IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED AUGUST,

Transcription

1 The final version of record is available at IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED AUGUST, Landing Behavior Analysis of Lunar Probe Based on Drop Tests and RFT in a Masataku Sutoh 1, Sachiko Wakabayashi 1 and Takeshi Hoshino 1 Abstract This paper addresses the influences of footpad shape and ground condition on the motion behavior of a lander in a vacuum. To evaluate the influences, we first developed a drop test apparatus that can conduct repeated drop tests in the vacuum chamber. The footpad drop tests were then conducted with various shaped footpads on different surface conditions. Subsequently, the motion behavior of the footpads in a vacuum was modeled, based on the resistance force theory (RFT) and its penetration characteristics were numerically analyzed. The usefulness of the RFT based model was discussed along with the experimental results. Finally, drop tests were conducted using a four-legged lander to comprehensively analyze its landing behaviors. From the footpad drop tests and numerical analysis based on the RFT, we confirmed the following: 1) the force acting on the footpad is enhanced, and the penetration depth is reduced in a vacuum, 2) the force and kinetic energy conversion rate are smallest for the curved footpad, and 3) an increase in the ground density had a relatively small impact on the penetration depth of the footpads in a vacuum. Furthermore, the drop tests using the lander model confirmed that even if some of the lander s footpads land on regolith simulant with different densities, this does not lead to postural imbalance or turnover of the lander in a vacuum. Index Terms Field Robots, Space Robotics. I. INTRODUCTION JAPAN Aerospace Exploration Agency, JAXA, plans lunar landing missions, in which various geological surveys will be conducted for future In-Situ resource utilization [1]. As one of the important technologies required for the missions, JAXA conducted research on landing technology of a space probe. The ground surface of the moon is covered with loose, granular regolith and the pressure is extremely low (1 7 and 1 1 Pa for day and night, respectively) [2]. When a space probe tries to land on the surface, its landing gear (i.e., footpads, landing legs) could sink, resulting in the probe overturning or rolling over in a worst-case scenario. For a safe and secure landing, it is thus essential to thoroughly understand the motion behavior of the footpads on regolith in a simulated lunar environment. Recently, behaviors of various landers on regolith were analyzed using numerical simulations. Liang et al., and Nohmi et al., analyzed contact dynamics between a lander and regolith Manuscript received: March, 31, 217; Revised June, 31, 217; Accepted August, 24, 217. This paper was recommended for publication by Editor Jonathan Roberts upon evaluation of the Associate Editor and Reviewers comments. 1 Masataku Sutoh, Sachiko Wakabayashi, and Takeshi Hoshino are with the Japan Aerospace Exploration Agency, Jindaiji- Higashimachi, Chofu, Tokyo , Japan sutoh.masataku, wakabayashi.sachiko, hoshino.takeshi@jaxa.jp Digital Object Identifier (DOI): see top of this page. using numerical simulations based on mechanical dynamics software (ADAMS) and finite element method (FEM) [3], [4]. To estimate the deformation of a lander landing on the ground, Xu et al., conducted a numerical simulation considering the stiffness of the lander body and legs [5]. Wei et al., and Ponnusamy et al., also investigated the motion behavior of landing gears using numerical simulations, and the landing gear prototypes were developed based on the simulation results [6], [7]. As seen above, for motion behavior analysis of landers, various numerical simulation studies are available; however, only few studies have experimentally analyzed the motion behavior. To experimentally investigate the motion behavior of landing gears, Huang et al., conducted drop tests, using footpads, in the atmosphere [8]. They reported on the drop tests being conducted using footpads of different masses, at various impact speeds. Furthermore, Yokoyama et al., and Yoshida et al., conducted drop tests and compared their behavior in the atmosphere and a vacuum [9], [1]. Our research group also reported the drop and friction tests conducted in the atmosphere and a vacuum [11]. Our previous study confirmed that the penetration depth of a footpad is drastically reduced in a vacuum. However, we did not measure time histories of forces acting on the footpads, or those of the penetration depth when the footpad impacted the ground. Thus, it was difficult to comprehensively model the motion behavior of footpads. In this study, we precisely investigate the difference in the motion behavior of a footpad, that was previously observed in [11] in the atmosphere and a vacuum, along with a numerical simulation. For the investigation, we developed a drop test apparatus that can conduct repeated drop tests in a vacuum chamber. Footpad drop tests were conducted with variousshaped footpads on different surface conditions. Subsequently, the motion behavior of the footpads in a vacuum was modeled based on a resistance-force theory (RFT), and the impact and penetration characteristics were numerically analyzed. The usefulness of the RFT based model was discussed along with the experimental results. Moreover, in addition to the footpad drop test, drop tests were conducted using a lander model, and the motion behavior of the lander was comprehensively analyzed. II. MOTION BEHAVIOR ANALYSIS OF A FOOTPAD BASED ON FOOTPAD DROP TEST When a space probe lands on the lunar surface, its footpads should softly make contact with the regolith. That is, the force acting on the footpads should be small, its kinetic energy Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

2 The final version of record is available at 2 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED AUGUST, 217 Sleeve sensor Weight (a) Flat edge (b) C4-chamfered edge Solenoid latch (a) (b) Notch (c) Landing direction Loadcell Footpad Fig. 1. Footpad drop test apparatus. (a) External view of the vacuum chamber, (b) internal view of the vacuum chamber, and (c) schematic illustration of the drop test apparatus. should dissipate gently, and the penetration depths of the footpads are required to be small. The priorities of these requirements can be determined depending on a given mission. In this study, we evaluate the influences of footpad shape and surface condition on the footpad behavior based on the above requirements. To evaluate the influences on the behavior of a footpad that drops vertically onto the ground, we developed a drop test apparatus that can conduct repeated drop tests. Then, drop tests were conducted using this apparatus both in the atmosphere and in a vacuum. In this section, the drop test apparatus is first discussed, and then the drop tests are explained in detail. A. Drop test apparatus Fig. 1 shows photographs and a schematic illustration of the drop test apparatus developed. As shown in the figure, a sandbox, with dimensions of 1.2 m 1.2 m.2 m, is located inside a vacuum chamber. This vacuum chamber has a dimension of 1.5 m 1.2 m. In the sandbox, a regolith simulant (FJS-1; Shimizu Corp. [12]) that mimics the mechanical properties of the lunar regolith is used to fill it to a depth of.15 m. A gantry robot that can freely move its end effector inside the sandbox (i.e., 1.2 m 1.2 m in XY-plane, and to a height of.2 m above the surface) is fixed on the sandbox. The drop test apparatus is mounted as an end effector on the gantry robot. As shown in Fig. 1(c), the footpad is fixed at the end of the notched cylinder rod. When the footpad is ready, a latch is pushed against the notch. The latch is pulled using a solenoid, and the footpad is released/dropped onto the regolith simulant. Meanwhile, when the footpad is retrieved, the gantry robot with the solenoid latch moves vertically down along with the rod and the latch is locked at the notch. A loadcell (Kyowa; LUR-A-1KNSA) is mounted on the cylinder rod, and the force acting on the footpad can (c) Curved edge Fig. 2. Sectional views of the three types of footpads used in the drop test. Each footpad has a diameter of 1 mm and a thickness of 16 mm. The footpad mass was set at 1.6 kg using an additional weight. be measured. Furthermore, a sleeve sensor (MACOME; ET- 85-L2) is attached parallel to the rod and the distance the footpad moved can be measured when the footpad drops. By moving the gantry robot, the height/position of the drop test apparatus can be adjusted. With this, in a single test series, the drop tests can be conducted several times at various points. The test sequence using the gantry robot and drop test apparatus is summarized as follows: 1) Conduct a drop test. 2) Move the gantry robot vertically down with the solenoid latch at the same position and latch the footpad. 3) Move the gantry robot up with the footpad at the same position. 4) Move the gantry robot with the drop test apparatus in the XY-plane with the footpad above the ground. 5) Repeat a drop test with the same/different height at a different position. In the tests described later, the drop tests were conducted at nine different points, i.e., three points for each of three different speed conditions. Each of the test points was at a different spot having enough distance between each other. Here, enough distance was determined based on preliminary tests to ensure no interference between impact points due to a compaction/ejection of the regolith simulant in the previous test. The gantry robot is also used for the ground preparation with a rake/leveler attached as its end-effector [13]. Moving the rake/leveler parallel to the surface while adjusting its tip height, the robot can dig, plow, or level the regolith simulant. With this ground preparation, the tests can be conducted in an identical ground condition each time. B. Footpad drop test overview and conditions The footpad drop tests were conducted in both the atmosphere and a vacuum. The pressure was set at and less than Pa for the atmosphere and the vacuum, respectively. To reduce pressure, a turbomolecular pump was used. Through this depressurization process, it is difficult to completely remove the gas trapped inside the regolith simulant. When the footpad impacts the simulant, the gas is pushed out and the pressure inside the vacuum chamber can increase. To prevent this, the pump was kept running during the tests. In the tests, three types of footpad, whose sectional views are shown in Fig. 2, were used. By adjusting Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

3 The final version of record is available at SUTOH et al.: LANDING BEHAVIOR ANALYSIS OF LUNAR PROBE BASED ON DROP TESTS AND RFT IN A VACUUM (a) Flat, LP (b) C4, LP (c) Curved, LP (d) Flat, CP (e) Flat, LP (f) C4, LP (g) Curved, LP (h) Flat, CP Fig. 3. Time histories of the force acting on the footpad and penetration depth in the footpad drop test. (a) (d) shows the results for the force, and (e) (h) shows those for the penetration depth. LP and CP stand for loosely and closely packed regolith simulants, respectively. the drop heights, the impact speeds used were.7, 1., and 1.5 m/s. Before each test, the simulant was raked and leveled using the rake and leveler mounted on the gantry robot. For all the footpads, the drop tests were conducted on loosely packed simulant (i.e., LP), whose relative density was roughly 3 %. In addition, for the flat footpad, the tests were also conducted on closely packed simulant (i.e., CP), whose relative density is roughly 7 %. In the tests, the force acting on the footpad was measured along with the penetration depth in a cycle of 1 khz. For repeatability, the tests were conducted three times. C. Experimental results Fig. 3 shows the time histories of force acting on the footpad and the penetration depth in the drop tests. Fig. 4 shows the maximum value of the force and penetration depth after it reached a constant level in Fig. 3. Note that in Figs. 3 and 4, the results for the impact speed of 1. m/s is shown; however, the same trend was also observed at other speeds. In Figs. 3(a), (b), and (d), two peaks are observed in the force in both the atmosphere and the vacuum. We consider that these peaks can be explained as follows: 1) around the times of the first peak, the footpad compacts the regolith simulant while slowing down and this results in a decrease in the force after the peak, and 2) around the times of the second peak, the footpad has fully compacted the simulant, slows down, and completely stops. In the following, the influences of the footpad shape and ground condition are discussed based on the shape of the peak. 1) Influence of footpad shape: From Figs. 3(a) and (b), a large peak is observed after a small peak for the flat- and C4-pads in the vacuum. Meanwhile, in the atmosphere, a large peak first appears, then the force increases slowly and a small peak is observed. This is because the bottom contact area of the flat/c4 footpad is almost the same during an increase in the penetration depth. Meanwhile, from (c), for the curved footpad, there is one large peak in the vacuum. In the atmosphere, after an increase in the force, a constant force is generated for a while before the peak appeared. This is because the bottom area of the curved footpad increases and gradually compacts the simulant along with an increase in the penetration depth. We discuss the above time history of the force along with the penetration depth shown in Figs. 3(e) (g). It is observed that in the atmosphere, the penetration depth still increases until the second peak of the force, and becomes almost constant after the peak. In the vacuum, although the interval between the two peaks was shorter, the similar tendency were observed in many tests. In both cases, there was no drastic increase in the penetration around the first peak and the value of the the second peak has a greater impact on the final penetration depth. Furthermore, from Fig. 4, it is observed that the force increased and the penetration depth reduced in a vacuum for all the footpads tested. The penetration depth was relatively small for the flat- and C4-footpads and largest for the curved footpads. 2) Influence of ground condition: As shown in Figs. 3 (a) and (d), the interval between the two peaks becomes shorter for the CP simulant in both the atmosphere and the vacuum. As a result, the penetration depth becomes constant in a shorter time. From Fig. 4, the force acting on the flat footpad increased and the penetration depth decreased on the CP simulant in both the atmosphere and the vacuum. Comparing the data obtained on the LP and CP surfaces shown in Fig. 4(b), the ratios of the penetration depths in the atmosphere and vacuum were 3.9 and 1.9 on the CP and LP simulants, respectively. From this, it seems that while the difference in the ground density has a great impact on the penetration depth in the atmosphere, its impact is relatively small in a vacuum. 3) Kinetic energy conversion and its rate: In the drop tests, the kinetic energy when a footpad impacts with the regolith Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

4 The final version of record is available at 4 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED AUGUST, Flat, LP C4, LP Curved, LP Flat, CP Flat, LP C4, LP Curved, LP Flat, CP (a) Force (b) Penetration Fig. 4. Maximum value of the force and penetration depth after it reached a constant level in the footpad drop tests. These values are an average from the three trials, and error bars indicate the maximum and minimum values. simulant, E, can be modeled as follows: E = W c + W e, (1) where W c and W e denote the works that the footpad compacts gases/void between the regolith simulant and that the footpad ejects the simulant, respectively [11]. In the tests, E is the same for all the footpads because the footpads impacted with an identical speed and mass. As above-mentioned, the forces acting on the footpads are larger and the penetration depths reach constant level in shorter times in vacuum than in the atmosphere. This trend can be explained using Eq. (1) as follows: in vacuum, much of the energy is converted into W c in a short time because there was almost no ejection of the simulant and W e seemed negligibly small. Furthermore, the curved footpad showed a smaller impact force and larger penetration depth, i.e., the time that the penetration reached constant was longer, than the flat- and C4-pads. This indicates that E that the curved footpad had was converted into W c in a longer time especially in vacuum. In other word, the kinetic energy conversion rate in vacuum, which is expressed as de dt using the time, t, was smallest for the curved footpad. Here, note that de dt dwc dt because W e is negligible. While the force that determines the penetration mainly acts on the flat area of the bottom surface for the flat- and C4-pads, it acts on the curved area for the curved pad. Thus, the curved pad can gently compact the ground and this contributes to a smaller kinetic energy conversion rate. This suggested that although the penetration can be larger, the curved footpad is appropriate for a lander from a view point of shock resistance. D. Discussions on influence of atmosphere From the experimental results, it is observed that there is a similar tendency observed in the vacuum and on the CP simulant. That is, the force increases and the interval between the two peaks shorten. In both cases, there is a smaller amount of gas trapped in the regolith simulant. From this, we considered that in the atmosphere/lp simulant, the gas trapped in the simulant acts as a cushioning material and damper. While the behavior of the cushioning material contributes to reducing the force acting on the footpad and kinetic energy conversion rate, that of the damper increases the time until the footpad stops completely, i.e., an increase in the interval between the two peaks. Furthermore, the tendency observed in the penetration depth of the footpad in the vacuum was similar to that on the CP simulant. In the atmosphere/lp simulant, when the footpad impacts the simulant, it pushes the gas trapped in the simulant, and this results in the extensive ejection of the regolith simulant as previously reported in [11]. Because of the lack of this effect in the vacuum/on the CP simulant, the penetration depth of the footpad is mitigated. III. MOTION BEHAVIOR ANALYSIS OF FOOTPADS BASED ON RESISTANCE FORCE THEORY In this section, we first review the stress model in the resistance force theory (RFT) proposed by Li et al., [14]. Subsequently, the model is applied to the motion analysis of a footpad and the relationship between the force and the penetration depth is discussed from a theoretical point of view. The usefulness of the RFT based model is explained along with the experimental results. A. Resistance force theory Li et al., modeled the vertical and horizontal forces, F z and F x, respectively, acting on a moving object on a granular media as: F z,x = ζα z,x (β, γ) z da (2) S Here, S is the surface area of the object in contact with the media, da is the area, z is the depth below the surface, and α z,x (β, γ) are element stresses per unit depth. β and γ are the angle of attack and angle of intrusion of an infinitesimal element, respectively. ζ is defined as a scaling factor and determined depending on the ground characteristics. Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

5 The final version of record is available at SUTOH et al.: LANDING BEHAVIOR ANALYSIS OF LUNAR PROBE BASED ON DROP TESTS AND RFT IN A VACUUM 5 Measuring the relationship between the force and penetration depth (i.e., sinkage) for a flat plate vertically pressed onto a ground (i.e., γ = π/2), ζ can be derived. Li et al., conducted tests using various materials and confirmed that Eq. (2) can be applicable to various types of materials with an appropriate ζ. It is noteworthy that in Eq. (2) ζ is the only parameter needed for an estimation of the behavior of various shaped objects contacting the granular media. Footpad area (S) r h d α z Landing direction γ = π/2 β z = f(x, d) Ground surface x z B. Application of resistance force theory to footpad In the RFT model, Li et al., assumed that the resistance force of the granular media increases with an increase in the sinkage. Meanwhile, in our experiments, there were two peaks in the force acting on the footpads along with an increase in the penetration depth. This suggested that the assumption in the RFT model is not always true to a landing behavior of a footpad. In the landing behavior of the footpad analyzed in Section II, the penetration increased until the second peak of the force and the force at this peak had a greater impact on the penetration. Based on this fact, modeling that the influence of the first peak in the force profile is negligible and the force monotonically increases with an increase in the penetration, we applied the RFT model for an estimation of the footpad behavior. In this modeling, while it is difficult to accurately estimate the force for all the penetration sequence, the relationship between the force and penetration can be precisely obtained around the value of the second peak. This relationship determines the final penetration depth and is especially beneficial for vacuum, where the interval between the two peak was short. As shown in Fig. 5, we expressed the sinkage of the footpad sectional view as z = f(x, d). Based on the resistance force theory, the force acting on the footpad, which moves vertically into the ground, can be derived by integrating the stresses on the entire contact surface area as: F z = 2π d 2π d ζα z (β, γ) z x 1 + ( dx dz )2 dzdθ, (d < h) ζα z (β, γ) z x 1 + ( dx dz )2 dzdθ. (d > h) d h Here, d denotes the depth of the bottom surface of the footpad, and r and h denote the radius and thickness of the footpad, respectively. For the footpad, h is defined as the measure of the vertical distance between the peak of its bottom surface and top surface. r is defined as a value that satisfies f(r, d) =. Considering the tangential lines on the footpad surface, β is derived as tan 1 ( dz dx ). Furthermore, assuming that the footpad (3) Footpad area (S) h (a) When d < h. d z α z (b) When d > h. Landing direction r γ = π/2 β z = f(x, d) Ground surface Fig. 5. Contact model of a footpad based on a resistance force theory. moves vertically without any rotation or horizontal movement, γ is obtained as π 2. Thus, Eq. (3) can be rewritten as d 2π ζα z (tan 1 ( dz dx ), π 2 ) z x 1 + ( dx dz )2 dz, (d < h) F z = d 2π ζα z (tan 1 ( dz d h dx ), π 2 ) z x 1 + ( dx dz )2 dz. (d > h) C. Influence of the footpad shape and ground condition on the penetration depth of the footpad In our experiments, while the landing behavior of the footpad was dynamic including the extensive ejection of the regolith simulant in the atmosphere, it seemed rather static with almost no ejection in vacuum. For the tests conducted at various impact speeds, the same tendency was observed. We consider that the static behaviors observed in vacuum are similar to those assumed in the RFT model. From this, the RFT model can be applicable to the motion behavior of the footpad, especially in a vacuum. As the lunar surface is in a vacuum, we discuss the influences of the footpad shape and ground condition on the penetration depth based on Eq. (4). The sinkage below the ground surface for the sectional view of each footpad shown in Fig. 2 can be expressed as: (a) z = f(x, d) = d ( < x < r) x (4) Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

6 The final version of record is available at 6 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED AUGUST, Flat C4 Curved 1 (a) (b) 5 Polyester wire Separation using nichrome wire Four-legged lander LP CP (a) Influence of footpad shape (b) Influence of ground condition Fig. 6. Relationship between force and penetration obtained from a numerical simulation based on the RFT model. (b) z = f(x, d) = { d ( < x < r c), x + r + d c (r c < x < r) (c) z = f(x, d) = a e a1x + d ( < x < r) Here, c is the chamfering length, and a n (n =, 1) is a constant that expresses the curve of a footpad. Furthermore, from the relationship between the force and penetration depth for the flat footpad shown in Figs. 3 (a) and (d), ζ of the regolith simulant is obtained for LP and CP, respectively. Using the sinkage functions, z = f(x, d), and x = g(z) derived from the sinkage functions for each footpad, the relationship between the force and penetration depth was obtained for different footpad shapes, as shown in Fig. 6(a). From the figure, it is observed that for a given force, the penetration depth of the curved footpad is relatively larger than other footpads. Using ζs for different ground conditions, the force is estimated for the flat footpad on the LP and CP surfaces along with the penetration depth, as shown in Fig. 6(b). For a given force, the penetration depth of the footpad reduces along with an increase in the ground density. The above trend observed in the simulation corresponds with those obtained in the experiments using footpads (see Fig. 4(b)). That is, using Eq. (4), the impact/penetration behaviors Footpad (c) Landing direction Ground surface Fig. 7. Drop test using a four-legged lander model. (a) External view of the vacuum chamber, (b) internal view of the vacuum chamber, and (c) schematic illustration of the drop test configuration. of various shaped footpads can be estimated on different ground conditions. For the maximum forces shown in Fig. 4, the values estimated from the simulation agreed well with those in the experiments. The ratios of the penetration depths of the curved footpad to the flat footpad were 1.9 and 2. in the experiment and simulation, respectively. In the simulations, the same ζ was used for all the footpads. The relationship between the force and penetration depth can be quantitatively well estimated for different shaped footpads based on the RFT model with an appropriate scaling factor, especially around the maximum force. This fact contributes to the design stage of a footpad for a lunar lander. IV. MOTION BEHAVIOR ANALYSIS BASED ON LANDER MODEL DROP TEST When a space probe tries to land on the lunar surface, the regolith, on which its footpads impact, can have different densities for each footpad. To evaluate the influence of the landing ground condition for each footpad on the lander motion behaviors, we conducted drop tests using a four-legged lander model. In this section, we introduce the lander model developed and the drop tests are discussed in detail. A. Four-legged lander model Fig. 7 shows the four-legged lander model developed. This model is a 1/6 scale model of a lander in lunar gravity. That is, its behavior corresponds to that of the lander having six times the size and 6 3 times the mass on the moon. The lander footpads were attached on a ball joint connected to a rod so that they could freely move on the joint. The lander specifications are summarized in Table I. A tiltmeter was mounted on the lander to confirm that the lander and its footpads were parallel to the regolith simulant surface before release. In the drop tests, the lander model was suspended using a polyester string from the roof of the vacuum chamber, as Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

7 The final version of record is available at SUTOH et al.: LANDING BEHAVIOR ANALYSIS OF LUNAR PROBE BASED ON DROP TESTS AND RFT IN A VACUUM Footpad 1 Footpad 2 Footpad 3 Footpad 4 Footpad 1 Footpad 2 Footpad 3 Footpad 4 Footpad 1 Footpad 2 Footpad 3 Footpad 4 (a) Case A (b) Case B (c) Case C Fig. 8. Penetration depth of each footpad in the drop tests using the four-legged lander model. The ground conditions for each case are listed in Table II. shown in Figs. 7(b) and (c). The top end of the string was fixed with a nichrome wire. For the lander release, an electric current was applied to the nichrome wire, which heated up and severed the string. B. Lander model drop test overview and conditions The drop tests using the four-legged lander model were conducted in both the atmosphere and a vacuum. The pressure was set at Pa and less than Pa for the atmosphere and the vacuum, respectively. Before the lander was released/dropped, the footpad bottoms were placed at a height of 1 cm above the simulant surface. Before each test, the lander model was removed from the chamber and the simulant was raked and then leveled by using the rake and leveler attached to the gantry robot. After this ground preparation, several ground points, into which the lander footpads drop, were compacted. The ground conditions are listed in Table II. After the drop tests, the lander was removed and the depth of the landing marks produced were measured using a laser displacement meter (Keyence; IL-6) mounted on the gantry robot. C. Experimental results and discussions Fig. 8 shows the penetration depth of each footpad in the drop tests using the lander model. It is observed that TABLE I FOUR-LEGGED LANDER MODEL SPECIFICATIONS. Item Mass Body size Height of the center of gravity Footpad size Value and unit 4.3 kg cm 23 cm 5.5 cm 1 cm TABLE II GROUND CONDITIONS FOR DROP TESTS USING THE FOUR-LEGGED LANDER. IN THE TABLE, LP/CP INDICATES THE REGOLITH SIMULANT WHERE EACH FOOTPAD DROPS INTO IS LOOSELY OR CLOSELY PACKED, RESPECTIVELY. THE FOOTPAD WAS NUMBERED CLOCKWISE. Footpad 1 Footpad 2 Footpad 3 Footpad 4 A LP LP LP LP B CP LP LP LP C CP CP LP LP in all the cases the penetration depth of the footpads was reduced in a vacuum. When footpad 1 landed on the CP simulant, the penetration depth of the footpad 3, which was placed diagonally to footpad 1, increased significantly in the atmosphere, as shown in Fig. 8 (b). The similar tendency was also observed in Fig. 8 (c). Meanwhile, in the vacuum, the penetration depths of all the footpads were almost the same regardless of the ground condition. These results correspond with an estimation based on the RFT model using scaling factors that appropriately express the ground conditions. After the lander landed on the regolith simulant, in case A, its roll and pitch angles were calculated as ±.5 using data shown in Fig. 8. In addition, in Cases B and C, when the pitch angle reached a maximum of 2 in the atmosphere, the roll/pitch angle was still ±.5 in the vacuum. That is, in a vacuum, the difference in the ground density does not contribute to the attitude of the lander. From the above results, it was suggested that, even if some footpads of a lander land on regolith with different densities, it does not lead to postural imbalance or turnover of the lander on the moon surface. V. CONCLUSION This study investigated the influence of the footpad shape and ground condition on the motion behavior of a lander in a vacuum. From the footpad drop tests and numerical analysis based on the RFT, we confirmed the following: 1) the force acting on the footpad was enhanced and the penetration depth was reduced in a vacuum, 2) the force and kinetic energy conversion rate were smallest for the curved footpad, and 3) an increase in the ground density had a relatively small impact on the penetration depth of the footpads in a vacuum. Furthermore, the drop tests using the lander model confirmed that even if some footpads of a lander land on the regolith simulant with different densities, this does not lead to postural imbalance or turnover of the lander in a vacuum. This finding contributes to not only a design of the lander footpad but also a control strategy for landing. In this study, vertical movement of the footpad was analyzed; however, when landing, the footpad moves horizontally as well. In future studies, the application of the RFT will be discussed for a lander s behavior under various complex landing scenarios, along with comprehensive modeling. Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

8 The final version of record is available at 8 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED AUGUST, 217 ACKNOWLEDGMENT The authors would like to thank Dr. Masatsugu Otsuki at Japan Aerospace Exploration Agency (JAXA) and Dr. Takao Maeda at Chuo University for discussion on the RFT model. Our gratitude also goes to Mr. Kazutoshi Sakamoto and Mr. Shoichi Yoshihara at Japan AeroSpace Technology Foundation (JAST) for their contributions to the system development and experiments described in this paper. REFERENCES [1] T. Hashimoto, T. Hoshino,, H. Otake, S. Tanaka, S. Wakabayashi, H. Morimoto, K. Masuda, M. Ohtake, M. Sutoh, and T. Shimada, Japanese lunar polar exploration mission, in Proc. 67th International Astronautical Congress (IAC), Sep. 216, pp. A3.2A.2(1) (3). [2] G. Heiken, D. Vaniman, and B. French, Lunar sourcebook: A user s guide to the Moon. Cambridge University Press, New York, NY, [3] D. Liang, H. Chai, and T. Chen, Landing dynamic analysis for landing leg of lunar lander using abaqus/explicit, in Proc. 211 IEEE Int. Conf. on Electronic and Mechanical Engineering and Information Technology, Heilongjiang, China, Aug. 211, pp [4] M. Nohmi and A. Miyahara, Modeling for lunar lander by mechanical dynamics software, in Proc. AIAA Modeling and Simulation Technologies Conf. and Exhibit, San Francisco, CA, Aug. 25, pp [5] L. Xu, H. Nie, J. Wan, Q. Lin, and J. Chen, Analysis of landing impact performance for lunar lander based on flexible body, in Proc. 211 IEEE Int. Conf. on Computer Science and Automation Engineering, Shanghai, China, Jun. 211, pp [6] X. Wei, Q. Lin, H. Nie, M. Zhang, and J. Ren, Investigation on softlanding dynamics of four-legged lunar lander, Acta Astronautica, vol. 11, pp , 214. [7] D. Ponnusamy and G. Maahs, Development and testing of leg assemblies for robotic lunar lander, in Proc. the 14th European Space Mechanisms and Tribology Symposium, Noordwijk, Netherlands, Sep. 211, pp [8] B. Huang, Z. Jiang, P. Lin, and D. Ling, Research on impact process of lander footpad against simulant lunar soils, Shock and Vibration, pp. 1 25, 215. [9] T. Yokoyama, H. Kanamori, and K. Higuchi, Estimate of impact force at landing on lunar surface with scale model experiment, in Proc. the Fifth International Symposium on Scale Modeling, Chiba, Japan, Sep. 26. [1] K. Yoshida, S. Shimizu, and K. Sekimoto, Scale modeling for landing behavior of a lunar probe and experimental verification, in Proc. the 16th Workshop on JAXA Astrodynamics and Flight Mechanics, Kanagawa, Japan, Aug. 27, pp [11] M. Sutoh, S. Wakabayashi, and T. Hoshino, Motion behaviors of landing gear for lunar probes in atmosphere and vacuum tests, IEEE Robotics and Automation Letters, vol. 2, no. 1, pp , 217. [12] H. Kanamori, S. Udagawa, T. Yoshida, S. Matsumoto, and K. Takagi, Properties of lunar soil simulant manufactured in Japan, in Proc. Sixth ASCE Specialty Conf. and Expo. on Engineering, Construction, and Operations in Space, Albuquerque, NM, Apr. 1998, pp [13] M. Sutoh, S. Wakabayashi, and T. Hoshino, Influence of atmosphere on lunar rover performance analysis based on soil parameter identification, J. Terramechanics, in press, 217. [14] C. Li, T. Zhang, and D. I. Goldman, A terradynamics of legged locomotion on granular media, Science, vol. 339, no. 6126, pp , 213. Copyright (c) 217 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.