• Title, Summary, Keyword: Direct Multiple-Shooting method

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Finding Optimal Controls for Helicopter Maneuvers Using the Direct Multiple-Shooting Method

  • Kim, Min-Jae;Hong, Ji-Seung;Kim, Chang-Joo
    • International Journal of Aeronautical and Space Sciences
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    • v.11 no.1
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    • pp.10-18
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    • 2010
  • The purpose of this paper deals with direct multiple-shooting method (DMS) to resolve helicopter maneuver problems of helicopters. The maneuver problem is transformed into nonlinear problems and solved DMS technique. The DMS method is easy in handling constraints and it has large convergence radius compared to other strategies. When parameterized with piecewise constant controls, the problems become most effectively tractable because the search direction is easily estimated by solving the structured Karush-Kuhn-Tucker (KKT) system. However, generally the computation of function, gradients and Hessian matrices has considerably time-consuming for complex system such as helicopter. This study focused on the approximation of the KKT system using the matrix exponential and its integrals. The propose method is validated by solving optimal control problems for the linear system where the KKT system is exactly expressed with the matrix exponential and its integrals. The trajectory tracking problem of various maneuvers like bob up, sidestep near hovering flight speed and hurdle hop, slalom, transient turn, acceleration and deceleration are analyzed to investigate the effects of algorithmic details. The results show the matrix exponential approach to compute gradients and the Hessian matrix is most efficient among the implemented methods when combined with the mixed time integration method for the system dynamics. The analyses with the proposed method show good convergence and capability of tracking the prescribed trajectory. Therefore, it can be used to solve critical areas of helicopter flight dynamic problems.

Direct Multiple Shooting Induction of Taraxacum

  • Gou, Xiaoxia;Kim, Jae-Hak;Hong, Soon-Kwan
    • Korean Journal of Plant Resources
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    • v.22 no.6
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    • pp.522-527
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    • 2009
  • Plants of the genus Taraxacum are well-known as a traditional herbal remedy with a long history, and they have also been extensively used as food, chemicals and cosmetics. In this study, four Taraxacum species distributed in Korea (T. mongolicum, T. officinale, T. mongolicum variation and T. officinale variation) were utilized for an efficient method for direct multiple shooting induction and regeneration, using leaf blade, transition zone, petiole and root as explants in MS media with various hormone concentration and combination. MS medium containing IAA 0.2 mg/L and TDZ 1.0 mg/L showed the highest induction frequency of all the hormone combinations. Besides, the induction of T. mongolicum variation was most effective comparing with the other three species by the average induction frequency of four explants. While the induction effect of leaf blade explant was more obvious than the other three explants. This system exhibited a rapid propagation of shoots from the leaf blade explants and makes it convenient to make use of these Taraxacum species to develop their diverse applications in the future.

The Earth-Moon Transfer Trajectory Design and Analysis using Intermediate Loop Orbits (중개궤도를 이용한 지구-달 천이궤적의 설계 및 분석)

  • Song, Young-Joo;Woo, Jin;Park, Sang-Young;Choi, Kyu-Hong;Sim, Eun-Sup
    • Journal of Astronomy and Space Sciences
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    • v.26 no.2
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    • pp.171-186
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    • 2009
  • Various Earth-Moon transfer trajectories are designed and analyzed to prepare the future Korea's Lunar missions. Minimum fuel trajectory solutions are obtained for the departure year of 2017, 2020, 2022, and every required mission phases are analyzed from Earth departure to the final lunar mission orbit. N-body equations of motion are formulated which include the gravitational effect of the Sun, Earth and Moon. In addition, accelerations due to geopotential harmonics, Lunar J2 and solar radiation pressures are considered. Impulsive high thrust is assumed as the main thrusting method of spacecraft with launcher capability of KSLV-2 which is planned to be developed. For the method of injecting a spacecraft into a trans Lunar trajectory, both direct shooting from circular parking orbit and shooting from the multiple elliptical intermediate orbits are adapted, and their design results are compared and analyzed. In addition, spacecraft's visibility from Deajeon ground station are constrained to see how they affect the magnitude of TLI(Trans Lunar Injection) maneuver. The results presented in this paper includes launch opportunities, required optimal maneuver characteristics for each mission phase as well as the trajectory characteristics and numerous related parameters. It is confirmed that the final mass of Korean lunar explorer strongly depends onto the initial parking orbit's altitude and launcher's capability, rather than mission start time.