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Attitude Control Dynamics of Spinning Solar Sail “IKAROS” Considering

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Attitude Control Dynamics of Spinning Solar Sail “IKAROS” Considering Thruster Plume Osamu Mori, Yoji Shirasawa, Hirotaka Sawada, Ryu Funase, Yuichi Tsuda, Takanao Saiki and Takayuki Yamamoto (JAXA), Morizumi Motooka and Ryo Jifuku (Univ. of Tokyo) Abstract In this paper, the attitude dynamics of IKAROS, which is spinning solar sail, is presented. First Mode Model of out-of-plane deformation (FMM) and Multi Particle Model (MPM) are introduced to analyze the out-of-plane oscillation mode of spinning solar sail. The out-of-plane oscillation of IKAROS is governed by three modes derived from FMM. FMM is very simple and valid for the design of attitude controller. Considering the thruster configuration of IKAROS, the force on main body and sail by thruster plume as well as reaction force by thruster are integrated into MPM. The attitude motion after sail deployment or reorientation using thrusters can be analyzed by MPM numerical simulations precisely. スラスタプルームを考慮したスピン型ソーラーセイル「IKAROS」の姿勢制御運動 森 治，白澤 洋次，澤田 弘崇，船瀬 龍，津田 雄一，佐伯 孝尚，山本 高行（JAXA）， 元岡 範純，地福 亮（東大） 摘要 本論文ではスピン型ソーラーセイル IKAROS の姿勢運動について示す．スピン型ソーラーセイル を解析するために一次面外変形モデルおよび多粒子モデルを導入する．まず，一次面外変形モデ ルから導出される 3 つのモードが IKAROS の面外運動を支配していることを示す．このモデルは 非常に簡易であり，姿勢制御設計に有効であると言える．一方，多粒子モデルに対しては， IKAROS のスラスタ配置を考慮して，スラスタの反力だけでなくスラスタプルームが本体や膜面 に及ぼす力を組み込み，セイル展開後およびスラスタによるマヌーバ後の姿勢運動を数値シミュ レーションにより詳細に解析する． 1. Introduction for the numerical model. Considering the thruster configuration of IKAROS, the force on main body and A solar sail 1) is a space yacht that gathers energy for sail by thruster plume as well as reaction force by propulsion from sunlight pressure by means of a thruster are integrated into MPM. The Fast Fourier membrane. The Japan Aerospace Exploration Agency Transform (FFT) results from IKAROS flight data are (JAXA) successfully achieved the world’s first solar sail compared with those from simulation data. technology by IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun) mission 2) in 2010. JAXA is also studying the extended solar sail mission toward Jupiter and Trojan asteroids exploration via hybrid electric photon propulsion 3) as shown in Fig. 1. There are two types of solar sail as shown in Fig. 2. 4, 5) First is the mast type , which uses some rigid support structure to deploy and maintain the sail. The other is Fig. 1 IKAROS mission and extended solar sail mission the spin type which uses spinning centrifugal force. The deployment motion and attitude control of mast type are Mast type Spin type simpler than those of spin type. A lot of solar sail missions of mast type are studied as shown in Table 1. On the other hand, spin type can be accomplished with lighter-weight mechanisms than mast type because it ©NASA JAXA does not require rigid structural elements. Thus spin type should be selected in case of a large solar sail. Fig. 2 Mast type and spin type IKAROS demonstrates a spin type solar sail whose area is 200m2 for extended solar sail whose area is 2000m2. Table 1 Solar sail missions In this paper, the attitude dynamics of IKAROS, Mission Who Sail size [m2] Launch Type IKAROS JAXA 200 Launched on May 2010 Spin which is spinning solar sail, is presented. The out-of- NanoSail-D2 NASA 20 Launched on Nov. 2010 Mast Lightsail-1 TPS 32 Planning in 2011 Mast plane oscillation modes of IKAROS are derived from Cube Sail EADS - Surrey 25 Planning in 2011 Mast Cube Sail CU Aerospace 20 Planning in 2012 Mast First Mode Model of out-of-plane deformation (FMM) Lightsail-2 TPS 100 Planning in 2013 Mast 6) 7) analytically. Multi Particle Model (MPM) is used Ultra Sail CU Aerospace 100 Planning in 2015 Mast Extended solar sail JAXA 2000 Planning in 2019 Spin 2. Dynamics Model of Spinning Solar Sail x, y, z: angular velocity around three axes I1 and I2 are defined as This section presents IKAROS sail design and r b 3 introduces two dynamics model of spinning solar sail. The I1 2h r r dr (5) r a first one is a simplified analytical model and the other one rb 2 is a precise numerical model incorporating the flexibility of I 2 2h r r r ra dr (6) r the sail. a where (r): density of sail [kg/m3] 2.1. IKAROS Sail Design h: thickness of sail [m] Fig. 3 shows IKAROS sail design. The shape of the r : inner radius of sail [m] sail is a square whose diagonal distance is 20m. The sail a r : outer radius of sail [m] membrane is made of polyimide resign whose thickness b and constitutes the first-order mode of the out-of- is 7.5 m. It is connected the main body by tethers. The plane sail deformation w as follows. shape of the main body is a cylinder whose diameter is w r,,t r r t sin r r t cos (7) 1.6m. A tip mass whose weight is 0.5kg is attached to a a each tip of the membrane in order to support the where corresponds to the phase of the spin motion of spinning deployment. Thin film solar cell and steering the main body. device are attached on the membrane. Therefore Here we analyze the attitude dynamics of the solar IKAROS sail is not uniform. sail. State equations of the system can be described as the following equation. 20m dx Tip mass Ax (8) dt Tether Where T x x y (9) Main body I 0 0 2 0 0 1 N 1 I sc 2 Thin film solar cell I 0 0 0 2 1 N 1 0 (10) I sc 2 Steering device 1 0 0 0 0 0 A 0 1 0 0 0 0 I Fig. 3 IKAROS sail design 0 0 2 1 2 0 0 N sc I1 I 0 0 0 2 12 N 0 2.2. First Mode Model of out-of-plane deformation sc I1 (FMM) 1 An analytical dynamics model of the sail is derived I I I I x 1 2 considering first mode of deformation of the sail. Here 1 2 (11) I I we consider circular spinning solar sail configuration 2 x for analytical dynamics model shown in Fig. 4. The I z Nsc 1 (12) spinning solar sail consists of a main body and a large I x sail connected with the main body, which rotate around It can be said that the dynamical property of the system the Z-axis at a rate of . is determined by the following three parameters which In this research, we adopted the dynamic model 6) can be calculated by the moment of inertia of the main considering the first mode of sail deformation body and the sail. proposed by Nakano, et al. The conservation laws of I angular momentum and the equations of motion of sail 2 ,, N (13) I sc are 1 2 The characteristic equation of the system can be derived I 2 I1 I1 y x 0 (1) as the following equation. I I 2 I 0 (2) 2 2 1 1 x y 2 I 2 2 2 2 2 1 2 detsI A s s Nsc s 2 Nsc 1 0 1 2 I 2 I x J I y I 2 0 (3) 2 (14) 1 2 It is found that the following three modes of oscillation I y J I x I 2 0 (4) 2 constitute the nutation of the solar sail. where B0 , B1, B2 (B0 B1 B2 ) (15) I1: moment of inertia (MOI) of sail Table 2 shows them. In the IKAROS configuration, Ix: MOI of main body around X, Y-axis I2/I1=0.78. In the cases of ra=0 (sail is as large as main Iz: MOI of main body around Z-axis body) and ra=rb (sail is much larger than main body), I: MOI of overall spacecraft around X, Y-axis (=Ix+I1/2) I2/I1=1 and I2/I1=0, respectively. In all cases, one of J: MOI of overall spacecraft around Z-axis (=Iz+I1) three modes of oscillation is nearly equal to the spin rate model can also take into account the effect of bending . It is caused by nutation motion. The other two modes stiffness of each element and crease stiffness of folding are caused by sail motion. line by implementing rotational spring, however these characteristics have little effect on the global behavior ZB of the sail, and are not considered in this study. For the Main body scheme of numerical time integration, the explicit Sail Runge-Kutta-Gill method is employed. ra rb w(r, , t) YB z X B Fig. 4 First mode model of out-of-plane deformation Table 2 Three modes of oscillation analyzed by FMM y I2/I1 B0 B1 B2 0.01 0.929 28.9 29.4 0.5 0.919 2.76 3.29 x L K 0.78 0.884 1.50 1.99 C 0.99 0.442 1.01 1.06 Fig. 5 Multi particle model of IKAROS 2.3. Multi Particle Model (MPM) 3. Attitude Dynamics of IKAROS When a numerical modeling method which can This section shows the attitude dynamics of analyze the dynamics of spinning solar sail is required, IKAROS. The out-of-plane oscillation modes of the useful model includes Finite Element Method 8) following two motions are analyzed. (FEM) . However, when the FEM is applied for the - motion after sail deployment analysis of the dynamics of solar sail, it is thought that it - motion after reorientation using thrusters takes huge time to achieve the valuable information about the attitude motion of solar sail if a lot of 3.1.
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