THE Moon is approximately 384,400 km away from Earth,

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1 The final ersion of record is aailable at IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JULY, 8 Motion modeling and localization of skid-steering wheeled roer on loose terrain Masataku Sutoh, Yutaro Iijima, Yuta Sakakieda, and Sachiko Wakabayashi Abstract The motion behaior of a skid-steering roer on loose terrain is modeled experimentally, and a position estimation method based on the model is proposed. Skid steering is a steering method adopted for arious ehicles and robots. In this method, the ehicles steer by controlling a ratio between the rotational elocities of their left and right wheels. For controlling a skidsteering roer, whose wheels can slip on the lunar and planetary surfaces, which are coered with loose regolith, it is important to model accurately the roer s motion behaiors on loose terrain. To this end, we conducted traeling tests using a four-wheeled roer in a sand field and analyzed the motion behaiors of the roer on loose terrain. In the tests, the elocities of the roer s left and right wheels were controlled, and the roer traeled with arious turning patterns. From the test datasets, we deried a mathematical model that expresses a relationship between the input and output elocities of the roer s wheels. Furthermore, the effectieness of a position and motion estimation method based on the model was confirmed from experiments conducted in the sand field. Index Terms Field Robots, Space Robotics and Automation, Localization. I. INTRODUCTION THE Moon is approximately 8, km away from Earth, and the distance to Mars from Earth is approximately million km on aerage. If a roer on the Moon and Mars is teleoperated from Earth, the time delay in communication, which is approximately. seconds and. minutes in a oneway transmission to/from the Moon and Mars, respectiely, cannot be aoided. This delay might jeopardize the roer mission. Thus, lunar and planetary roers are expected to trael with autonomy. As one of the key elements for the autonomy, the roer position and motion should be accurately estimated on the lunar and Martian surfaces. Position estimation, i.e., localization, is a fundamental technology required for an automatic/autonomous robot. Thus, arious studies hae been reported for robots on Earth. For field robots that work outdoors, localization methods based on the Global Positioning System (GPS) are widely used,,. Odometry/dead-reckoning, which counts the rotations Manuscript receied: March, 9, 8; Reised June, 7, 8; Accepted July,, 8. This paper was recommended for publication by Editor Jonathan Roberts upon ealuation of the Associate Editor and Reiewers comments. *This work was supported by the Japan Aerospace Exploration Agency. Masataku Sutoh, Yutaro Iijima, and Yuta Sakakieda are with Shinshu Uniersity, -- Tokida, Ueda, Nagano, , Japan sutoh, f7d, f8g@shinshu-u.ac.jp Sachiko Wakabayashi is with the Japan Aerospace Exploration Agency, 7-- Jindaiji-Higashimachi, Chofu, Tokyo, 8-8, Japan wakabayashi.sachiko@jaxa.jp Digital Object Identifier (DOI): see top of this page. of the wheels installed on a robot, is a position estimation method with a low computational cost,. When a robot traels under a shielding object such as a tree, the GPS-based localizations cannot accurately estimate the robot position. To preent this problem, wheel odometry was utilized along with the GPS, to interpolate the GPS data 6, 7. For indoor robots that cannot depend on the GPS, simultaneous localization and mapping (SLAM), which uses cameras and/or laser range finders, has been widely studied 8, 9. Visual odometry (VO) based on camera image processing is widely utilized for outdoor and indoor robots,. Although there exist arious position and motion estimation methods proposed for robots on Earth, those applicable to lunar and planetary roers are limited. First, the GPS cannot be used for roer position estimation, because it has not been deeloped on the Moon and Mars. Furthermore, the surfaces of the Moon and Mars are coered with loose regolith, and the wheels of the roer can slip. Thus, it is difficult to estimate the roer position using the wheel odometry. Laser-based SLAM is also unsuitable because the roers trael on open lunar and planetary surfaces where objects/walls that should reflect the laser are not always aailable. NASA s Mars Exploration Roers (MERs) basically used VO for their position estimation,. The VO-based localization worked well; howeer, with a central processing unit (CPU) with MHz mounted on MERs, the roers were required to stop for approximately min on aerage for the calculation. Thus, it was only commanded during specific types of motion, such as relatiely short dries that occurred on steep slopes. In general, the performances of CPUs used for spacecraft are not so high. For a roer with a high autonomy, which enables an exploration with a small interention from its ground operators, roer position and motion should be estimated in real time with a small computational cost. Various model-based approaches hae been studied to estimate/predict the position and motion of a ehicle/robot. For a skid-steering ehicle that can steer by controlling the elocity ratio of its left and right wheels, Wong et al. proposed a dynamic model of the ehicle based on the interaction between its track and ground,. Yu et al. extended Wong s model to express the motion behaior of a skid-steering wheeled robot 6. Gupta et al. proposed a motion plan for a skid-steering wheeled robot based on Yu s model and experimentally confirmed its usefulness 7, 8. Martinez et al. proposed a kinematics model of a skid-steering tracked robot considering instantaneous centers of rotations (ICRs) of both treads 9. Mandow et al. expanded Martinez s model and deeloped a model for a wheeled robot. Endo et Copyright (c) 8 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 ersion of record is aailable at IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JULY, 8 y elocity, Ω, as l (x fl, y fl ) x G (t) = t cos θdτ, () y G (x rl, y rl ) Ω θ (x fr, y fr ) y G (t) = t sin θdτ, () (x rr, y rr ) r θ(t) = t Ωdτ. () O Fig.. Dead-reckoning model of a skid-steering wheeled roer. al. modeled the slippage of a skid-steering tracked robot and proposed a position estimation method based on the model. Their model expressed the relationship between the slip ratios and input elocities of the robot s left and right tracks. Howeer, these studies targeted robots traeling on hard surfaces, e.g., turf and plywood in ; those traeling on loose surfaces were not within the scope of the research. Yamauchi et al. experimentally confirmed the effectieness of Endo s model on sand. The model was alidated from experiments using a tracked robot that traeled with small turning radii, i.e., those smaller than its track tread. The usefulness of their model has not yet been confirmed for a skid-steering wheeled roer that traels with larger turning radii on loose terrain. Skid steering enables a ehicle/robot to moe forward/backward and turn with only one actuator on each wheel/track. This characteristic contributes to a mass and power reduction for a lunar and planetary roer. Thus, this study targets a skid-steering roer. In this study, motion behaiors of a skid-steering wheeled roer are experimentally modeled on loose terrain, and a position and motion estimation method is proposed based on the model. To this end, we first reiew a dead-reckoning model used for a position/motion estimation of a skid-steering roer. Traeling tests conducted using a four-wheeled roer in a sand field are described. The output elocities of the roer s left and right wheels are modeled based on the tests. The effectieness of a position and motion estimation method based of the model was alidated from experiments conducted in the sand field. x G II. DEAD-RECKONING MODEL OF A SKID-STEERING ROVER In this study, we target the motion behaior of a skidsteering wheeled roer on flat terrain and consider the roer position in the xy plane, as shown in Fig.. The roer position, x G (t), y G (t), and direction angle, θ(t), at a time, t, can be expressed using the roer traeling elocity,, and angular x and Ω are deried using the traeling elocities of the roer s left and right wheels, r and l, as Ω = / / /T /T r l, () where T denotes the wheel tread of the roer, which is defined as the distance between the wheels on the left and right sides of the roer. When the roer turns, the turning radius, R, can be expressed as R = Ω = T r/ l + r/ l (). For position and motion estimation of a roer that traels and slips on loose terrain, how we accurately obtain r and l in Eq. () is a major issue. Measuring the angular elocities of the roer s right and left wheels, ω r and ω l by using encoders, the rotational elocities of the wheels, r and l, can be obtained as r l = r ωr ω l, (6) where, r denotes the wheel radius including the grouser height. In this study, we assume that the front and rear wheels on each side of the roer always had the same elocity. When a roer skid-steers on loose terrain, its left and right wheels slip. Thus, it is difficult to estimate and Ω in Eq. () using r and l. If a gyroscope is mounted on a roer, Ω can be directly measured; howeer, still cannot be obtained. In this study, we experimentally model r and l in Eq. () as a function of r and l. Measuring r, l, and Ω using encoders and a gyroscope, respectiely, we estimate the roer position (x G, y G, θ) based on the model deeloped. III. TRAVELING TEST AND WHEEL VELOCITY MODELING For modeling the relationship between the input and output elocities of the roer s wheels, we conducted traeling tests using a four-wheeled roer in a sand field. In the tests, the roer traeled with arious turning radii by controlling the elocity ratios of its left and right wheels. In this section, the four-wheeled roer used is first introduced, and the traeling tests are explained along with the modeling. Copyright (c) 8 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

3 This is the author's ersion of an article that has been published in this journal. Changes were made to this ersion by the publisher prior to publication. The final ersion of record is aailable at SUTOH et al.: MOTION MODELING AND LOCALIZATION OF SKID-STEERING WHEELED ROVER ON LOOSE TERRAIN Markers (b) Grael (a) Silica Fig.. Traeling tests conducted using ALPS on a field coered with arious types of sand at the Japan Aerospace Exploration Agency. Fig.. A skid-steering wheeled roer named ALPS being deeloped by our research group. A. Four-wheeled roer, ALPS In our research group in Shinshu, a four-wheeled roer named the Autonomous roer for Lunar and Planetary exploration in Shinshu (ALPS) is being deeloped. Fig. and Table I show the oeriew and specifications of ALPS, respectiely. ALPS can be manually/autonomously controlled by commands sent from a user operated PC ia a local-area network. The commands are receied on an on-board computer installed on ALPS. Each of the four wheels of ALPS is equipped with a motor (RE, Maxon) that is controlled using a motor drier. By manipulating the motors, ALPS can moe forward/backward and skid-steer. The rotational elocities of the wheels, r and l, are measured using an encoder installed on each motor. A gyroscope (CRH-, SILICON SENSING) is mounted on ALPS and used to measure the roer angular elocity, Ω. All the deises are powered by two on-board batteries (CUE-D7, IDX). B. Traeling tests We conducted traeling tests using ALPS in a sand field at the Adanced Facility for Space Exploration at the Japan Aerospace Exploration Agency, JAXA. This sand field has an area of approximately m and is coered with silica into a depth of. m. The field has a space of. m. m. m coered with grael. The silica and grael consist mainly of particles haing sizes of..6 mm and mm, respectiely. In our tests, ALPS traeled on a flat area coered with these two types of materials (see Fig. ). In the field, the motion capture system (OptiTrak, Prime ) is arranged. Using the system, the motion of ALPS was TABLE I S PECIFICATIONS OF SKID - STEERING WHEELED ROVER, ALPS. W HEELBASE IS DEFINED AS THE DISTANCE BETWEEN EACH WHEEL ON EITHER THE LEFT OR RIGHT SIDE OF THE ROVER. Item Mass Size (L W H) Wheel size ( b) Wheel tread (T ) Wheelbase Value and unit. kg 6 6 cm 8 cm 8 cm (including grouser) cm cm tracked with an accuracy of. mm at Hz. In the tests, fie infrared markers were attached on the ALPS s body center and near each wheel for the motion capture. In the traeling tests, ALPS traeled with arious turning radii by controlling the elocity ratios of its left and right wheels. The turning radii were set at ±.,.6,.,.,. m, and (i.e., moing forward). Turning right and left were assigned positie and negatie signs, respectiely. The input elocity and target turning angle were calculated based on the encoder counts. The front and rear wheels on each side of the roer were controlled at the same elocity. Table II lists the experimental condition in detail. The input traeling elocity, r +l, was set at. cm/s for all the cases. Before eery test, the ground surfaces were loosened using a scoop and leeled using a leeler so that the tests could be conducted in an identical ground condition. Each test was conducted twice to confirm the repeatability. C. Modeling and discussion Fig. shows the trajectories of the marker attached on the ALPS body center. The figure shows that when ALPS turned with target turning radii of. and. m, the arcs that ALPS actually traeled are larger than the target radii. This difference between the turning radius targeted and the arc that ALPS traeled is discussed in detail below based on the elocity ratio of the roer s left and right wheels. In Fig. (a), it was obsered that ALPS initially moed in a direction opposite to the commanded turn (which is especially noticeable in the grael case). In preliminary tests conducted TABLE II E XPERIMENTAL CONDITION IN THE TRAVELING TESTS. T HE TRAVELING ANGLE WAS ADJUSTED TO PREVENT THE ROVER RUNNING OFF THE AREA COVERED WITH A MATERIAL. T HE VALUES ARE THOSE TARGETED. Turning radius m r /l Turning angle -(silica)/-(grael) -9(silica)/-(grael) (silica)/+(grael) +(silica)/+(grael) Copyright (c) 8 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 ersion of record is aailable at IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JULY, r / l - Exp. data: silica Exp. data: grael Approx. cure: silica Approx. cure: grael. Input: R. Silica Grael x m r / l -.. (a) Turning radius:. m Fig.. Relationship between the input and output elocities of the roer s left and right wheels. From the approximation cures deries from the experimental data, r/ l is expressed as r/ l n, where n was obtained as.7 and.7 on the silica and grael, respectiely Input: R. Silica Grael x m (b) Turning radius:. m Fig.. Trajectory of the roer traeling with arious turning radii. In the figure, the trajectories of the infrared marked attached on the ALPS body center were plotted. The trajectories are drawn from one illustratie trial, not the aerage of the two trials. at our laboratory, this behaior was not obsered when ALPS turned right/left on a leeled ground. This suggested that the center of graity of ALPS is located at its body center. Based on this obseration, we consider the ground prepared was not completely leel in the field tested. As the results, ALPS sidesliped and moed in a direction opposite to the commanded turn. Rearranging Eq. (), the traeling elocities of the roer s right and left wheels, r and l, are obtained as, r l = + ΩT ΩT. (7) Defining the positions of the markers attached on ALPS at a time t as (x G (t), y G (t)), (x fl (t), y fl (t)), (x fr (t), y fr (t)), (x rr (t), y rr (t)), and (x rl (t), y rl (t)), and Ω in Eq. (7) can be deried as = x G(t + dt) x G (t), (8) dt Ω = Ω r + Ω l, (9) where Ω r and Ω l denote the roer angular elocities calculated using (x fl, y fl ) and (x fr, y fr ), and (x rr, y rr ) and (x rl, y rl ), as folllows: tan Ω r = tan Ω l = xfr (t+dt) x rr(t+dt) y fr (t+dt) y rr(t+dt) tan dt xfl (t+dt) x rl (t+dt) y fl (t+dt) y rl (t+dt) tan dt xfr (t) x rr(t) y fr (t) y rr(t) xfl (t) x rl (t) y fl (t) y rl (t)., () () From Eqs. (7) (), r and l can be estimated using the positions of the fie markers. We plotted the ratio of the roer s input elocities, r / l, along with that of the output elocities, r/ l, on the graph shown in Fig.. The data plotted on the graph are the aerage alues of the two trials, and the error bars indicate the maximum and minimum alues. The figure shows that the approximation cures well correspond with the experimental data on both materials. From these cures, we modeled r/ l as, r l = n r l. () Here, n was obtained as.7 and.7 on the silica and grael, respectiely. It is noteworthy that the characteristics of these materials, such as size and friction, seem substantially different each other. From this obseration, there is a possibility that n depends on the roer parameters such as mass, wheel tread, and wheel shape, rather than the terrain characteristics. Eq. () is a powerful equation that can estimate the output elocity ratio of the roer s left and right wheels for a gien input elocity ratio using one parameter n. In addition to the aboe experiments conducted in the JAXA s sand field, we conducted more trials in another sand field, as shown later in the appendix. Using the datasets obtained in these experiments, the alidity of Eq. () was further confirmed. Copyright (c) 8 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 ersion of record is aailable at SUTOH et al.: MOTION MODELING AND LOCALIZATION OF SKID-STEERING WHEELED ROVER ON LOOSE TERRAIN 6 Ground truth (A) Encoder (B) Gyroscope (C) Proposed 6 Ground truth (A) Encoder (B) Gyroscope (C) Proposed x m x m (a) Turning radius:. m (b) Turning radius:. m Fig. 6. Roer position estimation results. It can be obsered that in both cases, the roer positions estimated based on our proposed method best match with the ground truth. We deried Eq. () for a wheeled roer with a gentle turn, i.e., the turning radii greater than its wheel tread. For a sharp turn, the roer s right and left wheels are required to rotate in opposite directions and this results in a drastic increase in wheel sinkage on loose terrain. Thus, we beliee that for a wheeled roer, a sharp turn should be aoided and modeling of gentle turning behaior is important. Yamauchi et al. also proposed an equation that expresses the relationship between the slip ratios and input elocities of the roer s left and right tracks. Their equation was deried based on experiments in which a tracked roer turned sharp, i.e., the turning radii were usually smaller than its track tread. Using our experimental datasets shown in Fig., we found that Yamauchi s equation cannot estimate the slip ratios of the roer wheels when the roer traels with a large turning radius. When the roer traels with a large turning radii, the difference between the elocities of the roer s left and right tracks/wheels is small. Our obseration showed that the traeling elocity, rather than the slip ratio, is more appropriate to express the motion behaior of the roer in such condition. Thus, we beliee that Eq. () represents a more comprehensie model that can express the motion behaior of the roer traeling with turning radii larger than its wheel tread. IV. ROVER POSITION ESTIMATION We can estimate the roer position using the wheel elocity model expressed by Eq. (). We conducted traeling tests using ALPS in the JAXA s sand field and alidated the position estimation method based on the model. In this section, the procedure of the roer position estimation is described, and the position estimation experiments conducted in the sand field are explained in detail. A. Roer position estimation procedure The estimation procedure of roer position using the wheel elocity model is summarized as follows: ) Using the encoders and gyroscope installed on the roer, the input wheel elocities, r and l, and the roer angular elocity, Ω, are measured, respectiely. ) Using Eq. (), the output elocity ratio of the roer s left and right wheels, r/ l, is estimated for gien r and l. ) From Eqs. () and (), r and l can be obtained for a measured Ω. ) Using r and l, is obtained from Eq. (). ) Substituting and Ω into Eqs. () (), the roer position (x G, y G, θ) can be estimated. B. Position estimation experiments ALPS traeled in the JAXA s sand field, and its position was estimated along with the trael. The motion of ALPS, i.e., the ground truth, was measured using the motion capture system arranged in the field. In the tests, ALPS was commanded to trael along a rounded rectangle line of roughly m m on a flat terrain coered with silica. When ALPS turned near the corners of the rectangle, it turned 9 based on the direction angle estimated from the gyroscope. The target radii for this turning were set at. and. m. The input traeling elocity was set at cm/s based on the encoder counts. Measuring the input elocities of the ALPS s left and right wheels, r and l, and the roer angular elocity, Ω, by using the encoders and gyroscope, respectiely, the roer position was estimated in the aboe-mentioned procedure. Before eery test, the ground surface was loosened using the scoop and leeled using the leeler so that the tests could be conducted in identical ground conditions. To confirm the repeatability, each test was conducted twice. C. Position estimation results and discussion Fig. 6 shows the ground truth of the ALPS s traeled trajectory along with the positions estimated in arious methods. In the figure, the positions estimated by (A) encoders, (B) encoders and gyroscope, and (C) our proposed method were Copyright (c) 8 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 ersion of record is aailable at 6 IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JULY, 8 Aerage position error m... R (A) Encoder (B) Gyroscope (C) Proposed Fig. 7. Aerage position error. The errors were calculated as the aerage of (x x e) + (y y e) in the path, where (x, y) and (x e, y e) are the ground truth and estimated positions, as shown in Fig. 6, respectiely. plotted for comparison. In Method (A), and Ω in Eq. () were estimated using r and l deried from Eq. (6). In this method, the roer direction angle could not be accurately estimated, and the position estimated was substantially separate from the ground truth. In Method (B), although r and l deried from Eq. (6) were used for an estimation of, Ω was directly measured using the gyroscope. In this method, the direction angle roughly corresponded with the ground truth; howeer, the position estimated differed from the ground truth, because the roer traeling elocity,, was not accurately estimated. In Method (C), the position estimated best matches the ground truth. Fig. 7 shows the aerage position errors obtained in arious methods. In the figure, the errors were calculated as the aerage of (x x e ) + (y y e ) in the path, where (x, y) and (x e, y e ) are the ground truth and estimated positions, as shown in Fig. 6, respectiely. The figure shows that the errors are smallest in the proposed method. Although the roer position is most accurately estimated by our method, the error in the turning radius of. m is larger than that in the turning radius of. m. We beliee this was caused by the difference in the ground conditions. In the tests, the ground was set manually as identically leel as possible; howeer, it was difficult to make it completely leel. In fact, the data obtained from the motion capture system suggested that the roer tilt in the roll direction was larger when the roer traeled with a.-m turning radius. That is, the ground was not perfectly leel, the roer tilt could make the roer sideslip and induce the large estimation error. It is noteworthy that if the parameters used in the ICRbased method 9 were manually tuned to fit our experimental data, the ICR-based method can estimate the roer position as well. Howeer, if the parameters were deried and used in the method explained in 9 (i.e., combination of turning in place and moing straight motions), the position was not accurately estimated. This could be because the ICR-based method was not deeloped on loose terrain, where the wheels of the roer can sink as it moes. In this sense, our method could be more appropriate for a motion estimation of the roer traeling on R loose terrain. Using the wheel elocity model expressed by Eq. (), the input elocities of the roer s left and right wheels can be back-calculated for a target turning radius. That is, our model contributes to arious motion controls of a roer on loose terrain. In addition, the similar n in Eq. () were obtained on materials haing substantially different characteristics. Although further experiments are necessary to confirm this tendency, there is a possibility that the roer position and motion can be roughly estimated on arious types of terrain by setting n as.7.7. Of course, if n is first identified onsite by using external sensors, e.g., cameras and laser range finders, which can be used in a real planetary roer exploration, the roer position and motion can be estimated using the identified n more accurately. V. CONCLUSION The motion behaiors of a skid-steering wheeled roer on loose terrain were experimentally modeled, and a position estimation method was proposed based on the model. To this end, we first explained the dead-reckoning models of a roer that was used for the roer position estimation. Subsequently, traeling tests were conducted using the four-wheeled roer in a sand field coered with arious materials. Based on the test results, we deried an equation that could express the relationship between the input and output elocity ratios of the roer s left and right wheels. Furthermore, the position estimation experiments were conducted using the roer in the sand field. The experiments confirmed the effectieness of the position estimation method based on the proposed model. This study targeted the position and motion estimation of a roer that traels on a flat terrain. Assuming the roer tilts were neglected in the roll and pitch directions, the wheel elocity model was deried. Our method is beneficial especially in a motion planning scenario in which the roer aoids inclined and uneen terrains and turns on relatiely flat terrain. For a roer that explores on inclined and uneen terrains, the model should be expanded. As future directions of this study, the model deried on flat terrain can be expanded for position and motion estimation of the roer on a sloped/uneen terrain and further integrated for roer motion control. APPENDIX In addition to the arc driing experiments conducted in the JAXA s sand field as presented in Section III, we further conducted more trials at our laboratory in Shinshu Uniersity and confirmed the effectieness of Eq. (). As shown in Fig. A., the trials were conducted using ALPS in a sandbox haing a size of. m. m. m. The sandbox was coered with silica haing a similar property to that of the silica in the JAXA s field. In the tests, ALPS traeled with arious turning radii. Although the input traeling distance was set at cm because of the limited space in the sandbox, the input elocity and turning radius were set as identical as those shown in Table II. The motion of ALPS was measured in the same method, as described in Section II. Before eery test, the ground surfaces were loosened using a scoop and leeled using a leeler so that Copyright (c) 8 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 ersion of record is aailable at SUTOH et al.: MOTION MODELING AND LOCALIZATION OF SKID-STEERING WHEELED ROVER ON LOOSE TERRAIN 7 Sandbox Motion Capture Camera Roer Fig. A.. Arc driing experiments conducted using ALPS in a sandbox coered with silica. r / l - Experimental data Approximation cure r / l - Fig. A.. Relationship between the input and output elocities of the roer s left and right wheels obtained on the sandbox. The tendency obsered on the graph shown in Fig. was further confirmed from the tests in another sand field. the tests could be conducted in an identical ground condition. Each test was conducted three times. We plotted the ratio of the roer s input elocities r / l, along with that of the output elocities, r/ l, on the graph shown in Fig. A.. The data plotted on the graph are the aerage alues of the three trials, and the error bars indicate the maximum and minimum alues. From the figure, it was confirmed that r/ l can be clearly expressed by an approximation cure obtained from Eq. (). Here, n was obtained as.7. It is noteworthy that the alue of n obtained in this sandbox was almost the same as that obtained in the silica area at the JAXA s field. ACKNOWLEDGMENT The authors would like to thank Associate Professors Takashi Kawamura and Satoshi Suzuki at Shinshu Uniersity and Dr. Genki Yamauchi at the Public Works Research Institute for discussion in this research. Our gratitude also goes to Dr. Tsuneaki Yamabe at Shinshu Uniersity for his adise on the system deelopment described in this paper. REFERENCES S. Thrun, M. Montemerlo, H. Dahlkamp, D. Staens, A. Aron, J. Diebel, P. Fong, J. Gale, M. Halpenny, G. Hoffmann, et al., Stanley: The robot that won the DARPA Grand Challenge, J. Field Robotics, ol., no. 9, pp , 6. F. Capezio, A. Sgorbissa, and R. 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