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  2h 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  2h 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    I  sc   1     I   0 0 0  2  12 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 detsI  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 Runge-Kutta-Gill method is employed. Sail r r a b 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. Motion after Sail Deployment parameters are varied. So, Multi Particle Model (MPM) The deployment method of IKAROS consists of two is used for the numerical model in this study. The stages as shown in Fig. 6. In the first stage deployment, characteristics of MPM are that it takes less time for each quarter of the sail is extracted like a Yo-Yo dynamics simulation and can perform more stable despinner and the sail forms a cross shape. If the analysis than FEM, because MPM is a model which deployment is performed dynamically, each quarter is substitutes the elements of sail for particles connected twisted again around the main body just after the by springs and dampers. deployment. Therefore the first stage deployment is Fig. 5 illustrates the MPM of IKAROS. The sail is performed quasi statically by activating the guides that modeled by mass-spring network and the main body is hold the sail through the relative rotation mechanism. modeled by rigid body. Mass of each particle is The second stage deployment is performed dynamically determined based on a designed value and actual by activating the guides and releasing the hold of the measured value of membrane, tether, tip mass, thin film sail. The sail expands quickly to form a square shape. solar cell and steering device, and ununiform mass Fig. 7 shows the angular velocities of main body at distribution is considered. The inter-particle tension T second stage deployment. The oscillations of angular can be described as following form: velocities of x and y axes are occurred and damped  KL  L0  KL L  L0  gradually after second stage deployment start, because T   (16) the second stage deployment is performed dynamically. KL  L0  KL L  L0  The spin rate of z-axis is 0.0417Hz (=). where K, L0, L, α and  denote spring constant, natural length of spring, distance between two particles, Fig. 8 shows the FFT results of x-axis angular coefficient of compression stiffness and damping ratio, velocities of IKAROS flight data and MPM numerical respectively. Assuming that the sail resists a simulation data after sail deployment. The first peak compression slightly, nonlinear spring model using frequency of flight data, 0.0371Hz (=0.890) is equal coefficients of compression stiffness are employed. The to that of numerical simulation data, 0.0366Hz spring constant K is determined by applying the (=0.878) as shown in Table 3. They are also equal to principle of virtual work on an element so as to satisfy B0 (=0.884) which is one of three modes analyzed the relations of strain energy. This model assumes that by FMM as shown in Table 2. Because it is nearly equal the stress in the direction along each spring depends to the first peak is caused by nutation motion. The only on the strain in the same direction, so that the other peaks of flight data and MPM data are equal to elasticity matrix is approximated to be diagonal. This B2 (= 1.99) and B1 (= 1.50), which are the other

two modes analyzed by FMM. Thus the motion after 3.2. Motion after Reorientation using Thruster sail deployment is governed by three modes derived IKAROS has following three methods of from FMM. reorientation. - reorientation using thrusters 9) First stage deployment (quasi static) - reorientation using steering devices - reorientation using solar pressure torque The oscillatory motion of the sail is occurred due to the impulsive torque by thrusters. We consider the Second stage deployment (dynamic) attitude maneuver using thrusters. IKAROS has four thrusters on the main body to perform spin up, spin down, reorientation as shown in Fig. 9. - spin up: thrusters 1 and 3 Guide - spin down: thrusters 2 and 4 Fig. 6 Deployment method of IKAROS - reorientation: thrusters 1 and 2, or thrusters 3 and 4 In this thruster configuration, the thruster plume Second stage deployment start impinges on main body and sail. Thus the force on main 30 1 body and sail by thruster plume as well as reaction force by thruster should be considered as shown in Fig. 10.

ωx Figs. 11 and 12 shows plume flow model and plume impingement model. Plume flow and plume 20 0 impingement are formulated by source flow method and ω y free molecule flow, respectively. The force by thruster

Z Spin Rate , [deg/s] plume is integrated into multi particle model by X,Y Spin Rate , [deg/s] ωz Spin rate (z-axis) [deg/s] (z-axis) Spin rate following three steps as shown in Fig. 13.

10 -1

Angular velocities (x,y-axes) [deg/s] 1) Calculate the force on center of triangle element of 10000 20000 sail using plume flow and impingement models. Time , [sec] 2) The force is decomposed into normal and shearing Fig. 7 Angular velocities of main body at second stage forces. deployment 3) These forces are distributed to three particles.

When the spin rate of z-axis is 0.247Hz (=), the B B B    wx 0 0 1 2 10 reorientation using thrusters 3 and 4 is performed. Fig.

-1 14 shows the angular velocities of main body. The 10 oscillations of angular velocities of x and y axes are -2 10 occurred due to the impulsive torque by thruster and

-3 10

SPECTRUM thruster plume. 10-4 Fig. 15 shows the FFT results of x-axis angular

-5 10 velocities of IKAROS flight data and MPM numerical

-6 simulation data after reorientation using thrusters. The 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 frequency (Hz) first peak frequency of flight data, 0.0488Hz (=0.198) (a) IKAROS flight data

-2 wx is equal to the second peak frequency of numerical 10 simulation data, 0.0469Hz (=0.190); the second peak frequency of flight data, 0.0391Hz (=0.158) is equal

-3 10 to the first peak frequency of numerical simulation data, 0.0371Hz (=0.150) as shown in Table 4. They are SPECTRUM

-4 10 equal to B2 (=1.99) and B1 (=1.50) which are two of three modes analyzed by FMM as shown in Table 2. Because they are not equal to , the first and

10-5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 frequency (Hz) second peaks are caused by sail motion. The other peaks (b) MPM numerical simulation data of flight data and MPM data are equal to B  (= 0 Fig. 8 FFT results of x-axis angular velocities after sail 0.884), which are the other one modes analyzed by deployment FMM. Thus the motion after re-orientation using thrusters is governed by three modes derived from Table 3 First peak of motion after sail deployment FMM.

First peak [Hz] Fight data 0.0371 (=0.890) MPM data 0.0366 (=0.878)

Re-orientation

Main body ωy Tank Thruster 2 Thruster 1

Thruster 3 Thruster 4

Fig. 9 Attitude maneuver using thrusters ωx

Force on main body by thruster plume Main body Force on membrane Membrane by thruster plume Fig. 14 Angular velocities of main body when Reaction force Thruster reorientation using thrusters is performed by thruster plume Thruster B0 B1 B2 -1 wx Fig. 10 Reaction force by thruster and force on main 10

body and sail by thruster plume -2 10

-3 10 Free molecule Transition flow SPECTRUM (freezing) -4 10 region Continuum r -5  10

Plume axis 10-6 r, 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Nozzle frequency (Hz) Flow types in a plume (a) IKAROS flight data

-3 wx expanding into vacuum 10

10-4 Fig. 11 Plume flow model: source flow method

-5 10

-6 10 SPECTRUM Pw -7 Incident plume Pi 10

-8 10

 i -9 10 Tw 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Diffuse reflection Specular reflection frequency (Hz) p (2  )ppiw   , : Reflection coefficients Fig. 15 FFT results of x-axis angular velocities after    (These parameters are independent) i reorientation using thrusters Fig. 12 Plume impingement model: free molecule flow Table 4 First and second peaks of motion after reorientation using thruster First peak [Hz] Second peak [Hz] Normal vector Fight data 0.0488 (=0.198 0.0391 (=0.158) of triangle element MPM data 0.0371 (=0.150) 0.0469 (=0.190)

Thruster Normal force 4. Conclusions Center of triangle elements  In this paper, the attitude dynamics of IKAROS was presented. Sharing force 1) First Mode Model of out-of-plane deformation Plume axis (FMM) and Multi Particle Model (MPM) were Fig. 13 Integrating force by thruster plume into multi introduced to analyze the out-of-plane oscillation mode particle model of spinning solar sail. 2) Three modes of out-of-plane oscillation were derived from FMM analytically. One of them is caused by nutation motion, because it is nearly equal to the spin rate. The other two modes are caused by sail motion. 3) The out-of-plane oscillation was occurred after sail deployment. The first peak frequency of flight data was

equal to that of MPM numerical simulation data. It is [5] J. D. Hinkle, P. Warren and L. D. Peterson, equal to a mode which is caused by nutation motion. “Geometric Imperfection Effects in an Elastically 4) The out-of-plane oscillation was also occurred after Deployable Isogrid Column,” Journal of Spacecraft and re-orientation using thrusters. The first and second peak Rockets, Vol.39, pp.662-668, 2002. frequencies of flight data were equal to those of MPM [6] T. Nakano, O. Mori and J. Kawaguchi, “Stability of numerical simulation data. Spinning Solar Sail-craft Containing A Huge They are two modes which are caused by sail motion. Membrane,” AIAA Guidance, Navigation and Control 5) These motions are governed by three modes derived Conference and Exhibit, AIAA-2005-6152, 2005. from FMM. [7] Y. Shirasawa, O. Mori, Y. Miyazaki, H. Sakamoto, 6) FMM is very simple and valid for the design of M. Hasome, N. Okuizumi, H. Sawada, S. Matunaga, H. attitude controller. MPM is the model incorporating the Furuya and J. Kawaguchi, “Evaluation of Membrane flexibility of the sail and valid for precise numerical Dynamics of IKAROS Based on Flight Result and simulations. Simulation Using Multi-Particle Model,” 28th International Symposium on Space Technology and Science, 2011-o-4-05v, 2011. References [8] Y. Miyazaki, H. Sakamoto, Y. Shirasawa, O. Mori, [1] R. M. Colon, “Solar Sailing, Technology, Dynamics H. Sawada, M. Yamazaki and IKAROS Demonstration and Mission Applications,” Springer-Praxis, 1999. Team, “Finite Element Analysis of Deployment of Sail [2] O. Mori, Y. Tsuda, H. Sawada, R. Funase, T. Membrane of IKAROS,” 28th International Symposium Yamamoto, T. Saiki, K. Yonekura, H. Hoshino, on Space Technology and Science, 2011-o-4-06v, 2011. Minamino, T. Endo and J. Kawaguchi, “World's First [9] R. Funase, Y. Shirasawa, Y. Mimasu, O. Mori, Y. Mission of Solar Power Sail by IKAROS,” International Tsuda, T. Saiki and J. Kawaguchi, “Fuel-free and Conference on Space, Aeronautical and Navigational Oscillation-free Attitude Control of IKAROS Solar Sail Electronics, SANE2010-95, 2010. Spacecraft Using Reflectivity Control Device,” 28th [3] J. Kawaguchi, “A Solar Power Sail Mission for A International Symposium on Space Technology and Jovian Orbiter and Trojan Asteroid Flybys,” Science, 2011-o-4-09v, 2011. COSPAR04-A-01655, 2004. [4] G. Greschik and M. M. Mikulas, “Design Study of a Square Solar Sail Architecture,” Journal of Spacecraft and Rockets, Vol.39, pp.653-661, 2002.