Technical Challenges and Study on Guided Reentry Flight for Capsule

21 JSTS Vol. 27, No. 2

30°and vertical velocity (descending velocity) of 10 m/s, which are nominal conditions for full-scale HRV water landing, were below 10g in the axial Z direction. At this condition, simulation and test Technical Challenges and Study on results showed good agreement. Test accelerometer results at pitch angles below 30° were unreadable or too high, and image analysis results were low compared with simulation results. The test model Guided Reentry Flight for Capsule Spacecraft and/or measurement methods need to be improved for future testing. Trends in maximum acceleration 1) 1) 1) 1) to pitch angle, vertical velocity and horizontal velocity were observed. Shuichi MATSUMOTO , Yoshinori KONDOH , Takane IMADA and Naoki SATO

As described in section two, this paper presents the first phase of our research, which is to 1) estimate the magnitude of impact to the vehicle during water landing. In the future, we will also Japan Aerospace Exploration Agency (JAXA), 2-1-1, Sengen, Tsukuba, Ibaraki, 305-8505, Japan evaluate the impact during land landing, investigate the characteristics of impact TEL / FAX: +81-50-3362-7281 / +81-29-868-5969 transmission/attenuation to the vehicle and assess the load to the human body. We would like to progress this research, referring the research of not only manned space vehicle but also automobile crash, etc. ABSTRACT Previously-realized Japanese capsule spacecraft, OREX (Orbital Re-entry EXperiment), USERS ACKNOWLEDGMENTS capsule, and HAYABUSA reentry capsule, were all ballistic reentry capsules, which flew without any

The authors express their great appreciation to Ms. Nozaki who designed and manufactured the guidance during reentry and had large splashdown areas. To establish practical recovery systems from capsule models and to Mr. Imada, Mr. Seki and Mr. Akagi who helped with the water landing tests. the International Space Station (ISS), JAXA has been studying reentry capsules using guided reentry flight, which enable capsules to narrow their splashdown area within 5 km and reduce aerodynamic acceleration less than 4 G. To improve reentry guidance accuracy, we use accurate real-time REFERENCES prediction guidance using numerical integration for reentry spacecraft and IMU-GPS-ST integration [1] Y. Suzuki and T. Imada, “Concept and Technology of HTV-R: An Advanced Type of H-II navigation. Transfer Vehicle”, 28th ISTS, 2011-g-09, 2011. This paper describes the characteristics of guided reentry flight and technical challenges on guided [2] T. Jones, T. Johnson, D. Shemwell and C. Shreves, “Photogrammetric Technique for Center of reentry flight for capsule spacecraft and presents guidance and control methods of guided reentry Gravity Determination”, AIAA2012-1882, 2012. [3] J. McCullough and J. Lands, ”Apollo Command Module Land-Impact Tests”, NASA TN D-6979, flight for the technical challenges. 1972. [4] R. Drexel and H. Hunter, “Apollo Experience Report - Command Module Crew-Couch/Restraint and Load-Attenuation Systems”, NASA TN D-7440, 1973. 1. Introduction [5] A. Taniei, C. Lawrence and E. Fasanella, “Validation of Finite Element Crash Test Dummy Models for Predicting Orion Crew member Injuries During a Simulated Vehicle Landing”, OREX (Orbital Re-entry EXperiment) (Refs. 1, 2), USERS capsule (Ref. 3), and HAYABUSA NASA/TM-2009-215476, 2009. reentry capsule (Ref. 4) were all ballistic reentry capsules and flew without any guidance during [6] E. Nakano, H. Uchikawa, H. Tanno, H. Akagi, T. Seki, T. Shimoda and R. Sugimoto, ”Overview th reentry, meaning their splashdown areas were very large. For example, OREX’s splashdown area was of the Research on Water landing of Manned Space Vehicle”, JSASS 56 Space Sciences and a large error ellipsoid with a semi-major axis of 200 km, as shown in Fig. 1. To establish practical Technology Conference, 3G05, 2012. (in Japanese). [7] R. Sugimoto, E. Nakano, H. Uchikawa, H. Tanno and T. Shimoda, “Water Landing Simulation of recovery cargo from the International Space Station (ISS), JAXA has been studying a Japanese Slow-Descending Capsule”, JSASS 57th Space Sciences and Technology Conference, 2J04, 2013. unmanned reentry cargo capsule, HTV-R (Ref. 5) with a target recovery area within 5 km. JAXA has (in Japanese) also been performing an advanced concept study of Japanese manned reentry capsules attempting to [8] E. Nakano, H. Uchikawa, H. Tanno, T. Imada, H. Akagi, T. Seki, T. shimoda and R. Sugimoto, land on the Japanese mainland. “Overview of the Research on Water Impact of Reentry manned Space Capsule”,JSASS 57th Space Sciences and Technology Conference, 2J03, 2013. (in Japanese) One of the key technologies for HTV-R and Japanese manned reentry capsules is guided reentry [9] H. Tanno, T. Komuro, K. Sato, K. Itoh and M. Takahashi, ”Miniature data-logger for flight, which enables capsules to narrow their splashdown areas to within 5 km and reduce aerodynamic force measurement in impulsive facility”, AIAA 2010-4204, 2010. aerodynamic acceleration to less than 4 G. A small splashdown area is important for practical [10] E. Fasanelle, “Multi-Terrain Earth Landing Systems Applicable for Manned Space Capsules”, recovery cargo, while small aerodynamic acceleration is important for manned reentry capsule. To ASCE 11th Earth and Space Conference, 2008. realize guided reentry flight, we investigated the technical challenges for guided reentry flight and have been studying guidance, navigation and control methods to solve the technical challenges. In this paper, we assume the shape, body characteristics and constraints of the reentry capsule as shown in Figs. 3 and 4 and Tables 1 and 2.

Latitude (degS) Flight Trajectory Planed Trajectory

Planned Splashdown Point (Lat: 2.4degS, Lon: 157.5degW)

Estimated Splashdown Point (Lat: 1.8degS, Lon: 158.3degW)

3s Erorr Ellipsoid

Longitude (degW)

Fig. 1 Splashdown Area of OREX Fig. 2 Photograph of OREX

Fig. 3 Shape of Vehicle Fig. 4 Concept of the HTV-R

Table 2 Constraints of reentry Table 1 Vehicle Model Aerodynamic Acceleration less than 4 G Vehicle Weight 5900 kg Aerodynamic Heating Rate less than 1 MW/m2 Reference Cross Section 13.9 m2 Total Aerodynamic Heating less than 130 MJ/m2 L/D 0.3 Bank Angle ± Drag 1.4 within 90 deg Curvature radius of Nose 5.0 m Angular Rate of Bank within ±20 deg/s Angular Acceleration of Bank within ±2 deg/s2

2. Technical Challenges on Guided Reentry Flight for Capsule Spacecraft

2.1 Characteristics of Guided Reentry Flight Guided reentry flight of capsule spacecraft has the following characteristics, which is why improving the reentry accuracy of capsule spacecraft is difficult.

(a) Low lift-to-drag ratio (L/D) (b) Range guidance by controlling bank angle only (c) Low guidance capability on the final phase of reentry flight

The first characteristic is the low lift-to-drag ratio (L/D), due to capsule shape. The typical L/D of capsule spacecraft is within the range 0.2 to 0.4, whereas that of winged spacecraft such as the Space Shuttle exceeds 1.0. The low L/D limits the scope of range correction capability, which is a severe

23 JSTS Vol. 27, No. 2

Latitude (degS) constraint for reentry guidance. The low L/D also results in large aerodynamic acceleration on Flight Trajectory spacecraft because low L/D spacecraft have small deceleration during flight in atmospheric areas of Planed Trajectory low density and flight of higher velocity in high-density atmospheric regions. Planned Splashdown Point The second characteristic is the fact that the bank angle is the only controlling parameter for both (Lat: 2.4degS, Lon: 157.5degW) downrange and crossrange guidance. A capsule spacecraft can generate aerodynamic lift by offsetting its center of gravity from the body center axis. By controlling the bank angle, a capsule changes the Estimated Splashdown Point (Lat: 1.8degS, Lon: 158.3degW) vertical component of lift for downrange guidance, while controlling the period to keep the bank angle at the right- or left-hand side allows a capsule to execute crossrange guidance. This cross coupling of 3s Erorr Ellipsoid downrange and crossrange guidance on the bank angle hinders accurate reentry guidance. The third characteristic is the low guidance capability on the final phase of reentry flight. Since the flight path angle on the final phase of capsule reentry flight becomes deeper than that on the initial and Longitude (degW) middle phases of the reentry flight, the range guidance capability on the final phase becomes about Fig. 1 Splashdown Area of OREX Fig. 2 Photograph of OREX one tenth of that on the middle phase. Accordingly, errors in the final phase such as wind errors make reentry guidance accuracy worse.

2.2 Technical Challenges on Guided Reentry Flight Considering the characteristics of guided reentry flight for capsule spacecraft as mentioned in section 2.1, we identified the following technical challenges on guided reentry flight.

(1) Guided reentry flight to meet severe acceleration requirements for manned spacecraft The acceleration requirement for Japanese manned spacecraft is less than 4 G, for which guided reentry flight is essential. This requirement is severe for low L/D spacecraft such as capsule, although not problematic for high L/D spacecraft such as the Space Shuttle. Since low L/D spacecraft have small deceleration during flight in low-density atmospheric regions and flight with higher velocity in high-density atmospheric regions, the aerodynamic force, which is in proportion to the atmospheric density and square of velocity, becomes large for low L/D spacecraft. For practical reentry guidance Fig. 3 Shape of Vehicle Fig. 4 Concept of the HTV-R analysis in particular, we must consider the following condition and errors, which increase the aerodynamic force under certain circumstances. Table 2 Constraints of reentry Table 1 Vehicle Model Aerodynamic Acceleration less than 4 G Vehicle Weight 5900 kg (a) Nominal bank angle must set the medium range Aerodynamic Heating Rate less than 1 MW/m2 Reference Cross Section 13.9 m2 The nominal bank angle must set the medium range to compensate for positive and negative Total Aerodynamic Heating less than 130 MJ/m2 L/D 0.3 downrange errors during downrange guidance, which means that the vertical component of the lift Bank Angle ± Drag 1.4 within 90 deg becomes small in proportion to the bank angle cosine. For example, if the maximum L/D is 0.3 and Curvature radius of Nose 5.0 m Angular Rate of Bank within ±20 deg/s the nominal bank angle is 60 degrees, the vertical lift component is 0.15. 2 Angular Acceleration of Bank within ±2 deg/s

(b) Aerodynamic force error 2. Technical Challenges on Guided Reentry Flight for Capsule Spacecraft Even if there is 25% aerodynamic force error and the L/D becomes smaller than nominal, maximum acceleration must be less than 4 G. 2.1 Characteristics of Guided Reentry Flight Guided reentry flight of capsule spacecraft has the following characteristics, which is why (c) Reentry flight path angle error improving the reentry accuracy of capsule spacecraft is difficult. Capsules returning from the International Space Station (ISS) must consider the reentry flight path angle error due to the orbit altitude variation of the ISS from 350 to 450 km. The maximum (a) Low lift-to-drag ratio (L/D) error of HTV-R is 0.18 degrees and the error makes the aerodynamic force larger. (b) Range guidance by controlling bank angle only (c) Low guidance capability on the final phase of reentry flight (2) High reentry accuracy under the worst conditions and maximum reentry flight errors For practical logistic recovery such as the HTV-R, the reentry guidance accuracy required is less The first characteristic is the low lift-to-drag ratio (L/D), due to capsule shape. The typical L/D of than 5 km. Moreover, in an advanced concept study involving the Japanese manned reentry capsule, capsule spacecraft is within the range 0.2 to 0.4, whereas that of winged spacecraft such as the Space the capsule attempts to land on the Japanese mainland. For this purpose, the targeted reentry guidance Shuttle exceeds 1.0. The low L/D limits the scope of range correction capability, which is a severe accuracy is within 1 km at the point of parachute deployment. Meeting these requirements is a

24 significant technical challenge for capsule spacecraft with the characteristics mentioned in section 2.1 under the worst conditions and maximum reentry flight errors. In terms of reentry guidance accuracy, the following factors are critical:

(a) Large aerodynamic force error The aerodynamic force error of capsule spacecraft has two kinds of error source: the estimation error of aerodynamic force via a wind tunnel test and computational fluid dynamics and aerodynamic force generated by center-of-gravity offset errors. We set 25 % of aerodynamic force errors on guidance analysis at this early study phase. Reentry guidance must cope with this significant aerodynamic force error, which is related to the guidance capability and must be considered at the stage of reentry trajectory design.

(b) Large upper-level wind error Upper-level wind e.g. circumpolar westerlies is large and liable to variation at an altitude from 10 to 30 km, whereas the guidance capability of capsule spacecraft becomes small at the altitude range. The maximum upper-level wind exceeds 100 m/s. Even if the guidance uses an upper-level wind model, the variation in wind remains, which is the most severe error for accurate reentry guidance.

(c) Blackout of the GPS signal during the reentry flight Since the onboard guidance cannot correct reentry errors caused by navigation errors, navigation accuracy is one of the critical factors for reentry guidance. If capsules can use GPS navigation during all reentry phase, navigation is not an issue for reentry guidance. However, there is the black out of GPS signal during reentry flight of an altitude around from 95 km to 40 km during which time capsule spacecraft cannot use GPS navigation and must use inertial navigation. This means that accumulated navigation errors on inertial navigation during GPS signal black out become critical for reentry guidance accuracy, due to the lack of time for guidance after recovery from blackout and the lack of guidance capability in the final phase of reentry flight.

(d) Angular acceleration Since capsule spacecraft cannot perform closed-loop range guidance during bank reversals, which are attitude maneuvers involving changing the bank angle to the same angle on the opposite side, reentry guidance accuracy worsens in proportion to the time required for bank reversal. Capsule spacecraft are also subject to an angular acceleration limit caused by the gas jet thrusters used to control attitude. We set ± 2 deg/s2 for the maximum/minimum angular acceleration of capsule spacecraft during this early study phase.

3. Guidance and Control Methods for the Technical Challenges on Guided Reentry Flight

3.1 Reference Reentry Trajectory Design to meet the acceleration constraint

(1) Relation between reference bank angle and maximum aerodynamic force To limit the maximum acceleration to within 4 G, it is necessary for capsule spacecraft to use the vertical lift component, which helps keep capsule spacecraft in areas of low atmospheric density and decelerates velocity before they traverse high-atmospheric-density areas. To study the relation between the reference bank angle and maximum aerodynamic force quantitatively, in the case of the HTV-R’s reentry path angle and maximum L/D, which are -1.35 degrees and 0.3 respectively, we evaluated the relation between bank angle and maximum aerodynamic force; shown by “no error” in Fig. 5. The figure indicates that the bank angle must be less than 60 degrees for maximum acceleration less than 4 G in the nominal case. We also evaluated the relation for ±25% aerodynamic

25 JSTS Vol. 27, No. 2 significant technical challenge for capsule spacecraft with the characteristics mentioned in section 2.1 force errors in Fig. 5. It is understood that the errors which make L/D smaller, -25% error on lift under the worst conditions and maximum reentry flight errors. In terms of reentry guidance accuracy, coefficient (CL) and +25% error on drag coefficient (CD), are more severe for maximum aerodynamic the following factors are critical: acceleration. Accordingly, to meet the maximum acceleration requirement under the aerodynamic force errors, the reference bank angle should be smaller than that in the nominal case. (a) Large aerodynamic force error The aerodynamic force error of capsule spacecraft has two kinds of error source: the estimation (2) Range control capability under aerodynamic force errors error of aerodynamic force via a wind tunnel test and computational fluid dynamics and To carry out reentry guidance, the reference trajectory of the capsule spacecraft must be set aerodynamic force generated by center-of-gravity offset errors. We set 25 % of aerodynamic force carefully so that the capsule can reach the target point even if maximum errors are presumed in errors on guidance analysis at this early study phase. Reentry guidance must cope with this reentry flight. In this section, we examined the range of the reference bank angle from the range significant aerodynamic force error, which is related to the guidance capability and must be control perspective and subject to aerodynamic force errors. For simplification, the case of -25% error considered at the stage of reentry trajectory design. on CD represents the maximum L/D case, while that of -25% error on CL represents the minimum L/D case. Fig. 6 shows the relation between bank angle and the vertical L/D components. In the case (b) Large upper-level wind error of reentry flight with a constant bank angle, since the flight range is in proportion to the vertical L/D Upper-level wind e.g. circumpolar westerlies is large and liable to variation at an altitude from 10 components, even if there are aerodynamic force errors, by choosing a bank angle which represents to 30 km, whereas the guidance capability of capsule spacecraft becomes small at the altitude range. the same L/D as that of no aerodynamic force errors, the capsule can reach the same target point. The maximum upper-level wind exceeds 100 m/s. Even if the guidance uses an upper-level wind Figure 6 shows that if a nominal reference bank angle is set to 52 degrees, in the case of a -25% error model, the variation in wind remains, which is the most severe error for accurate reentry guidance. on CL and by flying at a bank angle of 35 degrees, the capsule can reach the target point within the acceleration constraint, and in the case of -25% error on CD, by flying at a bank angle of 62 degrees, (c) Blackout of the GPS signal during the reentry flight the capsule can reach the target point within the acceleration constraint. Since the onboard guidance cannot correct reentry errors caused by navigation errors, navigation (3) Reference trajectory for guided reentry flight accuracy is one of the critical factors for reentry guidance. If capsules can use GPS navigation Two reference reentry trajectories were designed for this study: one with an initial flight path angle during all reentry phase, navigation is not an issue for reentry guidance. However, there is the black (FPA) of -1.35 degrees and the other with an initial FPA of -2.0 degrees. The reference bank profiles out of GPS signal during reentry flight of an altitude around from 95 km to 40 km during which are as follows: time capsule spacecraft cannot use GPS navigation and must use inertial navigation. This means that accumulated navigation errors on inertial navigation during GPS signal black out become (i) Reference reentry trajectory whose FPA is -1.35 degrees critical for reentry guidance accuracy, due to the lack of time for guidance after recovery from Reference bank profile: 62 degrees (velocity³7.5 km/s), 50 degrees (velocity<7.5 km/s) blackout and the lack of guidance capability in the final phase of reentry flight. (ii) Reference reentry trajectory whose FPA is -2.0 degrees (d) Angular acceleration Reference bank profiles: 52 degrees (for all velocities) Since capsule spacecraft cannot perform closed-loop range guidance during bank reversals, which are attitude maneuvers involving changing the bank angle to the same angle on the opposite side, The reference trajectories are shown in Figs. 6 and 7, while the results of error sensitivity analysis reentry guidance accuracy worsens in proportion to the time required for bank reversal. Capsule for aerodynamic acceleration, heat rate and total heat are shown in Tables 3 and 4. In the analysis for spacecraft are also subject to an angular acceleration limit caused by the gas jet thrusters used to the reference reentry trajectory whose FPA is -1.35, maximum aerodynamic acceleration exceeds 4 G, control attitude. We set ± 2 deg/s2 for the maximum/minimum angular acceleration of capsule which occurs in the error of the initial flight path angle of -0.18 degrees. Conversely, the reference spacecraft during this early study phase. reentry trajectory whose FPA is -2.0 meets all constraints.

3. Guidance and Control Methods for the Technical Challenges on Guided Reentry Flight

3.1 Reference Reentry Trajectory Design to meet the acceleration constraint

No errors -25% CD Error

-25% CL Error Reference bank angle -25% CL Error 52 degrees

+25% CD Error Bank angle which No Error can compensate aerodynamic errors +25% CD Error -25% CL Error Bank angle which can meet Minimum L/D for negative aerodymamic maximum 4 G error requirement Fig. 5 Relation between bank angle and maximum aerodynamic force Fig. 6 Relation between bank angle and vertical L/D

120 35

Flight Pass Angle: -1.35deg 30 100 Flight Pass Angle: -2.0deg )

s 25 80 / s ) / m m k ( 20 (

60 o d e i t u t a i

r 15 t e l l A e

40 c c 10 A

20 5 Flight Pass Angle: -1.35deg Flight Pass Angle: -2.0deg 0 0 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 6000 7000 8000 Velocity (m/s) Velocity (m/s) Fig. 7 Reference Trajectory (Velocity – Altitude) Fig. 8 Reference Trajectory (Velocity - Acceleration)

Table 3 Error analysis for the trajectory, FPA=-1.35 Table 4 Error analysis for the trajectory, FPA=-2.0

Maximum Maximum Total Maximum Maximum Total AerodynamicAerodynamic Aerodynamic Aerodynamic Aerodynamic Aerodynamic Acceleration heat rate Heat Acceleration heat rate Heat 2 2 2 2 Nominal 3.35 G 0.33 MW/m 90.64 MJ/m Nominal 3.31 G 0.43 MW/m 72.89 MJ/m 2 2 2 2 Worst 4.60 G 0.47 MW/m 116.40 MJ/m Worst 3.66 G 0.60 MW/m 92.14 MJ/m

3.2 Accurate Reentry Guidance to meet the severe reentry accuracy requirement.

(1) Real-time prediction guidance using numerical integration To realize high reentry accuracy under the worst conditions and reentry flight errors, we propose real-time prediction guidance using numerical integration, which is an explicit guidance law using real-time numerical integration to predict the accurate range during reentry flights (Ref. 6). This method is very accurate and robust for reentry flight errors. Although range prediction using numerical integration includes such advantages, the heavy computational load involved prevents its use for reentry guidance. We thus improved the range prediction algorithm to reduce the computational load while retaining guidance accuracy. The improvements are summarized as follows:

27 JSTS Vol. 27, No. 2

- Only one-time range prediction per guidance cycle - Integration Time is valuable for the distance to target No errors -25% CD Error - To omit integration terms which do not affect range prediction

-25% CL Error - To use high-performance 64 bit space-qualified MPU, HR5000 (Ref. 7) Reference bank angle -25% CL Error 52 degrees The range guidance equation for the real-time prediction guidance using numerical integration is shown in Eq. (1). The range prediction at the present cycle is R1, while the bank angle command is shown in Eq. (2).

+25% CD Error Bank angle which ¶ )/( D )/( No Error can compensate -= 0 × - -= -× +25% CD Error aerodynamic errors )/()/( 0 )( ( / ) 00 0 )( (1) ¶ 0 - 01 -25% CL Error Bank angle which C L D ref L D ref

Minimum L/D for can meet L D L D R R L D R R maximum 4 G R R R negative aerodymamic (cos(f + Df - f00 ))cos() error requirement 0 )cos()cos( +f=f 0 -× )( (2) Fig. 5 Relation between bank angle - 01 c ref and maximum aerodynamic force where R R Fig. 6 Relation between bank angle and vertical L/D R R (L / D ) 0 :( L/D command priviousat guidance cycle D :(L/D) Increment of L/D for increment of anglebank Δφ 0 f ： 120 35 0 angleBank commend priviousat guidance cycle

Flight Pass Angle: -1.35deg ： 30 fD Increment of anglebank for calculatio ofn sensitivit matrixy 100 Flight Pass Angle: -2.0deg

) ： toRange target frompoint present point s 25 80 / s ) / m

m ： k ( 20 toRange target point when spacecraft flies at the anglebank of privious gudaince cycle ( 0ref n

60 o d e i t u R t a ：

i + r 15 predicted torange target point when spacecraft flies at the angebank Δφ)(φ t 1 e l l A e

40 c c 10 R A

20 5 Flight Pass Angle: -1.35deg R Flight Pass Angle: -2.0deg (2) Reentry guidance error analyses 0 0 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 6000 7000 8000 We evaluated position errors at the end of reentry for the flights with and without reentry guidance Velocity (m/s) Velocity (m/s) by the single error simulation analysis, in which the guidance errors caused by the three sigma value Fig. 7 Reference Trajectory (Velocity – Altitude) Fig. 8 Reference Trajectory (Velocity - Acceleration) of each solo error factor in reentry flight. In the analyses, reentry guidance commences from the reentry interface point at an altitude of 120 km and ends at an altitude of 10 km as shown in Fig. 10 Table 3 Error analysis for the trajectory, FPA=-1.35 Table 4 Error analysis for the trajectory, FPA=-2.0 and IMU inertial navigation is used. The error model used in reentry guidance analysis in this paper is

shown in Table 5. Maximum Maximum Total Maximum Maximum Total AerodynamicAerodynamic Aerodynamic Aerodynamic Aerodynamic Aerodynamic Figure 11 shows the position errors of the reentry flight without reentry guidance, in which more Acceleration heat rate Heat Acceleration heat rate Heat than 100 km position errors are remained. Using reentry guidance, the position errors are significantly 2 2 2 2 Nominal 3.35 G 0.33 MW/m 90.64 MJ/m Nominal 3.31 G 0.43 MW/m 72.89 MJ/m reduced as shown in Figs. 12 and 13; Fig. 12 shows the reentry guidance error analysis results of the 2 2 2 2 Worst 4.60 G 0.47 MW/m 116.40 MJ/m Worst 3.66 G 0.60 MW/m 92.14 MJ/m variable-gain guidance used by Gemini (Ref. 8) and Fig. 13 shows those of the real-time prediction guidance using numerical integration. Comparing the results of the variable-gain guidance (Fig. 12) and the real-time prediction guidance (Fig. 13), we found that the real-time prediction guidance using 3.2 Accurate Reentry Guidance to meet the severe reentry accuracy requirement. numerical integration is more accurate than the variable-gain guidance.

Table 5 Error Factors using Reentry Guidance Analysis Error Factor Error Initial Cross Range Direction ±100 km Position/ Down Range Direction ±4 km Velocity Inertial Velocity ±1 m/sec Error Flight Path Angle ±0.18 deg Flight Direction Angle ±0.04 deg Initial Position ±45 m Navigation Velocity ±0.09 m/s Error Attitude ±0.3 deg IMU Error Acceleration Bias ±130 mG Gyro Bias Drift ±0.096deg/hr Air Altitude 10-30km: ±10% Density 60-80km: ±50% Error 100-120km: ±70% Vehicle Coefficient of Lift ±25% Fig. 9 Wind Error Error Coefficient of Drag ±25%

Reentry Guidance Error Analysys : No Guidance Vehicle Weight ±1ton Initial Err. Wind Error See Figure 9 Acc. Err. 26 Gyro Err. Density Err. Vehicle Err. Wind Err. 25.5 Nav. Err. )

N g e d ( 20km

e 25 d u t i t

a L

24.5

169 169.5 170 170.5 171 Longitude (degE)

Fig. 11 Error Analysis results (No Reentry Guidance) Fig. 10 Reentry Simulation Condition

Reentry Guidance Error Analysys : Valiable gain method with IMU Nav Reentry Guidance Error Analysys : Realtime Prediction Guidance with IMU Nav 25.1

25.08 25.2 25.06

25.04 25.1 ) ) 25.02 N N g g e e d d ( ( 1km 5km 10km

10km5km 20km

25 e 25 e d d u u t t i i t t a a 24.98 L L 24.9 Initial Err. 24.96 Initial Err. Acc. Err. Acc. Err. Gyro Err. 24.94 Gyro Err. 24.8 Density Err. Density Err. Vehicle Err. Vehicle Err. Wind Err. 24.92 Wind Err. Nav. Err. Nav. Err. 24.7 24.9 169.7 169.8 169.9 170 170.1 170.2 170.3 169.9 169.95 170 170.05 170.1 Longitude (degE) Longitude (degE) Fig. 12 Guidance Error Analysis results of Fig. 13 Guidance Error Analysis results of Variable-Gain Guidance Real-time Prediction Guidance

29 JSTS Vol. 27, No. 2

Table 5 Error Factors using Reentry Guidance Analysis (3) Enhanced Navigation accuracy Error Factor Error As shown in Figure 13, there are two major error sources affecting guidance error, wind and initial Initial Cross Range Direction ±100 km navigation errors on attitude. To improve guidance error caused by the latter error, we applied IMU-GPS Position/ Down Range Direction ±4 km integrated navigation for reentry. We assumed the GPS navigation could not be used from an attitude of 95 to Velocity Inertial Velocity ±1 m/sec 40 km due to signal blackout during reentry. The guidance error analysis results using IMU-GPS integrated Error Flight Path Angle ±0.18 deg navigation are shown in Figure 14. The guidance error caused by the initial navigation errors on attitude are Flight Direction Angle ±0.04 deg improved to within 10 km by using the IMU-GPS integrated navigation. We also applied on-orbit alignment Initial Position ±45 m using IMU-ST integrated navigation. Figure 15 shows the results of guidance error using IMU-ST integrated Navigation Velocity ±0.09 m/s navigation, in which the guidance error caused by the initial navigation error on attitude can be reduced to Error Attitude ±0.3 deg within 5 km. IMU Error Acceleration Bias ±130 mG Gyro Bias Drift ±0.096deg/hr Reentry Guidance Error Analysys : Realtime Prediction Guidance with IMU-ST Nav. Reentry Guidance Error Analysys : Realtime Prediction Guidance with IMU-GPS Nav. 25.1 25.1 Air Altitude 10-30km: ±10% Initial Err. Initial Err. Acc. Err. 25.08 Acc. Err. 25.08 Density 60-80km: ±50% Gyro Err. Gyro Err. Density Err. Error 100-120km: ±70% Density Err. 25.06 25.06 Vehicle Err. Vehicle Err. Vehicle Coefficient of Lift ±25% Fig. 9 Wind Error Wind Err. Wind Err. 25.04 Error Coefficient of Drag ±25% 25.04 Nav. Err. Nav. Err. )

) 25.02 25.02 N

Reentry Guidance Error Analysys : No Guidance N g

Vehicle Weight ±1ton g e e d ( d 1km 5km 10km

Initial Err. ( 1km 5km 10km

e 25

Wind Error See Figure 9 e 25 Acc. Err. d d 26 u t u

Gyro Err. i t t i t Density Err. a a 24.98 L 24.98 Vehicle Err. L Wind Err. 25.5 Nav. Err. 24.96 24.96 )

N g e 24.94 d

( 24.94 20km

e 25 d u t i t 24.92 a 24.92 L

24.5 24.9 24.9 169.9 169.95 170 170.05 170.1 169.9 169.95 170 170.05 170.1 Longitude (degE) Longitude (degE) 24 Fig. 14 Guidance Error Analysis results of Fig. 15 Guidance Error Analysis results of

169 169.5 170 170.5 171 Longitude (degE) Real-time Prediction Guidance Real-time Prediction Guidance using IMU-GPS Integrated Navigation using IMU-ST Integrated Navigation Fig. 11 Error Analysis results

(No Reentry Guidance) Fig. 10 Reentry Simulation Condition 4. Conclusion In this paper we extracted technical challenges for capsule spacecraft and examined the guidance and control methods for guided reentry flight to solve the technical challenges. We designed a reference reentry Reentry Guidance Error Analysys : Valiable gain method with IMU Nav Reentry Guidance Error Analysys : Realtime Prediction Guidance with IMU Nav 25.1 trajectory, which satisfied reentry conditions under maximum errors in the reentry phase. Using real-time prediction guidance, which featured numerical integration and IMU-GPS integrated navigation and IMU-ST 25.08 integrated navigation, we improved the reentry guidance to within 5 km excepting guidance error made by 25.2 25.06 wind. If a recovery system including ground equipment can upload upper-wind information measured by the

25.04 ground site to a reentry capsule spacecraft before its reentry flight, the guidance error caused by upper-level 25.1 wind can be significantly reduced. ) ) 25.02 N N g g e e We will continuously improve reentry guidance accuracy by improving the real-time prediction guidance d d ( ( 1km 5km 10km

10km5km 20km

25 e 25 e d d using numerical integration. u u t t i i t t a a 24.98 L L 24.9 Initial Err. 24.96 Initial Err. Acc. Err. Acc. Err. Gyro Err. 24.94 Gyro Err. 24.8 Density Err. Density Err. Vehicle Err. Vehicle Err. Wind Err. 24.92 Wind Err. Nav. Err. Nav. Err. 24.7 24.9 169.7 169.8 169.9 170 170.1 170.2 170.3 169.9 169.95 170 170.05 170.1 Longitude (degE) Longitude (degE) Fig. 12 Guidance Error Analysis results of Fig. 13 Guidance Error Analysis results of Variable-Gain Guidance Real-time Prediction Guidance

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