Consideration for Future Orbit Plan of IKAROS

Transcription

1 Consideration for Future Orbit Plan of IKAROS Yuya Mimasu 1), Ryu Funase ), and Jun ichiro Kawaguchi ) 1) Deartment of Aeronautics and Astronautics, Kyushu University, Fukuoka, Jaan ) JAXA Sace Exloration Center, Jaan Aerosace Exloration Agency, Sagamihara, Jaan Abstract The orbit of a solar sail can be controlled by changing the attitude of the sacecraft. In this study, we consider the sinning solar ower sail IKAROS (Interlanetary Kite-craft Accelerated by Radiation Of the Sun), which is managed by Jaan Aerosace Exloration Agency (JAXA). The IKAROS attitude, i.e. the direction of the sin-axis is nominally controlled by the rhumb-line control method. By utilizing the solar radiation torque, however, we are able to change the direction of the sin-axis by only controlling its sin rate. With this sin rate control, we can also control indirectly the solar sail's trajectory. The main objective of this study is to construct the orbit control strategy of the solar sail via the sin rate control. We evaluate this strategy in terms of the consumtion of the roellant comared to the nominal control method. ) IKAROS の今後の軌道計画に関する一考察 1) 三桝裕也 1), 船瀬龍 ), 川口淳一郎 九州大学大学院工学府航空宇宙工学専攻宇宙航空研究開発機構月 惑星探査プログラムグループ ) 摘要ソーラーセイルの軌道は, 探査機の姿勢を変更することにより制御される. 本論文においては, 宇宙航空研究開発機構 (JAXA) によって運用が行われている小型ソーラー電力セイル IKAROS (Interlanetary Kite-craft Accelerated by Radiation Of the Sun) を対象に行った研究の内容を報告する.IKAROS の姿勢は, 通常ラムライン制御を用いてスピン軸の変更を行うが, 太陽輻射圧トルクを利用することにより, スピンレートを制御することでスピン軸を変更することが可能である. つまり, スピンレートを制御することにより, 最終的に探査機の軌道を変更することも可能となる. 本研究における目的はスピンレート制御によるソーラーセイルの軌道制御手法を提案し, 燃料消費量に対する有用性を評価することである. 1. Introduction 1.1 Background It is well known that the thrust force of the solar sail due to the solar radiation ressure deends on the orientation of the sail with resect to the Sun direction. Therefore, the orbit of the solar sail can be controlled by changing the attitude of the sacecraft. In this study, we consider the sinning solar ower sail IKAROS (Interlanetary Kite-craft Accelerated by Radiation Of the Sun, shown in Fig. 1), which was launched on 1 st of May in 1 1). The IKAROS attitude, i.e. the direction of the sin-axis is nominally controlled by the rhumb-line control method ). By utilizing the solar radiation torque, however, we are able to change the direction of the sin-axis only by controlling its sin rate. The direction of the sin-axis can trace the Sun direction automatically without any roellant as was roven by the Hayabusa s flight oeration 3). With this sin rate control, we also control the solar sail s trajectory. The main objective in this study is to construct the orbit control strategy of the solar sail Fig. 1. Solar ower sail IKAROS via the sin rate control secified for IKAROS trajectory. This means that we need to take into account the attitude and orbit dynamics simultaneously. 1. Objective By utilizing the attitude drift motion, the acceleration direction of the solar sail toward the along-track direction can be changed. This means that the solar sail can accelerate and also decelerate with resect to the along-track direction with the SRP torque effect. As the short eriod simulation examle, we select the targeting roblem to the Venus vicinity of the IKAROS trajectory. In this simulation, we define several aim oints in the shere of influence of the Venus, and evaluating 1

2 each targeting result by the amount of the fuel consumtion. Therefore, in this targeting simulation, the objective function for the otimization is the sin rate variation during the simulation eriod. Finally we comare the fuel consumtion of this orbit steering method by the sin rate control with the orbit control by the nominal attitude control method.. IKAROS Characteristics The solar sail demonstration sacecraft IKAROS investigated by JAXA has the cylindrical body and the square sail membrane as shown in Fig. 1. This sacecraft was launched on 1 st May 1 as the sub-ayload of the PLANET-C; the Venus climate orbiter (which is also develoed by JAXA). On 9 th June 1, IKAROS finally succeeded to deloy the membrane in dee sace to become the world s first oerational solar sail, and at resent it is in the nominal oeration mode. Because IKAROS was inserted into the transfer orbit to the Venus with PLANET-C, it nominally goes to Venus as shown in Fig.. Although it is already able to reach the neighborhood of Venus without any orbit corrections, it is necessarily that the orbit correction by the hoton acceleration generated by solar sailing for recise targeting. The main secifications of IKAROS are summarized in Table 1. Table 1. Main Secifications of IKAROS Parameter Secification Size of Membrane: 14 x 14 [m] Material of Membrane: Polyimide Total Mass: < 37 [kg] Moment of Inertia: (Ix, Iy, Iz) = (434, 434, 868) [kgm ] Secular Reflectivity:.719 Diffusive Reflectivity:.117 Absortivity:.16 Attitude Control: Sin Attitude Actuator: gas-liquid equilibrium thrusters Nominal Mission Period Half Year z [km] IKAROS Earth Venus Fig.. IKAROS trajectory to Venus y [km] x [km] Fig.. Orbit of IKAROS to the Venus The sail membrane of IKAROS consists of 7.5m Polyimide and it is evaorated by aluminum in 8 [nm] thickness. A olyimide has the high thermal, mechanical and chemical resistance roerties and is very light. Although the secular reflectivity of the membrane itself is relatively high due to the reflective roerties of aluminum, the averaged secularity is degraded by several devices on the membrane. The main devices are the Flexible Solar Array (FSA) 4) and the Reflectivity Control Device (RCD). The FSA is a thin ower collector. If the large ower collection system using this FSA can be constructed, it would be ossible to load the high ower ion engine on a future solar sail sacecraft 5). The RCD is mounted on the edge of the sail membrane, and it can generate a torque by changing the induced force on each small element s surface 6). By using this RCD, the sacecraft would not need any roellant to control the attitude. Although the RCD has the caability to become a feasible attitude actuator in the future, it is one of the exerimental instruments at the current stage. Therefore, IKAROS uses the gas-liquid equilibrium thrusters 7) as the nominal attitude actuator. 3. Attitude Drift Motion By utilizing the solar radiation torque, the sacecraft can y ine: Inertial Reference Frame orb, y sun, z sat change the direction of its sin-axis without using any sun: Sun-Pointing Frame roellant. In the return hase to the Earth, Hayabusa roved y orb: Orbit Reference Frame SF the feasibility of this auto Sun trace control method 3) SF: Sin Free Body Frame. When the x sin axis closely oints to the Sun direction, the sacecraft can sat x SF x sun obtain the secific SRP torque that enables the sin axis to trace the Sun direction automatically. The attitude dynamics of Sin axis CM of sacecraft = z this control can be understood within the inertial reference SF x orb frame and also in the Sun-ointing frame as defined as Fig. 3. y sat s Here we should note that if the direction of the sin axis oints toward the exact Sun direction, there would be no SRP torque Orbit Orbit lane (under the assumtion that the lever arm is only along the sin axis). Therefore, the sin axis should be a few degrees away from the Sun direction in order that the SRP torque can be z orb z sun Fig. 3 Definition of reference frames generated. In the sin-free body-fixed coordinate system rotating with resect to the inertial sace (Sun-ointing frame in Fig. 3), the Euler equations around the x and y axis can be exressed as follows by using the longitude and latitude (see Fig. 3) when the sail is assumed to be a simle flat late.

3 IT x H y k sin cos S (1) () IT y Hx k sin S with the angular rate SF and the angular momentum vector of the sacecraft H s/c : T T ω SF ( x, y, ), H S / C ( I T x, I T y, H ) (3) (4) where, I T denotes the moment of inertia around the transverse direction with resect to the sin direction, denotes the total sacecraft angular momentum (i.e., H nearly equal to I z ), s denotes the longitude of the Sun direction. Here, the SRP torque arameter k is introduced, which can be written as; k = P A(c abs + c dif ) / cl (5) P is the solar flux (= 1367 [W/m ]), A is the cross-sectional area of the membrane, L is the lever arm length between centers of mass and SRP, and c is the light seed, c abs and c dif denote the coefficients of absortion and diffusion, resectively. Equations (1) and () can be reduced as follows by using the relationshi between the angular rates; x and y cos under the assumtion that the angles and s are sufficiently small, so we can aroximate; n (6) (7) n s where n denotes the nutation rate roortional to the sin rate (i.e., n = H /I T = (I z /I T ), and denotes the SRP torque arameter which has the unit of the angular acceleration ( = k/i T ). Although this is the case when the sail shae is assumed to be a flat late, if the sail is deflected and distorted, the SRP torque can be inclined angle and Eqs. (6) and (7) are transformed as follow: n ( cos ( s )sin ) (8) (9) n sin ( s )cos Equations (8) and (9) can be maniulated into the following differential equations with the relationshi = - s ; (4) () (1) n cos n n s cos (1) (11) (4) () (1) n cos n n s sin The steady-state solutions of Eqs. (1) and (11) is given by the trivial solutions. n n s cos, s sin (1) (13) The characteristic angular frequencies * j (j = 1, ) can be derived from the characteristic equations of Eqs. (1) and (11) as follows with the relationshi / n << 1: * j sin i cos ( j 1, ) (14) - (15) n n If the sin-axis follows the exact direction of the equilibrium oint calculated in Eqs. (1) and (13), there would not be any long-term coning drift motion around the equilibrium direction. However, the fact that a certain initial ointing error remains leads to the very long-eriodic coning drift motion. Once we understand the attitude dynamics introduced above, this drift motion can be described as a siral motion. Therefore, we simlify this sin-axis drift motion in the Sun-ointing frame by the following equations: k k sin{ kt k1} k (16) (17) k k cos{ kt k1} k where t = t k - t k-1 is the time interval from t k-1 to t k, the subscrit k denotes the index of the arameter at time oint t k, k is the angular length at time t k, and k-1 is the hase angle at the revious time ste t k-1, defined as follows; t cos n k e ( k1 k ) ( k1 k ), k 1 atan( k1 k, k1 k ), k sin (18) () n By using Eqs. (16) (), we can determine the angles and at each oint in time t k when the initial, and the sin rate are defined. Thus, once the initial sin axis direction is determined, angles and are the functions of the sin rate. 4. Orbit Steering via Sin Rate Control The orbit of a solar sail is controlled by the normal ointing direction of the membrane. This is because the acceleration due to the solar radiation ressure (SRP) is a function of the Sun angle s and the normal direction vector n. The acceleration model is described as follow under the assumtion that the normal direction of each membrane segment is aligned with a certain direction in total, and the membrane area is given; 3

4 P A R a (cos s ){( cabs cdif ) s [ cdif cse (cos s )] n} (1) mc r 3 where R denotes the distance between Sun and Earth (= 1 [AU]), r denotes the actual distance between the Sun and the sacecraft, c abs denotes the absortivity, c dif denotes the diffusive reflectivity, c se denotes the secular reflectivity. The factor /3 in front of the c dif is due to the assumed Lambertian diffuse reflection of the front surface, s and n denote the Sun direction vector and the normal vector, resectively. As described by Eq. (1), the acceleration induced by SRP force deends on the attitude of the sacecraft. Therefore the trajectory of the solar sail can be controlled with this SRP force by varying the sin-axis direction. Considering the acceleration in the orbit reference frame (see Fig. 3), we can describe the comonents of the acceleration vector in Eq. (1) as follows; ( / 3cdif cos s cse cos s ) cos sin S A R a ( / 3c dif cos s cse cos s )sin () mc r ( c ) cos ( / 3 cos cos ) cos cos abs cdif s cdif s cse s with the Sun direction vector s = (.,., 1.) T, the normal vector of the membrane n = (cossin, sin coscos) T. For the simulations, we use Eq. () to model the acceleration. 5. Simulation with Otimization 5.1 Simulation Cases and Conditions In order to verify the feasibility of the orbit control by changing the sin rate, we imlement the simulations with the otimization for the fuel consumtion of the attitude control. In the simulation, the orbit is changed by solar sailing with the attitude change, and we imlement two attitude control cases i.e., the sin rate control case and the nominal control case (rhumb line control) for comarison. When the sacecraft is in the cruising hase (i.e., interlanetary transfer orbit), the SRP effect has the dominant effect in the orbit and attitude of the sacecraft. Therefore, we choose the eriod from the deloyment of the membrane (outside the Earth's shere of influence) to the arrival at the Venus Shere Of Influence (SOI) as the cruising hase. The state variables are the osition and velocity of the sacecraft, and the sin rate at each oint of time with the initial sin rate taken as 1 [rm]. In order to avoid an excessive deflection of the membrane, the sin rate is qualified above.5 [rm]. The common simulation conditions are summarized in Table. Table Simulation Conditions of Otimization Eoch 1/6/9 [UT] (Sail Deloyment) Final Eoch Free Initial Sin Rate 1 [rm] = 6. [deg/s] Sin Rate at t k (k > ).5 < k < 5. [rm] SRP Torque Parameter 3.88 x 1-7 [rad/sec ], = 3 [deg] Initial Position 7 million [km] from Earth Final Position Surface of Venus SOI In order to see the difference of the attitude evolution and the fuel consumtion due to the different final arrival oint, we target the several aim oints. These aim oints are defined on the surface of the Venus SOI as illustrated in Fig. 4. The aim oints are defined in the B-lane coordinate system. In the B-lane coordinate system in this study, the first axis B S is same direction as the aroaching relative velocity, and the third axis corresonds to the oosite normal direction of the Earth's equatorial lane. Then the second axis is defined as the normal direction toward these two axes. We define the standard aim oint that the sacecraft reaches when the sin axis direction always oints to the Sun direction ( and are always [deg]). Fig. 4 Geometry of aim oint on SOI surface 5. Otimization for Two Attitude Control Cases The attitude is controlled by changing the sin rate in the simulation. In order to evaluate the fuel consumtion of the sin rate control method, we also imlement the simulation for the nominal attitude control method which is erformed by the rhumb line control. The desired result in both attitude control cases is that the sacecraft reaches the SOI of Venus with the B S Trajectory of Sacecraft B-Plane Venus B R Trajectory Plane B T Incoming Asymtote Surface of SOI Aim Point V 4

5 minimum consumtion of roellant. For the sin rate control method, the minimized arameter is the difference of the sin rate between time t k and t k+1 (which means the consumtion of the roellant). Similarly, in the simulation of the nominal attitude control case, the minimization of the fuel consumtion is also imlemented. For this otimization, the summation of the angles between the sin-axis directions at each time ste is minimized. The fuel consumtion is calculated in the case when the sin rate is 1. [rm]. The objective function for the nominal attitude control case is defined as the angle tilt between the sin axis direction at t k and t k+1. Therefore, each objective function is defined as follow; N N J Min ( k 1 k ), J Min tilt (3) (4) k 1 k 1 By using these objective functions, the simulations are erformed. 5.3 Orbit and Attitude Dynamics in Simulator In order to consider the orbit dynamics in this otimization, we imlement simulation with the direct collocation using non-linear rogramming (DCNLP) 8). In the DCNLP, the trajectory is discretized in several segments. At each discrete time oint, the osition and velocity should be connected smoothly with the control arameters by comlying with the dynamics equations (the Keler equation in this simulation). As the control variable, the SRP accelerations described in Eq. (1) are taken into account. On the other hand, the attitude dynamics is the faster system comared to the orbit dynamics. Thus it takes time to calculate, if we numerically simulate the attitude in addition to the orbit (because we should discretize in a second through the simulation eriod, though the simulation eriod should be months or year). Therefore we aly the simlified attitude dynamics described in Eqs. (16) - () to the simulation for the sin rate control case. In this way, the orbit and attitude dynamics can be considered simultaneously, and finally the accelerations are determined by the sin rate. On the other hand, there is no constraint of the attitude in the simulation of the nominal attitude control case (i.e., almost attitude free motion). 6. Simulation Results 6.1 Fuel Consumtions The simulation results are shown in the following figures. -4 Figure 5 shows the aim oints in which the simulation is finally converged or not. Because of the directional roerty of the - sin rate control, there are several aim oints at which the simulation is not converged. Therefore, in these cases, there are no simulation results. The result of the fuel consumtions of the sin rate control cases are summarized in Fig. 6. As shown in this figure, it can be seen that the orbit steering by the sin rate control has an advantageous and disadvantageous area with resect to the aim oints. Figure 8 shows the results of the fuel 4 consumtions by the nominal attitude control method. The fuel consumtion of the nominal attitude control (rhumb line 6 control) is mainly caused by tracing the Sun, because the SRP effect to the attitude motion is not taken into account in this 8 case. Comaring Figs. 6 and 7, the fuel consumtion by the sin rate control is smaller than that of the nominal attitude control method only in the case when the aim oint is located at hase angle 15 [deg] in all radius length. Br [km] Venus r = 5 km r = 1 km r = 15 km r = km 18 [deg] In-Orbit Plane Direction 9 [deg] Out-Orbit Plane Direction Define aim oints radially from Sun-ointing case 7 [deg] Bt [km] Fig. 5 Aim oints in simulations [deg] Fuel Consumtion [kg] r = 5 [km] r = 1 [km] r = 15 [km] r = [km] Phase Angle from Orbit Plane Direction [deg] Fig. 6 Fuel Consumtion of sin rate control Fuel Consumtion [kg] r = 5 km r = 1 km r = 15 km r = km Phase Angle from Obit Plane Direction [deg] Fig.7 Fuel Consumtion of nominal attitude control 5

6 6. Otimized Attitude Motion and Sin Rate Behaviour Although we conduct several simulations, we show one examle of the simulation results. The shown result is obtained from the case when the aim oint is defined at r = [km] and the hase angle equals to 15 [deg], at which the fuel consumtion is minimum. The attitude motion resulted from the minimization of the fuel consumtion is shown in Fig. 8, and the sin axis direction is moved within small area (~1 [deg]) The history of sin rate as the control variable is shown in Fig. 9. This control history generates the attitude motion in Fig. 8. The trajectory and acceleration direction in this case are shown in Fig. 1. The acceleration vectors are almost Sun-ointing in this case due to the small attitude motion. Phi [deg] Sin Axis Direction Equilibrium Points Psi [deg] Sin Rate [rm] Time from Eoch [day] Fig. 8 Attitude motion by sin rate control Fig.9 Otimized sin rate behavior a) b) c) Fig. 1 - a) In x-y lane, - b) In y-z lane, - c) In z-x lane, IKAROS trajectory and acceleration direction in inertial frame 7. Conclusions In this study, we roose the original orbit steering technique of the solar sail which controls the orbit by changing the sin rate of the sacecraft. In addition, for this attitude drift motion, we aly the actual observed motion in the IKAROS oeration. By using this orbit steering method, the fuel consumtion is larger than the nominal control case in the almost case. However, we indicate there is advantageous direction for this orbit steering method, and the fuel consumtion is smaller than the nominal control case in the secific case. As the future study, we focus on that secific case and make clear the utility of this orbit steering method. References 1) Kawaguchi, J., et. al, IKAROS - Ready for Lift-off as the World's First Solar Sail Demonstration in Interlanetary Sace, 6th International Astronautical Congress, Daejeon, Reublic of Korea, 1-16 Oct., 9, Proceedings IAC-9-D ) Wertz, J. R. (Ed.), Sacecraft Attitude Determination and Control, Kluwer Academic, Dordrecht, Holland, The Netherlands, 1978, ) Kawaguchi, J., Shirakawa K., A Fuel-Free Sun-Tracking Attitude Control Strategy and the Flight Results in Hayabusa (MUSES-C), AAS 7-176, AAS Flight Mechanics Conference, Sedona, AZ, USA, Jan. 3 - Feb. 1, 7. 4) Tanaka, K., Soma, E., Sasaki, S., Kawaguchi, J., Develoment of Thin Film Solar Power Generation System and Alication to Solar Power Satellite, 1th SPS Symosium,.4-45, November, 9. 5) Kawaguchi, J., A Solar Power Sail Mission for A Jovian Orbiter and Trojan Asteroid Flybys, COSPAR, Proceedings COSPAR4-A-1655, Paris, France, 4. 6) Funase, R., Sugita, M., Miwa, Y., Mori, O., and Kawaguchi, J., Oscillation-Free Attitude Control of Sinning Solar Sail with Huge Flexible Membrane, ISTS7, Tsukuba, Jaan, July, 9, Paer 9-d-37. 7) Yamamoto, T., Mori, O. and Kawaguchi, J., New Thruster System for Small Satellite: Gas-Liquid Equilibrium Thruster, Transactions of the Jaan Society for Aeronautical and Sace Sciences, Sace Technology Jaan, Vol. 7 (9), ists6,.td 9-Td 33. 8) Enright, P., J., and Conway, B., A., Otimal Finite-Thrust Sacecraft Trajectories Using Collocation and Nonlinear Programming, Journal Guidance, Control and Dynamics, Vol. 14, No. 5, Set.-Oct. 1991,