Efficient algorithm for nonlinear trajectory optimization of spacecraft using generating functions

• Project/Area Number: 21760650
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Aerospace engineering
• Research Institution: Kyoto University
• Principal Investigator: BANDO Mai Kyoto University, 宇宙総合学研究ユニット, 特定助教 (40512041)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 軌道力学 / 軌道制御 / 惑星探査 / 航空宇宙工学 / 制御工学 / 正準変換 / ハミルトン・ヤコビ方程式

Research Abstract

Using a recently developed technique based on Hamilton-Jacobi theory, we develop a method to approximate the solution of the Hamilton-Jacobi equation which can solve nonlinear trajectory optimization of spacecraft. The proposed method is based on the successive approximation and Galerkin spectral method with Chebyshev polynomials. This approach is expected to derive the analytical solution of the optimal control problem in the large domain.

Research Products

• [Journal Article] Transactions of the Japan Society for Aeronautical and Space Sciences (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa, Orbital Design for Multiple Flyby Missions
  • Journal Title: Aerospace Technology Japan Vol.8, No.ists27 Pages: 9-13
  • Peer Reviewed
• [Journal Article] Solution to Lambert's Problem Using Generalized Canonical Transformations (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Journal Title: Advances in the Astronautical Sciences Vol.136 Pages: 587-603
  • Peer Reviewed
• [Journal Article] A New Lambert Algorithm Using the Hamilton-Jacobi-Bellman Equations (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Journal Title: AIAA Journal of Guidance, Control, and Dynamics Vol.33 No.3 Pages: 1000-1008
  • Peer Reviewed
• [Journal Article] Solution to Lambert's Problem Using Generalized Canonical Transformations (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Journal Title: Advances in the Astronautical Sciences Volume: 136 Pages: 587-603
  • Peer Reviewed
• [Journal Article] Orbital Design for Multiple Flyby Mission (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Journal Title: Transactions of the Japan Society for Aero nautical and Space Sciences, Aerospace Technology Japan Volume: 8
  • NAID: 130000675480
  • Peer Reviewed
• [Journal Article] A New Lambert Algorithm Using the Hamilton-Jacobi-Bellman Equations (2010)
  • Author(s): Mai Bando
  • Journal Title: AIAA Journal of Guidance, Control, and Dynamics 33
  • Peer Reviewed
• [Journal Article] A New Optimal Orbit Control for Two-Point Boundary-Value Problem Using Generating Functions (2009)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Journal Title: Advances in the Astronautical Sciences Vol.134 Pages: 245-260
  • NAID: 120007044555
  • Peer Reviewed
• [Journal Article] A New Optimal Orbit Control for Two-Point Boundary-Value Problem Using Generating Functions (2009)
  • Author(s): Mai Bando
  • Journal Title: Advances in the Astronautical Sciences 134 Pages: 245-260
  • NAID: 120007044555
  • Peer Reviewed
• [Presentation] 低推力宇宙機による地球接近小惑星軌道変更ミッション (2010)
  • Author(s): 坂東麻衣, 山川宏
  • Organizer: SICEシステムインテグレーション部門講演会3
  • Place of Presentation: 東北大
  • Year and Date: 2010-12-25
• [Presentation] 地球接近小惑星軌道変更ミッションのための軌道最適化 (2010)
  • Author(s): Mai Bando
  • Organizer: SICEシステムインテグレーション部門講演会
  • Place of Presentation: 東北大
  • Year and Date: 2010-12-25
• [Presentation] 地球接近小惑星軌道変更ミッションのための軌道最適化 (2010)
  • Author(s): 坂東麻衣, 山川宏
  • Organizer: 第54回宇宙科学技術連合講演会
  • Place of Presentation: 静岡
  • Year and Date: 2010-11-17
• [Presentation] 低推力宇宙機による地球接近小惑星軌道変更ミッション (2010)
  • Author(s): Mai Bando
  • Organizer: 第54回宇宙科学技術連合講演会
  • Place of Presentation: 静岡
  • Year and Date: 2010-11-17
• [Presentation] Application of Global Solution of Hamilton-Jacobi Equations to Optimal Low-Thrust Multiple Rendezvous Problem (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Organizer: 61st International Astronautical Congress
  • Place of Presentation: Prague
  • Year and Date: 2010-10-01
• [Presentation] Application of Global Solution of Hamilton-Jacobi Equations to Optimal Low-Thrust Multiple Rendezvous Problem (2010)
  • Author(s): Mai Bando
  • Organizer: 12th International Space Conference of Pacific-basin Societies (ISCOPS)
  • Place of Presentation: Prague チェコ共和国
  • Year and Date: 2010-10-01
• [Presentation] Low-Thrust Trajectory Optimization Using Second-Order Generating Functions (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Organizer: SICE Annual Conference
  • Place of Presentation: Taipei
  • Year and Date: 2010-08-19
• [Presentation] Low-Thrust Trajectory Optimization Using Second-Order Generating Functions (2010)
  • Author(s): Mai Bando
  • Organizer: SICE Annual Conference
  • Place of Presentation: Taipei 台湾
  • Year and Date: 2010-08-19
• [Presentation] Low-Thrust Multiple Rendezvous Trajectories Using Generating Functions (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Organizer: 20th JAXA Workshop on Astrodynamics and Flight Mechanics
  • Place of Presentation: 相模原
  • Year and Date: 2010-07-26
• [Presentation] Low-Thrust Multiple Rendezvous Trajectori es Using Generating Functions (2010)
  • Author(s): Mai Bando
  • Organizer: 20th JAXA Workshop on Astrodynamics and Flight Mechanics
  • Place of Presentation: 相模原
  • Year and Date: 2010-07-26
• [Presentation] ハミルトンヤコビ方程式を用いた宇宙機の軌道移行問題の数値解法 (2010)
  • Author(s): 坂東麻衣, 山川宏
  • Organizer: 天体力学N 体力学研究会3
  • Place of Presentation: 千葉大(招待)
  • Year and Date: 2010-03-19
• [Presentation] ハミルトンヤコビ方程式を用いた宇宙機の軌道移行問題の数値解法 (2010)
  • Author(s): 坂東麻衣
  • Organizer: 天体力学N体力学研究会
  • Place of Presentation: 千葉大学
  • Year and Date: 2010-03-19
• [Presentation] Solution to Lambert's Problem Using Generalized Canonical Transformations (2010)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Organizer: 20TH AAS/AIAA Space Flight Mechanics Meeting
  • Place of Presentation: SanDiego
  • Year and Date: 2010-02-15
• [Presentation] Solution to Lambert's Problem Using Generalized Canonical Transformations (2010)
  • Author(s): Mai Bando
  • Organizer: 20TH AAS/AIAA Space Flight Mechanics Meeting
  • Place of Presentation: サンディエゴ(米国)
  • Year and Date: 2010-02-15
• [Presentation] Application of Global Solution of Hamilton-Jacobi Equations to Nonlinear Trajectory Optimization of Spacecraft (2009)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Organizer: 19th JAXA Workshop on Astrodynamics and Flight Mechanics
  • Place of Presentation: Sagamihara
  • Year and Date: 2009-07-30
• [Presentation] Application of Global Solution of Hamilton-Jacobi Equations to Nonlinear Trajectory Optimization of (2009)
  • Author(s): Mai Bando
  • Organizer: 19th JAXA Workshop on Astrodynamics and Flight Mechanics
  • Place of Presentation: 相模原
  • Year and Date: 2009-07-30
• [Presentation] Orbital Design for Multiple Flyby Mission (2009)
  • Author(s): Mai Bando, Hiroshi Yamakawa
  • Organizer: 27th International Symposium on Space Technology and Science
  • Place of Presentation: Tsukuba
  • Year and Date: 2009-07-07
• [Presentation] Orbital Design for Multiple Flyby Mission (2009)
  • Author(s): Mai Bando
  • Organizer: 27th International Symposium on Space Technology and Science
  • Place of Presentation: 筑波
  • Year and Date: 2009-07-07