Fuel-free Attitude Control of Bias-momentum Solar Sail By Yuya MIMASU1), Go ONO1), Yuichi TSUDA1) 1)The Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan (Received 1st Dec, 2016) Solar sail is the fuel-free thrust system. Its trajectory can be changed without fuel by using the solar radiation pressure (SRP) induced by the sail. In general, however, the direction and the magnitude of the photon acceleration are controlled by the attitude of the sail, and the attitude control fuel is required. That is why, it is necessarily to reduce the fuel consumption of the attitude control in order to realize a real fuel-free solar sail. This research is one solution for this issue. The SRP is affected not only to the orbit, but also to the attitude of the spacecraft. This effect can be utilized to control the attitude of spacecraft. There is an appropriate example on Hayabusa2 case during coasting phase. The attitude dynamics model of the Hayabusa2 under the SRP had been studied. Especially, the attitude motion in the one-wheel bias-momentum control mode has been modeled in detail, and calibrated by using the actual flight data of Hayabusa2. The one-wheel bias-momentum control mode is the control mode in which the spacecraft is controlled by using only Z-axis reaction wheel. In this mode, the angular momentum vector precesses due to the SRP. According to the established model and flight result of Hayabusa2, the precession trajectory is changed by the body-phase angle with respect to the Sun direction. By utilizing this feature, the direction of angular momentum vector can be controlled by changing phase angle with respect to the Sun angle. The phase angle can be changed only by using one reaction wheel of Z-axis and usually unloading is not needed because just change the attitude orientation around Z-axis. It means that the spacecraft attitude can be controlled without fuel. Key Words: Bias-momentum, Precession, Angular Momentum Control, Orbit Control Nomenclature However, the attitude control of the solar sail needs fuel in general. Although there have been several study about fuel- S0 : solar constant free attitude control system of solar sail, usually it needs the c : light speed extra mechanism or technology. In this paper, we propose that RS/C : solar distance of spacecraft the fuel-free attitude control method for bias-momentum solar RE : representative solar distance of the Earth sail without any new technology or additional mechanism. This method applies the solar radiation pressure torque to Cspe : specular coefficient control the spacecraft attitude, and firstly verified on the Cdif : diffusive coefficient cruise phase of the Hayabusa2 mission. Therefore, we Cabs : absorption coefficient introduce the attitude control method of Hayabusa2 probe at B : Lambertian coefficient f first. : thermal emissivity s : Sun direction vector 2. Overview of Hayabusa2 n : normal vector of the effective area : right ascension in the inertial frame The main mission of the probe is to sample pieces of : declination in the inertial frame asteroid, and bring it back to the Earth in order to conduct : rotation angle around Z-axis of the body more advanced analysis on the ground. Hayabusa2 is planned I : moment of inertia tensor to arrive at the target asteroid in 2018, and return to the Earth : angular rate of the body-fixed frame in 2020 1, 2). with respect to the inertial frame During the cruise phase, Hayabusa2 controls its attitude by h : inertial angular momentum of the only one reaction wheel to bias the momentum around Z-axis reaction wheels of the body. This is to save the operating life of reaction st C1 : 1 integration constant wheels for other axes, because we experienced that two nd C2 : 2 integration constant reaction wheels of three equipped on Hayabusa were broken Subscripts after the touchdown mission. s : Sun direction 3. One-wheel attitude control mode 1. Introduction In the one wheel control mode, the angular momentum It is well known that solar sail is the fuel free trust system. direction is slowly moved in the inertial space (generally 1 called precession) due to the solar radiation torque. This Solar Array attitude motion caused by the balance of the total angular momentum and solar radiation pressure is known to trace the Center of Mass Sun direction automatically with ellipsoidal and spiral motion Sun Direction = s around Sun direction. Based on the knowledge in the past, the Angular Momentum Direction = L attitude dynamics model for Hayabusa2 mission had been Torque Direction 3) developed before the launch . According to the newly Center of ˆ Pressure T (L s) developed attitude dynamics model of Hayabusa2, the precession trajectory is almost the ellipsoid around the attitude Fig. 2 SRP torque direction equilibrium point, and this equilibrium point is determined mainly by the phase angle around Z-axis of the body. In Hayabusa and IKAROS mission4,5), this attitude motion In the actual operation of Hayabusa2, the spacecraft already was actually observed in the flight operation, and we have experience the one wheel control mode, and the attitude accumulated the experience and knowledge of the attitude motion in this mode is almost corresponds to the expected dynamics under the solar radiation pressure. Based on the motion based on the dynamics model developed before the knowledge in the past, the attitude dynamics model for launch. The precession trajectory is ellipsoid around the Hayabusa2 mission had been developed before the launch3). equilibrium point, and the attitude dynamics model is verified The detail about the dynamics is introduced in the section 5. by the actual flight data. In this one wheel operation, the In general three axis control operation, Hayabusa2 should Sun-aspect angle is restricted within a certain limit angle in follow the Sun direction in order to keep the Sun aspect angle terms of the thermal condition of the spacecraft. Because the within a certain restriction determined from the thermal precession radius is determined by the initial attitude and the condition. It takes fuel to keep Sun aspect angle because the equilibrium point, the Sun-aspect angle almost exceed the Sun direction automatically moves about 1 degree/day due to limit angle due to the precession without change of the the orbit motion. However, by using the attitude motion due to equilibrium point. At this operation, we execute the attitude the SRP, the angular momentum vector can trace the Sun maneuver around Z-axis to change the equilibrium point in direction automatically and fuel free to keep the Sun-aspect order to reduce the Sun-aspect angle and succeeded. After that, angle. The attitude motion in the inertial frame and we execute the maneuver again to change the equilibrium Sun-pointing frame is illustrated in Fig. 3. As shown in Fig.3, point to close point in order to make the small precession the angular momentum makes circle trajectory below the Sun trajectory. direction around the equilibrium point in the Sun-pointing frame. 4. Sun-direction-tracking mode ◆ Inertial Frame ◆ Sun-pointing Frame During the cruise phase, Hayabusa2 controls its attitude Orbit Plane Equilibrium only by one reaction wheel to bias the angular momentum Direction around Z-axis of the body. There are two main reasons: ・ To save the operating life of reaction wheels for other axes Precession ・ To save the fuel consumption. Angular Momentum Direction First reason is from the redundancy concept learned from Fig. 3 Sun tracking motion in inertial frame (left) and Sun-pointing Hayabusa experience. The second reason is related to utilize frame (right) the Solar Radiation Pressure (SRP). In this one wheel control mode, the angular momentum direction is slowly moved in the In the actual operation, we should consider about the transition inertial space (generally called precession) due to the SRP of the control mode. The 3-axis attitude of Hayabusa2 is torque. This attitude motion caused by the balance of the total nominally controlled by three RW’s as bias-momentum. Thus, the angular momentum and SRP is known to trace the Sun momentum of the X and Y axis should coast down before direction automatically under the appropriate condition spacecraft transits to the OWC mode. If the momentums are between SRP torque and angular momentum. The schematic coasted down without control, however, the reaction torque of the Sun tracking motion is illustrated in Fg.1 and the affects the spacecraft attitude as the disturbance and the attitude geometry of the angular momentum vector and the SRP torque starts tumbling. In order to avoid this, the attitude control mode is direction is shown in Fig.2. firstly transit to the 3-axis control mode by the thrusters called y Sun-Pointing Frame R3AX (RCS three-axis) control mode. In this R3AX mode, the S/C Fixed Frame y thrusters are ignited when the attitude or the angular rate of the Orbit spacecraft are over the limits of the state (few degrees for the Revolution x Direction attitude and few 0.1 degree/sec for the angular rate). Therefore, x the attitude is kept by thrusters when the RW’s are coasted down, z Sun H and after that the control mode transits to the OWC mode. Indeed, 0 z there are few degrees residual angle error and few 0.1 degree/sec residual angular rate, so the initial orientation of the angular SRP torque momentum vector of RW-Z is affected by these residual states Fig. 1 Sun tracking motion just after the transition to the OWC mode. 2 5. Attitude dynamics equations of solar sailing mode Substituting Eq. (4) into (9), and solve about and , the analytical solution can be derived as follow: It is known that the attitude dynamics of the spacecraft in the DH 3 2 2 2 2 t 2hz {M (D H) M} N P M 1 NP eq C1e cos t C2 tan deep space is dominated mainly by the SRP in general.