研究者業績

津田 雄一

ツダ ユウイチ  (Yuichi Tsuda)

基本情報

所属
国立研究開発法人宇宙航空研究開発機構 宇宙科学研究所 宇宙飛翔工学研究系 教授
東京大学 大学院工学系研究科 航空宇宙工学専攻 教授
学位
博士(工学)(2003年3月 東京大学)

J-GLOBAL ID
200901005218518613
researchmap会員ID
5000069162

外部リンク

学歴

 3

主要な受賞

 29

論文

 427
  • Fuminori Hanaoka, Osamu Mori, Yuichi Tsuda, Ryu Funase, Jun'ichiro Kawaguchi
    Advances in the Astronautical Sciences 130 PART 2 1765-1776 2008年  
    This paper describes the attitude dynamics and the control method of a spinning solar sail spacecraft. The solar sail considered here has no structure supporting membrane, therefore estimation of the effect of membrane flexibility is one of the problems to solve for the future validation flight. In this study, we established a dynamic model including membrane vibration to handle a coupled motion of a rigid spacecraft and a flexible membrane, and focus on the consideration of attitude control method. The result is confirmed with numerical simulation by use of Multi Particle Model(MPM).
  • Yoji Shirasawa, Yuichi Tsuda
    Advances in the Astronautical Sciences 130 PART 1 507-517 2008年  
    This paper presents a novel attitude control device which is called three dimensional reaction wheel(3DRW). 3DRW consists of only one levitated spherical mass which can rotate around arbitrary axes. This leads to the reduction of the weight and volume of the device as compared to existing reaction wheel. Furthermore, this device has no mechanical contact between rotor and stator, so the failure caused by the mechanical contact would be reduced. In this paper, the results of the analysis and experiment on the dynamics and control of 3DRW are shown. In the experiments of the rotation control, the air bearing system is used. Using this device, the characteristics of rotation of the spherical mass are obtained. For the experimental device, the generated torque of 3DRW is found to be up to 1.77x10-5Nm. To verify the feasibility of the attitude control system using 3DRW, the experiments of angular velocity feedback control are carried out. This shows that the target angular momentum can be obtained by Pi-control and verifies the feasibility of 3DRW as the attitude control device.
  • 戸田 知朗, 斎藤 義文, 津田 雄一, 前沢 洌, 篠原 育
    59th International Astronautical Congress 5 3113-3121 2008年  
  • Masayuki Sugita, Ryu Funase, Yuichi Tsuda, Osamu Mori, Fuminori Hanaoka, Jun'ichiro Kawaguchi
    International Astronautical Federation - 59th International Astronautical Congress 2008, IAC 2008 8 5114-5123 2008年  査読有り
    Solar sail is one of the promising propulsion systems for future deep space exploration missions as it does not require any fuel to acquire propulsive force. However, the attitude control system of the solar sail, which controls the direction of the sail and thus the propulsive force, has not been much studied, although this constitutes the essential part of the orbital control using solar sail. This paper discusses the attitude dynamics and the control method of a spinning type solar sail spacecraft. The spinning type solar sail has no rigid structure supporting its membrane. This type of mechanism has the advantage in its simple and lightweight structure, however, the attitude control is difficult due to the flexibility of the membrane. In this paper, we introduced a mathematical dynamics model including first vibration mode of the membrane which can handle coupled motion of a rigid spacecraft and a flexible membrane, and analytically developed a controller that can avoid unnecessary oscillatory motion. The performance of the controller and the effect of solar radiation pressure, which can deform the membrane of solar sail, on the controller were verified by numerical simulations using more precise multi-particle numerical model.
  • Fuminori Hanaoka, Osamu Mori, Yuichi Tsuda, Ryu Funase, Jun'ichiro Kawaguchi
    SPACEFLIGHT MECHANICS 2008, VOL 130, PTS 1 AND 2 130 1765-+ 2008年  査読有り
    This paper describes the attitude dynamics and the control method of a spinning solar sail spacecraft. The solar sail considered here has no structure supporting membrane, therefore estimation of the effect of membrane flexibility is one of the problems to solve for the future validation flight. In this study, we established a dynamic model including membrane vibration to handle a coupled motion of a rigid spacecraft and a flexible membrane, and focus on the consideration of attitude control method. The result is confirmed with numerical simulation by use of Multi Particle Model(MPM).
  • 戸田 知朗, 朴澤 佐智子, 斎藤 義文, 津田 雄一, 石丸 元, 冨田 秀穂
    4th International Workshop on TT&C Systems for Space Applications (A-218) 2007年9月  
  • Yuichi Tsuda
    IFAC Proceedings Volumes (IFAC-PapersOnline) 17(PART 1) 401-406 2007年  
    Japan Aerospace Exploration Agency (JAXA) is currently studying on the " Solar Sail " propulsion for future deep space explorations. JAXA has conducted extensive studies on spinner solar sail spacecraft system, utilizing centrifugal force to deploy the photon acceptance surface. The final objective is to realize the 7.5μm-thickness and 50m diameter polyimide membrane, combined with thin flexible solar cells, as the photon acceptance surface. Based on the simulator development done through several space and ground experiments on solar sail dynamics, this paper discusses the attitude control of this spinning solar sail system via conventional RCS controller, and also focusing on the utilization of reflectivity control devices attached on the sail, to control the spinning axis and rate of the solar sailer.
  • Fuminori Hanaoka, Masataka Arakawa, Shunsuke Okada, Yusuke Shibasaki, Yoji Shirasawa, Osamu Mori, Maki Shida, Yuichi Tsuda, Jun'ichiro Kawaguchi
    International Astronautical Federation - 58th International Astronautical Congress 2007 6 4142-4150 2007年  
    The proposed balloon experiment for deploying large-sized membrane, which is intended to be shown in this paper, is postponed to September, 2008. We are now designing a new structure and mechanism of a spacecraft which is to be validated at the balloon experiment. We proposed "Multi-step deployment" of membrane in this paper, which reduces the risk of complexity of the deploying system compared to conventional system. In addition, we analyzed the feasibility of attitude control required for orbital maneuver with conventional chemical thruster and positively solved. The amount of propellant is also calculated and found to be feasible. The system we discussed in this paper is to be equipped with a newly designed spacecraft planned in 2010s. Copyright IAF/IAA. All rights reserved.
  • Yusuke Shibasaki, Yuichi Tsuda, Junichiro Kawaguchi, Ryu Funase
    International Astronautical Federation - 58th International Astronautical Congress 2007 10 6887 2007年  
    The Moon is recognized as an important destination for space science and exploration. The National Aeronautics and Space Administration (NASA) has presented a new policy for space exploration that includes human expedition to the lunar surface. The other agencies that include the Japan Aerospace Exploration Agency (JAXA) have also planned to send spacecraft to the moon. To put the spacecraft into orbit around the moon, various methods are conceived. For example, one of them is that the special spacecraft, such as an orbital transfer vehicle (OTV), is used in each transfer segment. It is the very important thing in cost that OTV between Low Earth Orbit (LEO) and Lunar Low Orbit (LLO) is reused. To promote lunar exploration efficiently, reusable OTV between LEO and LLO is required. OTV has been studied at JAXA, which is based on further development of H-II Transfer Vehicle (HTV). The OTV system is roughly composed of the payload segment, the propulsion segment and the fuel cartridge. The payload segment is separated from OTV body on Lunar Transfer Orbit (LTO), and is transported to LLO. The propulsion segment and the empty fuel cartridge are returned to LEO through Earth Transfer Orbit. (ETO). This paper aims at improving the payload ratio of reusable OTV. In this research, we focus on optimization problems of return trajectories with small fuel consumption. Flight time in LTO should be short generally. When payload is empty, flight time isn't restricted. So, multi-impulse flight using electrical propulsion is used in ETO. Aero-assisted flight using aero-brake is also utilized near the Earth. In ETO, we discuss ballistic flight using chemical propulsion, multi-impulse flight using electrical propulsion and aero-assisted flight using aero-brake. Optimal return trajectories of OTV between the Earth and the Moon are proposed. This research can be also extended to the transfer vehicles between the Earth and the Lagrange point of Sun-Earth system. The L2 point in the Sun-Earth system may be utilized for a space port for the outer planets exploration in the future. In this paper, we show the concept of the OTV system and the result of the optimal return trajectories for OTV.
  • 戸田知朗, 朴澤佐智子, 斎藤義文, 津田雄一, 冨田秀穂, 石丸元
    電子情報通信学会技術研究報告 107(365(SANE2007 82-94)) 51-56 2007年  
    編隊飛行衛星システムによる観測が地球磁気圏の研究に適した手段であることはよく知られている事実である。JAXAの将来磁気圏探査ミッションもこの編隊飛行衛星技術の利点を最大限に生かそうと議論を重ねてきた。SCOPEはそのミッション名であり、5機から成る探査機群が1kmから1000kmの衛星間距離に至るまで協調して観測を遂行する計画である。その観測を成り立たせる基盤技術になる衛星間の通信方式として我々はS帯を用いた時分割多重方式の衛星間ネットワークを推進してきた。このミッションは衛星間通信に観測データの高速伝送のみならず、衛星間の測距、動作クロックの衛星間同期機能を持たせる要求があり、シミュレータによる実証を通じて我々の提案の要求への充足と有効性を証明した。
  • Ryu Funase, Shinichi Nakasuka, Nobutada Sako, Takeshi Fujiwara, Yuichi Tsuda, Shinichi Ukawa, Shinichi Kimura, Hidekazu Hashimoto, Keisuke Yoshihara, Toru Yamamoto
    Transactions of the Japan Society for Aeronautical and Space Sciences 50(168) 97-104 2007年  査読有り
    Capture of tumbling objects in space will be one of the important on-orbit service technologies in the future. It requires a series of technologies such as camera-image tracking of the target, target attitude motion estimation, and attitude control of the chaser to approach and grasp the target. Based on theoretical and simulation-based research, the University of Tokyo successfully performed an on-orbit experiment of some of these technologies on a Japan Aerospace Exploration Agency's (JAXA, formerly NASDA) microsatellite named "m-LABSAT." In this paper, the objectives and procedures of these experiments, the control and estimation algorithms, and the results are described. © 2007 The Japan Society for Aeronautical and Space Sciences.
  • 戸田 知朗, 斎藤 義文, 津田 雄一, 篠原 育, 前沢 洌
    Proceedings of 25th International Symposium on Space Technology and Science ISTS2006-f-14 2006年6月  査読有り
  • Atsushi Iwakura, Shinichi Tsuda, Yuichi Tsuda
    AIAA 57th International Astronautical Congress, IAC 2006 5 3514-3520 2006年  
    This paper presents a novel attitude control device called 3 Dimensional Reaction Wheel (3DRW). 3DRW consists of a spherical mass which can rotate around arbitrary axes by magnetic levitation. 3DRW is 3-DOF device with only one reaction mass which could make it possible to drastically reduce the weight and volume of the system as compared to existing reaction wheel. In addition to that, this device does not have mechanical contact between rotor and stator, so longer operating lifetime can be expected. In this paper, the concept of 3DRW is introduced, and the analysis and the result of simulations on the dynamics of rotation mass in a magnetic field are shown. Also the experiment setup of magnetic levitation and rotating, and its result are presented. Finally it is will mentioned how 3DRW system can be applied effectively for the small satellites.
  • Yuichi Tsuda, Osamu Mori, Shinsuke Takeuchi, Jun'ichiro Kawaguchi
    Space Technology 26(1-2) 33-39 2006年  
    Japan Aerospace Exploration Agency (JAXA) is currently studying "Solar Sail" populsion for future deep space explorations. One of the key technologies to realize a solar sail is how light and how compact we can make the photon acceptance surface. JAXA has conducted extensive studies on utlizing centrifugal force to deploy the photon acceptance surface. The final objective is to realize a 7.5μm-thickness and 50m diameter polyimide membrane, combined with a thin flexible solar cells, as the photon acceptance surface that will be needed around the Jupiter orbit. In August 9, 2004, JAXA launched the S-310 sounding rocket, which tested two different shapes of membranes during the zero-gravity flight. The first type of membrane looked like a "clover-leaf", and another is like a "fan". These two membranes, both of them having 10m diameter, were unfolded sequentially during the zero-gravity flight under the free spin condition, and their behavior was observed by onboard cameras. This paper focuses on the "clover-leaf" solar sail, which was fully deployed successfully, and introduces the S-310-34 experiments, and then shows the flight results and postflight evaluations. © 2006 Lister Science. All rights reserved.
  • Yasuhiro Kawakatsu, Osamu Mori, Yuichi Tsuda, Kota Tarao, Jun'ichiro Kawaguchi
    Advances in the Astronautical Sciences 124 II 1773-1787 2006年  
    Discussed in this paper are the results of the mission analysis of near Earth asteroid flyby missions using miniature Asteroid Interceptors. The Interceptor is an autonomous self-contained interplanetary probe with 10kg mass which is now under development in ISAS/JAXA. It has the capability of navigating itself autonomously to flyby the target asteroid using optical navigation system. The image of the asteroid taken by the camera onboard at the closest approach is the main science output of the mission. Firstly discussed is the mission by a single Interceptor, which enables the minimum size interplanetary mission. The interceptor is launched as a piggy back mission on a geostationary mission, separated on a geostationary transfer orbit (GTO), kicked by a solid rocket motor, and injected into an orbit suitable for encountering the asteroid. It is shown that the utilization of the Earth synchronous orbit and the Earth swing-by drastically increase the number of the possible target asteroids, which enables the selection of more scientifically interesting target for a given opportunity. The second mission concept discussed is the multiple asteroids exploration with a single launch. A straightforward application of the single Interceptor mission, that is, the mission by several independent Interceptors is shown firstly, and an option to overcome the difficulty in performing critical operation of multiple spacecrafts simultaneously is also discussed. The list of the target asteroid candidates, detailed mission sequence and maneuver parameters are shown for the assumed example mission.
  • Yuichi Tsuda, Yoshifumi Saito, Tomoaki Toda
    Advances in the Astronautical Sciences 124 II 1709-1720 2006年  
    JAXA is currently planning the next generation magnetosphere observation mission called "SCOPE"(cross-Scale Coupling in Plasma universE). SCOPE aims at observing the Earth's magnetotail with 5 satellites flying in formation to fully resolve the temporary and spatial distribution of the magnetospheric phenomena. For this observation, the clock synchronization and relative distance measurement between the spacecrafts are essential. This paper describes an onboard relative ranging and clock synchronization algorithm, which applies a simplified formulation, using two-way and three-way phase differences as the filter inputs to construct the onboard system suit to the SCOPE mission.
  • M. Fujimoto, Y. Tsuda, Y. Saito, I. Shinohara, Y. Kasaba, H. Kojima
    European Space Agency, (Special Publication) ESA SP (588) 249-254 2005年  
    In order to open the new horizon of research in the plasma universe, SCOPE will perform formation flying multi-scale observations combined with high-time resolution electron detection and will enable data-based study on the key space plasma processes from the cross-scale coupling point of view. Key physics to be studied are magnetic reconnection under various conditions, shocks in space plasma, collisionless plasma mixing at the boundaries, and physics of current sheets embedded in complex magnetic geometries. The SCOPE mission is made up of the 5 spacecraft (s/c) formation put into the equatorial orbit with the apogee at 30Re (Re: earth radius). One of the s/c is a large mother ship which is equipped with a full suite of particle detector including ultra-high sampling cycle electron detector. Among other 4 small s/c one remains near (∼10 km) the mother ship and the s/c-pair will focus on wave-particle interaction utilizing inter-s/c communication. Others are used for wave-particle interaction study when the distance from the mother ship is small (∼100 km) and are used as the plasma monitors at ion-scales when the distance is larger (100-300 0km). There is lively on-going discussion on the SCOPE-M3 collaboration, which would certainly make the coverage over the scales of interest better and thus make the mission success to be attained at an even higher level.
  • Yuichi Tsuda, Osamu Mori, Shinsuke Takeuchi, Jun'ichiro Kawaguchi
    International Astronautical Federation - 56th International Astronautical Congress 2005 5 2935-2941 2005年  
    Japan Aerospace Exploration Agency (JAXA) is currently studying on the "Solar Sail" propulsion for future deep space explorations. One of the key technologies to realize the solar sail is how light and how compact we can make the photon acceptance surface. JAXA has conducted extensive studies on utilizing centrifugal force to deploy the photon acceptance surface. The final objective is to realize the 7.5μmthickness and 50m diameter polyimide membrane, combined with thin flexible solar cells, as the photon acceptance surface that will be needed around the Jupiter orbit. In the August 9, 2004, JAXA has launched the S-310 sounding rocket, which tested two different shapes of membranes during the zerogravity flight. The first type of the membrane looks like a "clover-leaf", and another is like a "fan". These two membranes, both of them have 10m diameter, were unfolded sequentially during the zerogravity flight under the free spin condition, and their behavior was observed by onboard cameras. This paper focuses on the "clover-leaf" solar sail, which was fully deployed successfully, and introduces the S-310-34 experiments, and then shows the flight results and postflight evaluations.
  • Nobuaki Ishii, Yoshifumi Inatani, Satoshi Nonaka, Takashi Nakajima, Abe Takumi, Tsuda Yuichi, Takamasa Yamagami
    European Space Agency, (Special Publication) ESA SP (590) 13-18 2005年  
    In October 2003, a new space agency, JAXA (Japan Aerospace Exploration Agency) was reorganized and started as a primary space agency to promote all space activities in Japan. The Institute of Space and Astronautical Science (ISAS) belonged to JAXA and continued to promote space science and technologies using unique scientific satellites, sounding rockets and balloons. This paper summarizes sounding rocket and ballooning activities of ISAS in the fiscal year of 2003 and 2004, associated with satellite launch programs. In this time period, three sounding rockets and nineteen balloons were launched by ISAS. One of the sounding rocket, S-310-35 was an international collaboration between Japan and Norway, which was launched from Andoya Rocket Range (ARR), Andenes, Norway, so as to study the upper atmospheric dynamics and energetics associated with the auroral energy in the polar lower thermosphere. Through the combination with the national researchers and the cooperation with international organizations, ISAS will keep its own flight opportunities and be able to obtain many new scientific findings.
  • 戸田 知朗, 斎藤 義文, 津田 雄一
    3 1737-1744 2005年  
  • 中須賀真一, 酒匂信匡, 津田雄一, 永島隆, 船瀬龍, 中村友哉, 永井将貴
    電子情報通信学会論文誌 B J88-B(1) 41-48 2005年  査読有り
    2003年6月30日,東京大学中須賀研究室が開発した超小型衛星CubeSat-XI(1kg,10cm立方)がロシア連邦プレセツクより高度820kmの太陽同期軌道に打ち上げられた.その後,当初の予想を超え1年以上の長期にわたり順調に動作し,バス機器の軌道上実証,画像取得・ダウンリンクなどの実験を行って大きな成果を収めた.この衛星は学生の手作りにより開発された衛星で,その第一の目的は宇宙工学教育であるが,民生品をベースに低コスト・短期に衛星を提供することによる新しい宇宙開発を試行することをその先の目的としている.本論文では,CubeSat-XIの概要と軌道上実証の成果を述べ,その開発経験や成果を踏まえ,宇宙開発の低コスト化・短期開発化を目指した小型・超小型衛星開発のあり方を論じる.
  • Osamu Mori, Yuichi Tsuda, Maki Shida, Jun'ichiro Kawaguchi
    European Space Agency, (Special Publication) ESA SP (548) 117-122 2004年  
    ISAS/JAXA is studying a deployment method using centrifugal force for solar sail mission. In this paper, the clover type sail is investigated. The deployment sequence consists of two stages. In order to analyze the motion of the dynamic deployment, S-310 flight experiment is conducted. In this experiment, the clover type sail of 10 m diameter is deployed dynamically. Numerical simulations by multi-particle model are also conducted to analyze the complicated motion. The experiment and simulation results are compared with each other to validate the analytical model. On the other hand, we schedule to conduct a balloon experiment. The clover type sail of 20 m diameter is deployed statically. The mechanisms for first stage and second stage deployments are introduced.
  • Yusuke Nishimura, Yuichi Tsuda, Osamu Mori, Jun'ichiro Kawaguchi
    International Astronautical Federation - 55th International Astronautical Congress 2004 1 468-475 2004年  
    As one means of propulsion for the future deep space explorers, Japan Aerospace Exploration Agency (JAXA) is conducting research on the "Solar Sail", which is driven by the momentum of photons from the sunlight. Among several candidates of deployment and shape-forming strategies of the sail, JAXA has been focusing on the utilization of centrifugal force. However, it is very difficult to conduct the deployment experiment of the large membrane structure due to aerodynamic drag and gravity. Then, In August in 2004, we performed the experiment to deploy two types of membrane structures made by polyimide film with a sounding rocket. During the ballistic flight, two types of membranes are deployed in turn. We call the two sails "Clover-type sail" and "Fan-type sail", respectively. The cameras on the rocket recorded the images of the membrane and various sensors measured the behavior of the membrane. The data are transmitted to the ground as the telemetry. We succeeded in deploying the membrane whose diameter is 10 meters in space for the first time in the world. This paper deals with the experiment with the rocket and the result of the Clover-type sail.
  • Shinsuke Takeuchi, Yuichi Tsuda, Osamu Mori, Yoko Aoki
    International Astronautical Federation - 55th International Astronautical Congress 2004 4 2278-2285 2004年  
    A solar sail is one of propulsion systems for near future interplanetary mission, which utilizes solar pressure for thrust by reflecting sunlight with very large membrane. A solar sail is proposed for an engineering experiment satellite. Although a deployment experiment is necessary in order to verify the solar sail design, it is difficult to perform an experiment of large membrane on the ground because of its lower stiffness. To solve this problem, we used a sounding rocket. On the last August we launched our sounding rocket S-310 No.34 to investigate two solar sail designs « clover type sail (previously it was called reverse umbrella type sail)» and «fan type sail». The rocket was successfully launched and we got some pictures during deployment of the sails. In this paper we will report the result of the experiment.
  • Yuichi Tsuda
    International Astronautical Federation - 55th International Astronautical Congress 2004 1 99-105 2004年  
    A relative orbit maintenance strategy of multiple spacecrafts flying in formation is discussed. The optimal delta-V scheduling, formation position adjustment, and target points recombination algorithms are introduced to minimize the total delta-V required for formation changing based on the linearized orbital equation of motion around an arbitrary conic orbit. The resulting optimization scheme is not only applicable to high eccentricity orbits in which Institute of Space and Astronautical Science (ISAS) is interested for several future scientific missions, but also to a very large formation (with over 100 spacecrafts) due to the simple and fast optimization formulations.
  • Shinichi Nakasuka, Nobutada Sako, Yuichi Tsuda, Shinichi Ukawa, Ryu Funase, Fuyuto Terui, Shinichi Kimura, Keisuke Yoshihara, Toru Yamamoto
    54th International Astronautical Congress of the International Astronautical Federation (IAF), the International Academy of Astronautics and the International Institute of Space Law 1 651-658 2003年  
    On a NASDA's microsatellite named "μ-LABSAT," which was launched by H-IIA on December 14, 2002 (Fig.1), Communications Research Laboratory (CRL), National Aerospace Laboratory (NAL) and University of Tokyo (UT) have been jointly performing several orbital experiments as technology demonstration towards the future orbital servicing missions. In University of Tokyo's experiment which was held on May 14, 2003, the micro-satellite released a small object named "target," and its rotational motion was estimated by the images captured continually using a camera developed by CRL. Then satellite attitude control was performed by visual feedbacks of the target image position on the camera frame so that the target image may come to a certain point on the camera frame. This is a pre-experiment of so-called LOS (Line Of Sight) control, which will be indispensable during rendezvous and docking to the satellite to be serviced. In this paper, the objectives and procedure of these experiments, and the results will be described. Copyright © 2003 by the International Astronautical Federation. All rights reserved.
  • TSUDA Yuichi, SAKO Nobutada, EISHIMA Takashi, ITO Takahiro, ARIKAWA Yoshihisa, MIYAMURA Norihide, TANAKA Akira, NAKASUKA Shinichi
    The Journal of space technology and science : a publication of Japanese Rocket Society 16(1) 37-46 2000年3月1日  
    This paper describes outline of the University of Tokyo Intelligent Space Systems Laboratory(ISSL)'s CubeSat "XI" for the demonstration of the pico-satellite bus technology and validation of the commercial-off-the-shelf parts in space as well as the earth imaging mission. CubeSat project is the international joint program, which aims for developing and actually launching 10cm cubic satellites weighing less than 1kg to the earth's orbit. 18 CubeSats developed by Japanese and U.S. institutes are to be launched by the Russian launch vehicle "Dnepr" in Nowember 2002 to the Sun-synchronized orbit. The project in ISSL is conducted by 20 space engineering students as a material of education.

MISC

 283

書籍等出版物

 5

主要な講演・口頭発表等

 58

共同研究・競争的資金等の研究課題

 7

産業財産権

 6