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Trajectory Estimation of the Hayabusa Sample Return Capsule Using Optical Sensors

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Trajectory Estimation of the Hayabusa Sample Return Capsule Using Optical Sensors TRAJECTORY ESTIMATION OF THE HAYABUSA SAMPLE RETURN CAPSULE USING OPTICAL SENSORS Michael A. Shoemaker∗ and Jozef C. van der Hay Kyushu University, Fukuoka, Japan ∗Ph.D. Candidate, Department of Aeronautics and Astronautics, [email protected] yProfessor, Department of Aeronautics and Astronautics, [email protected] Abstract The sample return capsule for the Japanese Hayabusa asteroid mission will return to Earth in 2010. Because the capsule will reenter the atmosphere at night, it will appear as a bright light source during the high-heating portion of the trajectory. The present study describes the development of an operational capa- bility to optically observe this part of the reentry capsule's descent through the atmosphere. The trajectory is estimated via an Extended Kalman Filter (EKF), using ground-based and/or aerial measurements of the capsule's angular position. The EKF is tested with simulations of the Hayabusa reentry, as well as NASA's Stardust reentry from 2006. 1 NOMENCLATURE X = state vector = angle of attack, rad t = topocentric right-ascension angle, rad t = topocentric declination angle, rad C = axial force coefficient A = Earth gravitational parameter, m3=s2 CD = drag force coefficient = air density, kg/m3 C = lift force coefficient L 3 0 = reference air density, kg/m CN = normal force coefficient 2 n = capsule position from sensor n in Fi, m d = drag acceleration in Fi, m=s ! = Earth angular velocity in F , rad/s 2 i dt = drag acceleration in Ft, m=s Fi = inertial (J2000) reference frame Ft = Earth-relative-velocity reference frame 2 INTRODUCTION h0 = reference altitude, m h = altitude above ellipsoid, m ellp The main mission objective of the Japanese H = scale height, m Hayabusa spacecraft is to collect samples from an 2 l = lift acceleration in Fi, m=s asteroid and return those samples to Earth for analysis. The spacecraft was launched in 2003, l = lift acceleration in F , m=s2 t t rendezvoused with asteroid Itokawa in 2005, and m = mass, kg is currently on a return orbit to Earth. The sam- r = capsule position vector in Fi, m ple return capsule (SRC) is scheduled to reenter the atmosphere and land in Australia in June, rn = position vector of n-th sensor in Fi, m it 2010. Because the SRC will reenter the atmo- R = rotation matrix from Ft to Fi sphere at night, the capsule and surrounding air S = reference area, m2 will appear as a bright light source (i.e. “fireball”) during the portion of the trajectory with high t1i; t2i; t3i = x, y, z axes of Ft, expressed in Fi aerodynamic heating. Kyushu University, in col- v = inertial velocity vector in F , m/s i laboration with the Japan Aerospace Exploration ver = Earth-relative velocity in Fi, m=s Agency (JAXA), is developing an optical sensor and trajectory estimation system to observe this 1 part of the reentry capsule's descent through the detailed trajectory estimation function. NASA's atmosphere. Genesis capsule reentered during daylight, thus This optical sensor system, which will primar- the trajectory could not be measured relative to ily consist of ground-based cameras, is planned for the star background. But, ground-based optical deployment in various sites around the Australian cameras (visual and infrared) were used to observe desert where the SRC will land. The two primary the varying luminance as the capsule tumbled, purposes for this system are: (1) to provide real- allowing the capsule's attitude to be inferred[2]. time trajectory estimates to the JAXA ground Also, aircraft-mounted optical sensors were used teams for capsule recovery, (2) to allow for post- to photometrically measure the capsule's surface- flight verification of capsule performance. These averaged temperature[10]. optical measurements may play an important role On the other hand, the reentry of NASA's Star- in reconstructing the trajectory, because the SRC dust capsule in 2006 was observed during dark- lacks onboard data (e.g. accelerometer) recording ness, allowing the trajectory to be imaged against due to mass restrictions. Post-flight evaluation of the star background (see Fig. 1). The Star- the capsule flight performance may be useful in the dust sample return capsule, carrying samples from design of future interplanetary and Earth reentry comet Wild-2, entered the atmosphere at an iner- missions. tial velocity of 12.9 km/s (the fastest reentry for a The development builds on the lessons learned man-made object to date), and made a soft land- from the observation campaigns for the Genesis ing with parachutes in Utah. Because this super- and Stardust reentry vehicles in 2004 and 2006, orbital reentry occurred during darkness, it was a respectively[1][2]. The Genesis and Stardust op- good opportunity for conducting optical observa- tical observation campaigns included some trajec- tions of the capsule's heating. These observations tory reconstruction capabilities, but the primary were driven by a desire to study the thermal pro- requirement was to evaluate the thermal protec- tection system, which is applicable to the design tion system performance. In contrast, the present of the Orion Crew Exploration Vehicle[11]. study focuses on the development of a trajec- tory estimation capability using ground-based and aerial measurements of the SRC angular position. The SRC angular position will be measured by first taking images of the trajectory against the star background, then relating the SRC position in the images with the known star positions. An Extended Kalman Filter (EKF) is developed to estimate the SRC state during reentry. Similar EKFs have been developed in the past, for appli- cations such as estimating the reentry trajectories of low Earth orbit (LEO) space debris[3][4] and ballistic missiles[5][6][7]. First, Section 3 describes past studies on observ- ing super-orbital rentry missions. Section 4 gives an overview of the Hayabusa and Stardust reentry missions. The formulation for the EKF and the Figure 1: Stardust “fireball” image (from [1]). system model for this study are given in Section 5, and the simulations are discussed in Sections 6 and 7. Measurements collected during the Stardust reentry have been used by others for trajectory re- 3 PREVIOUS WORK construction. Visible and infrared video cameras were used to determine the time of parachute de- ployment and compare the observed reentry with There are several past examples of observing pre-flight predictions[12]. A DC-10 aircraft op- super-orbital reentry vehicles. The reentry of the erated by NASA and the University of North Apollo 8 spacecraft in 1968 was observed by one of Dakota, outfitted with numerous optical sensors, the Apollo/Range Instrumented Aircraft[8][9], but made observations of the capsule [1]. Video of the these observations were not used to perform any capsule against the star background, along with 2 GPS time stamps, were recorded from this air- 5 SYSTEM MODEL craft. Because the position of the aircraft was esti- mated from the onboard flight logs, and the angu- lar position of the stars are very accurate, the anal- 5.1 Estimator Dynamic Model ysis of images from this video allowed the time his- The equation of motion of the capsule is tory of the tracking angles to be measured. These angular measurements are used in this study to ¨ r = − 3 r + l + d (1) test our trajectory estimation method. r where the 2-body gravity, lift, and drag accelera- tions are considered. Figure 2 shows these forces 4 REENTRY OVERVIEW acting on the body, and several reference frame definitions. Frame Fi is the inertial frame cen- tered on the Earth, here taken to be the J2000 reference frame. Frame Ft is centered on the cap- 4.1 Hayabusa Reentry sule, with the x-axis aligned with the capsule's Details of the Hayabusa capsule design and reen- Earth-relative velocity vector ver, the y-axis in try sequence can be found in [13] and [14], respec- the cross-track direction, and the z-axis complet- tively. The Hayabusa capsule will separate from ing the right-handed coordinate system. The unit the main spacecraft several hours before reentry. vectors along these three Ft axes, expressed in Fi, are: The capsule reaches atmospheric interface (defined ver t1i = (2) by JAXA to be 200 km altitude) with an iner- jverj tial velocity and flight path angle of approximately t × r 12.1 km/s and -12 deg, respectively. At approx- t = 1i (3) 2i jt × rj imately 10 km altitude, the fore heat shield and 1i aft cover will jettison, and the main parachute t3i = t1i × t2i (4) and beacon antenna will deploy. JAXA's pri- The Earth-relative velocity, expressed in Fi, is de- mary method of locating the capsule after landing fined as: is direction-finding of the beacon signal. Radar- ver = v − ! × r (5) reflective material was also applied to the edges of the parachute canopy to allow tracking with the radar infrastructure in Australia. The optical tracking described in this paper represents an ad- ditional layer of backup landing-point prediction. 4.2 Stardust Reentry See [1],[11], and [12] for detailed descriptions of the Stardust reentry. The Stardust capsule had an inertial velocity and flight path angle at entry (de- fined by NASA to be 125 km altitude) of 12.9 km/s and -8.2 deg, respectively. As mentioned in Sec- tion 3, aircraft-mounted cameras recorded video of the capsule, from which angular measurements were derived. These measurements cover the cap- sule's descent from 97 to 46 km altitude, over a Figure 2: Reentry dynamics and reference frames time span of 55 s. The measurements were pro- vided at a rate of 1 Hz.
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