ANALYSIS OF TOUCH-DOWN DYNAMICS AND

SAMPLING SEQUENCE OF MUSES-C

Kazuya Yoshida1 Yoichi Nishimaki1 Hiroshi Kawabe1 Takashi Kubota2

1 Dept. of Aeronautics and Space Engineering, Tohoku University, Aoba 01, Sendai, 980-8579, Japan2 The Institute of Space and Astronautical Science, 3-1-1, Yoshinodai, Sagamihara, 229-8510, Japan

ABSTRACT

The Institute of Space and Astronautical Science, Japan (ISAS) is developing a spacecraft that obtains samples fromthe surface of an asteroid, then return to Earth. The spacecraft, named MUSES-C targets 1998SF36, one of near-Earth asteroids. Since the gravity of the asteroid is considerably small, the spacecraft will not be able to stand onits surface, and thus will have to acquire samples in a dynamic sequence. The touch-down behavior of the MUSES-Cis studied based on the dynamics model of a multibody system with frictional contact. To verify the mathematicalmodel, experiments with a miniature model have been carried out under the micro-gravity environment in a drop-shaft facility, MGLAB. Full-scale experiments with the hardware components of the proto-flight model have been alsocarried out using the ISAS’s robot simulator. Nominal and critical cases of the touch-down sampling are examined bycomparing the results of experiment and numerical simulation.

INTRODUCTION

The Institute of Space and Astronautical Science,Japan (ISAS) launches an exploration robotic probenamed MUSES-C toward 1998SF36, one of near earthobjects, with 300-600 [m] across. The mission MUSES-Cis the world’s first attempt of sample and return from anasteroid.

Considering versatility to the micro-gravity of theasteroid’s surface, and to unknown surface conditionssuch as flatness and hardness, the “crush sampling” and“touch-and-go” strategy is taken among various candi-date strategies. The accepted strategy minimizes thephysical contact with the surface of uncertainty, yet en-sures the sample acquisition. The physical contact willbe made at the endtip of a conical probe supported bya deployable compliant structure. During the contact, aprojectile is projected inside the probe to crash the sur-face. The ejected fragments of the surface will be con-centrated in the conical probe and collected in a samplechamber located at the top corner of the cone [1][2].

This touch-down sampling is one of the most criticalevents in the mission. If the strength of the probe struc-ture is not enough, or the spacecraft tumbles over thesurface, the mission will fail. Therefore it is very impor-tant to properly assess the impact forces at the contactand tumbling motion after the contact.

For the understanding of the touch-down dynamics,including the impact and tumbling, we have carried outvarious experiments and numerical analyses. One of theexperiments was with a drop-shaft facility to have physi-cal micro-gravity environment, and the contact behavior

was studied using a miniature model of the spacecraft.Another experiment was hardware verification with afull-scale proto-flight model of the sampling probe usinga mechanical motion simulator to represent the relativemotion between the probe and the surface [3].

This paper summarizes the study on this uniquestrategy of “touch-and-go” sampling, from initial discus-sion to final pre-flight assessments. The topics cover (1)a general discussion of possible strategies for samplingfrom a minor body, (2) modeling of the dynamics of thespacecraft including structural compliance and frictionalcontact, (3) experimental verification to understand thecontact dynamics, and (4) detailed assessments on criti-cal cases.

SMPLING FROM A MINOR BODY

Candidate StrategiesKey consideration in the sampling on a minor body

is versatility to micro-gravity and unknown hardness ofthe surface. As a general discussion, the following strate-gies are considered possible candidates (see Figure 1):(a) Anchor and Drill: Drilling is a common ideato obtain core samples from surface to interior. How-ever to achieve the drilling, the spacecraft must be an-chored firmly on the surface to accommodate the reac-tion (see Figure 1 (a)). Both drilling and anchoring willbe easier on soft surface, such as the surface of a comet.ROSETTA, an European comet probe takes this strategy[4].(b) Harpoon and Penetrator: Figure 1 (b) describesan idea to penetrate a sampling probe into the target

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Figure 1: Variety of sampling strategies

Figure 2: Sampling sequence of MUSES-C

using its kinetic energy. If properly designed, sampleswill be packed in the penetrator, and if tethered theycan be retrieved. In this strategy, the spacecraft needshovering over the sampling site, but landing or touch-down is not needed. Hovering may be less critical thantouch-down when without tether. But with tether, itsdeploy and retrieval becomes a challenging issue.(c)(d) Crash Sampling: If a bullet-like projectileis projected with certain velocity, the surface will becrashed and fragments are ejected. Then, one idea is tocollect such fragments in an orbit (see Figure 1 (c)). Thedust collection technology used in STARDUST mission[5] will be applied here. But as the distance between thecrash and sampling sites is far away, the sample acquisi-tion becomes uncertain and, even if obtained, it is diffi-cult to distinguish the point where each fragment comesfrom.

Another idea is to collect the crushed fragments onor at close vicinity of the surface, as shown in Figure 1(d). In this option, the spacecraft is required to makephysical contact with the surface although, if the projec-tile is projected inside a probe that has a conical shape,the ejected fragments will be deflected along the cone andconcentrated at the top corner. With this strategy, sam-ples are efficiently collected from a specific point of thesurface. The strategy is applicable for a wide range of sur-face hardness from basalt, for example, to regolith. Also,since the sampling will be completed instantaneously, thetime of the physical contact with the asteroid’s surfacecan be short, then the sampling sequence will be like“touch-and-go.”

Sampling Sequence of MUSES-C and Critical Is-sues

From the above four candidates, the last strategywas chosen for MUSES-C and a number of tests havebeen carried out to make a detailed design. In the flightmodel, the projectile of 5 [g] is projected at 300 [m/s].The test results show that several hundred milligramsto several grams of fragmented target materials can becollected by a single sampling action [6].

Figure 2 illustrates the sampling sequence. The

spacecraft descends toward a specific point of the aster-oid using a vision-based autonomous guidance system,so that the contact velocity is controlled within 0.1 [m/s]vertically and 0.08 [m/s] horizontally.

The conical probe is supported by Double-reverseHelical Spring (DHS), a dedicated deployable structurewith compliance. The length of this sampling device,termed Sampler Horn hereafter, is 1 [m]. Then the maxi-mum clearance beneath the bottom of the spacecraft be-comes less than 1 [m] during the sampling. Local ob-stacles that may interfere this clearance will be detectedand avoided using optical sensors. Local inclination atthe contact point of the sampler horn is assumed lessthan ± 30 [deg] as a design criteria.

As soon as the contact is detected, the projectileis projected. The momentum of the projectile reactionis about 1.5 [Nms], which is negligible comparing to themomentum of the spacecraft itself that is about 40 [Nms].However, the tumbling motion caused by the contact re-action through the sampler horn is much more critical,because the horn is mounted on the spacecraft with about0.7 [m] of offset from its centroid.

The DHS deforms during the contact. The magni-tude of the deformation depends on stiffness of the springand touch-down conditions. We need to check if the de-formation is within an acceptable range. For example,if the projectile is projected after the horn tip is largelydeformed, it may hit the horn itself but not the asteroid.

After the sampling, gas-jet thrusters will be used tolift the spacecraft off the surface. As the spacecraft startstumbling immediate after the contact, the delay of firingthe lift-off thrusters will result in a critical situation.

In order to be aware of such potential risks, themotion of the spacecraft for various touch-down and lift-off conditions is carefully examined in this paper.

MATHEMATICAL MODEL

Equation of MotionA schematic model of MUSES-C is illustrated in

Figure 3. The spacecraft is modeled by a multibody sys-tem including compliant elements. The sampler horn isdiscretized into multiple rigid segments, so that each jointrepresents compliant characteristics in bending angle θ,axial and lateral deformation ε. The endtip of the hornreceives the external force from the ground contact.

The equation of motion of this system is given bythe following equation. F e is a contact force applied atthe endtip of the sampler horn. The deformation of thehorn, that is made of a compliant structure, is describedby ε and θ.

H

v0

ω0

ε

θ

+ c =

F 0

N 0

fτ

+ JT

e F e (1)

where

H : inertia tensor of the entire system

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Figure 3: A schematic model ofMUSES-C

(a) Double-reverseHelical Spring

(b) axial deformation ofDHS

(c) lateral deformation ofDHS

Figure 4: Model of the sampler horn

c : velocity dependent terms

v0 : velocity of the spacecraft base

ω0 : angular velocity of the spacecraft base

F 0 : thruster force on the base

N0 : thruster moment on the base

ε : axial and lateral deformation of DHS

θ : bending angle of DHS

f : axial and lateral force on DHS

τ : bending moment on DHS

Je : Jacobian matrix

F e : ground contact force

Contact ModelThe contact force F e is divided into a component

perpendicular to the contact surface, Fn, and a compo-nent tangent to it, Ft. The magnitude of Fn is modeledusing a penetration depth into the surface, d:

Fn = Kw(d)r +Dw(d)s (2)

where we assume r = s = 1 for simplicity.Ft is switched between static friction and kinetic

friction using a threshold value µ0:For static friction (Ft/Fn < µ0)

Ft = Kt(dt)r +Dt(dt)s (3)

For kinetic friction (Ft/Fn > µ0)

Ft = µFn (4)

Sampler HornAs introduced previously, double-reverse helical

spring (DHS, see Figure 4 (a)) is used for the samplerhorn. DHS shows high stiffness when it is fully stretched,but it shows compliance otherwise. For the sampler horn,the length of the DHS is constrained not to become full-stretch. The axial and lateral compliance of the samplerhorn thus identified as shown in Figure 4 (b) and (c).The characteristics are nonlinear.

(a) experimental setup in thedrop-shaft capsule

(b) simulation model of thespacecraft with an offsetprobe, touching over an

inclined surface

Figure 5: MGLAB experiment for the study of contact dynamics inmicro-G environment

EXPERIMENTAL VERIFICATION

MGLAB ExperimentsThe experiments using a miniature model were con-

ducted in Micro-Gravity Laboratory of Japan (MGLAB),a drop-shaft facility providing 4.5 [s] duration of micro-gravity environment. In this series of experiments, thebasic characteristics of the mathematical model with fric-tional contact and compliant probe were verified. Figure5 (a) shows the experimental setup in the drop-shaft cap-sule. In this setup, four sets of a miniature spacecraftmodel as shown in Figure 5 (b) are installed, so thatthey are simultaneously projected with a certain velocityto hit a test surface by the compliant probe, during the4.5 [s] of free-fall. The contact force is monitored by aforce/torque sensor mounted behind the contact surface,and the motion of the spacecraft model is recorded by avideo camera.

From careful analysis, it became clear that the com-pliance of the probe has a dominant effect on the normal(perpendicular) contact force, and the frictio does on thetangential contact force. And that, by tuning those pa-rameters on the compliance and friction, the motion pro-file obtained from the video can coincide with the motionobtained from numerical simulation, using Equations (1)-(4) [7].

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Figure 6: The proto-flight model of the Double-reverseHelical Spring (DHS) mounted on the 3-D Hardware Sim-ulator (HWS)

ISAS HWS ExperimentsAnother series of experiments were carried out with

the 3-D Hardware Simulator (HWS) in ISAS, using aproto-flight model of DHS, see Figure 6. The HWScan demonstrate relative motion between the DHS probeand the contact surface by using a 9 axis motion table.The motion is computed based on a numerical dynamicsmodel using the input from the force/torque sensor thatmeasures the contact reaction force on the spacecraft.With this facility, the touch-down and lift-off sequence isverified using a real hardware setup.

The touch-down is detected by a laser range finder(LRF) to sense the endtip deformation of the samplerhorn. Its sensing resolution is ±1 [cm].

The touch-down experiments were carried out forvarious combination of vertical and horizontal approach-ing velocities, and inclination and friction of the contactsurface. Detailed analysis will be made in the followingsection though, regarding the contact detection, it wasconfirmed that the LRF successfully detected the con-tact within 0.3 [s] in average, and the cases with longerdelay are the cases with smaller deformation during thecontact.

CRITIAL ANALYSIS

Touch-Down ConditionsIn this section, the touch-down and lift-off sequence

is analyzed to check critical conditions. The touch-downconditions used in the HWS experiments and numericalsimulations are listed in Table 1.

For the analysis of critical cases, the ground clear-ance is evaluated. As shown in Figure 7, “local” incli-nation of the surface in the scale of the horn diameteris denoted by ψ, whereas “global” inclination of the sur-

Table 1 Touch-down conditions

mass of the spacecraft, m 430 [kg]m.o.i. (pitch), Iy 150 [kg/m2]

vertical velocity, vz - 0.1 [m/s]horizontal velocity, vx 0.08, - 0.08 [m/s]local inclination, ψ - 45 ∼ 45 [deg]global inclination, φ ± 5 [deg]friction coefficient, µ 0.1 ∼ 1.5

ζζ

Figure 7: Touch-down parameters for critical analysis

-45 -35 -25 -15 -5 5 15 25 35 450 10 50 91 30 250

0 2750 3000 3250 3500 3750 4000 4250 4500 4750 5000 525

0 5500 525-0 550 5-0 5250 475-0 50 45-0 4750 425-0 450 4-0 4250 375-0 40 35-0 3750 325-0 350 3-0 3250 275-0 30 25-0 275

Figure 8: Result of parametric survey on touch-downclearance (vx = 0.08, vz = −1.0 [m/s], t = 3 [s] after thecontact)

-45 -35 -25 -15 -5 5 15 25 35 450 10 50 91 30 00

0 01

0 02

0 03

0 04

0 05

0 06

0 07

0 08

0 09

0 10

0 09-0 10 08-0 090 07-0 080 06-0 070 05-0 060 04-0 050 03-0 040 02-0 030 01-0 020-0 01

Figure 9: Result of parametric survey on horn displace-ment (vx = −0.08, vz = −1.0 [m/s], t = 0.5 [s] after thecontact)

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face in the scale of the solar array’s span is denoted by φ.Then the clearances under the corner of the spacecraft ζ1and under the solar panel ζ2 are evaluated. The resultsshow ζ1 is always smaller than ζ2.

Critical CasesFigure 8 depicts the result of parametric survey ob-

tained by numerical simulation for critical cases regard-ing the clearance ζ1 at 3 [s] after the contact. The casesof positive vx are shown because those of negative vx areless critical, due to asymmetric design of the spacecraft.The results show that the friction coefficient does notgive significant influence, but the “local” ground angleψ makes major influence. Particularly, in the cases ofpositive large ψ, the clearance becomes less than 0.3 [m],and if any actions are not taken, the spacecraft will hitthe surface. For this reason, the spacecraft must startthruster propulsion within a few seconds after the con-tact.

Figure 9 depicts the result of parametric survey ob-tained by numerical simulation for critical cases regard-ing the lateral deformation of DHS, ε at 0.5 [s] after thecontact. In this evaluation, the cases of negative vx arealways critical. The results show that the friction coeffi-cient does not give significant influence, but the “local”ground angle ψ makes major influence, again. Partic-ularly, in the cases of negative large ψ, the deformationbecomes more than the radius of the sampler horn. If theprojectile is projected in such a situation, the projectilewill hit the horn, not crush the asteroid.

Motion Sequence with Lift-Off ThrustersThe touch-down motion sequences are illustrated in

Figure 10, for six different cases. The conditions are clas-sified into nominal and critical as listed in Table 2.

In each set of figure, the top raw is the motion ob-tained from the HWS experiment. In the HWS experi-ments, the sampler horn is always vertical and the rela-tive motion is represented by the motion of the groundplane, i.e. the pictures are the observation w.r.t. thespacecraft fixed coordinate. The middle raw shows thegraphical representation of the above experiment. Herethe pictures are rendered w.r.t. the ground fixed coordi-nate, so that the tumbling motion of the spacecraft canbe clearly seen. Note that the deformation of the sam-pler horn is not expressed here. The bottom raw depictsthe result of the corresponding simulation including thedeformation of the horn.

For the cases with thrusters, four of 20 [N] thrustersare fired at 0.15 [s] after the contact detection, accordingto the design baseline of the flight model.

In the cases of A1 and B1, the tumbling motionafter the contact is in a non-negligible order. Particularly,case B1 is critical. But with the powered lift-off by thethrusters, the spacecraft’s crush on the ground can beavoided (cases A2 and B2.)

In the case of C1, the tumbling is relatively smallalthough, the lateral deformation of the horn becomeslarge. The thruster lift-off will help to terminate the

Table 2: Nomical and critical cases

Nominal Critical 1 Critical 2vx [m/s] 0.00 +0.08 - 0.08vz [m/s] - 0.10 - 0.10 - 0.10ψ [deg] 0 +30 - 30φ [deg] 0 0 0

deformation (case C2.)

CONCLUSIONS

In this paper, the touch-down sampling sequences ofMUSES-C are examined by experiment and simulation.The MUSES-C uses a novel sampling strategy of “impactsampling” and “touch-and-go,” versatile to unknown sur-face hardness and micro-gravity environment on a smallplanetary body. The sampling technology is very promis-ing though, the spacecraft can start tumbling after thetouch-down with the surface of the asteroid. Throughthe experimental and numerical assessments, it is highlyrecommended that the projection for impact samplingand thrusters for lift-off shall be started immediately af-ter the contact detection. The projectile projection laterthan 0.5 [s] or starting the thruster propulsion later than3 [s], may cause critical situation.

REFERENCES

[1] A Proposal of the Asteroid Sample Return Mission:MUSES-C, The Institute of Space and AstronauticalScience, 1996. (in Japanese)

[2] J. Kawaguchi, K. Uesugi and A. Fijiwara, Readinessof the MUSES-C Project and the Spacecraft FlightModel Status, 22nd Int. Symp. on Space Technologyand Science, ISTS 2000-o-3-06v, Morioka, Japan,2000.

[3] K. Yoshida, T. Kubota, S. Sawai, A. Fujiwara,M. Uo, MUSES-C Touch-down Simulation on theGround, AAS/AIAA Space Flight Mechanics Meet-ing, Paper AAS 01-135, Santa Barbara, California,pp. 1-10, February 2001.

[4] http://www.rosetta-lander.net/ (as of Nov. 2002)

[5] http://stardust.jpl.nasa.gov/ (as of Nov. 2002)

[6] H. Yano, S. Hasegawa, M. Abe, A. Fujiwara,MUSES-C Impact Sampling Strategy for Micrograv-ity Asteroids, Paper B1.3-0018-02, World SpaceCongress, Houston, Oct. 2002.

[7] K. Yoshida, A. Noguchi, H. Katoh, Frictional Con-tact Dynamics in Micro Gravity, 23rd InternationalSymposium on Space Technology and Science, ISTS2002-d-10, Matsue, Japan, 1–6, 2002.

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A1: Nominal case (No Thrusters)

B1:Critical case 1 (No Thrusters)

C1:Critical case 2 (No Thrusters)

A2: Nominal case (With Thrusters)

B2: Critical case 1 (With Thrusters)

C2: Critical case 2 (With Thrusters)

Figure 10: Comparison of HWS experiment and corresponding simulation for 6 different cases

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