the ma- the entire trajectory. The complexity of the mission design neuver capacity of the spaceplane, and the reentry window parameters (orbital semi-major axis, inclination, orbit ma- to return to the ground and so on. ©2017 JSASS 138 Trans. Japan Soc. Aero. Space Sci., Vol. 60, No. 3, 2017 Thus, the optimization objective for the entire trajectory is to maximize the total coverage time (abbr. TCT). Denote the performance index by J ¼ TCT ¼ Tða; i; tmÞð1Þ where T is a function of a, i and tm. 3. Optimization Models for Trajectory of Each Phase In this section, the generic dynamic optimization models for the four flight phases as well as the specific constraints Fig.
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