SHAPE EFFECTS OF WHEEL GROUSERS ON TRACTION PERFORMANCE ON SANDY TERRAIN

1 SHAPE EFFECTS OF WHEEL GROUSERS ON TRACTION PERFORMANCE ON SANDY TERRAIN Kenji Nagaoka a, Kazumasa Sawada a, and Kazuya Yoshida a a Tohoku University, {nagaoka,sawdaa,yoshida}@astro.mech.tohoku.ac.jp Abstract This paper presents the effects of different wheel grouser shapes on the traction performance of a grouser wheel traveling on sandy terrain. Grouser wheels are locomotion gears that allow small and lightweight exploration rovers to traverse on the loose sand on lunar and planetary surfaces. However, in-depth research has not been conducted pertaining to the effects of grouser shapes on the traction performance for such applications. In this study, we developed a single wheel testbed and experimentally investigated the effects of four grouser shapes (parallel, slanted, V-shaped, and offset V-shaped) on the traction performance of linear movement on flat sand. The wheel slip, sinkage, traction and side force acting on the wheel axle, the wheel driving torque, and the efficiency of each wheel were examined. Thereafter, the effects on the lateral slope traversability of a small and lightweight four-wheeled rover with different grouser shapes were also examined. The traversability experiment demonstrated the vehicle mobility performance in order to contribute to the design optimization of rover systems. These experimental results and their comparisons suggested that, of the shapes studies herein, the slanted shape was the optimal grouser design for use in wheeled rovers on lunar and planetary soil. Keywords: grouser wheel, effect of grouser shapes, traction performance on sand, exploration rover 1. Introduction Mobility is an essential technology for the successful navigation of rover missions on lunar and planetary surfaces. Wheels with grousers (or lugs) serve as the locomotion gears of the unmanned exploration rovers. Also known as grouser wheels, this technology improves the mobility on loose sand, such as fine lunar regolith. The typical shape of a grouser wheel is shown in Fig. 1. Grouser wheels enable the rovers to tightly grip the soil without the presence of critical slippage between the wheel surface and soil particles. In addition, the grousers can exert competent traction by the increased amount of subsoil backward due to their sufficient height. Hence, grousers have been attached to the wheels of various rover systems. On the other hand, this increased traction is inextricably linked to larger wheel sinkage, which produces critical wheel slippage resulting in sand miring. In general, rovers are expected to avoid such sinkage and slippage, as this leads to localization error and immobility. Therefore, a feasible grouser shape design is required to maximize the wheeled mobility of rovers on sandy terrain. Thus far, the mobility performance of grouser wheels has been studied through experiments and numerical simulations. In our laboratory, the soil stress distributions acting on the grouser wheel have been experimentally investigated, and thereby, we clarified that the soil thrust caused by the grouser is a major factor in the grouser wheel traction (Higa et al. 2016; Higa et al. 2018). In the previous research, plate-like grousers were investigated, as shown in Fig. 1. Furthermore, research pertaining to the two-dimensional observation of the soil flow beneath the wheel has been The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the International Society for Terrain Vehicle Systems (ISTVS), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ISTVS editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ISTVS meeting paper. EXAMPLE: Author's Last Name, Initials. 2014. Title of Presentation. The 10th Asia-Pacific Conference of ISTVS, Kyoto, Japan. For information about securing permission to reprint or reproduce a technical presentation, please contact ISTVS at 603-646-4405 (72 Lyme Road, Hanover, NH 03755-1290 USA)

2 (a) Schematic illustration. (b) Example of a typical rover equipped with grouser wheels: SORATO HAKUTO/ispace. Fig. 1. Typical grouser wheel model. conducted by utilizing particle image velocimetry (PIV), a recent image processing technique (Skonieczny et al. 2012). In particular, when the grouser height is sufficiently high, the dynamic change of the soil flow generated by the grouser can be observed (Yamano et al. 2018). On the other hand, the traction performance of a wheel with plate-like grousers that are attached at a circumferential angle, termed slanted grouser, have been experimentally investigated (Watyotha et al. 2001; Ding et al. 2011). The effects of chevron type grousers (Inotsume et al. 2014), termed V-shaped grouser, and chevron type grouser with a circumferential offset angle difference (Watyotha and Salokhe 2001), termed offset V-shaped grouser herein, have been independently discussed through single wheel experiments. In contrast, the effects of several grouser shapes, including parallel, V-shaped, and offset V-shaped grousers, have been numerically analyzed based on the discrete element method (Du et al. 2017). Although a numerical approach can simulate the dynamic three-dimensional soil flow during wheel travel, experimental verification is required for practical wheel design. Wheels without sufficiently high grousers have been strenuously researched in terramechanics (Bekker 1969; Wong 2008), and their tractive limitations were presented based on typical terramechanics models (Nagaoka et al. 2012). However, scholarly research involving the modeling of such these grouser wheels is currently lacking (Irani et al. 2011; Zhou et al. 2014). In particular, when compared to the actual measurement results of our previous research (Higa et al. 2016; Higa et al. 2018), the mathematical models proposed in other related works do not match the actual wheel-soil interaction; however, they successfully simulate the qualitative vehicle performance, such as the correlation between wheel slip and drawbar pull. The effects of grouser angle (Taylor 1973) and grouser spacing (Taylor 1974) have been partially investigated. Furthermore, the slope traversability of a wheeled rover with typical plate-like grousers has been analyzed in our laboratory (Ishigami et al. 2009; Inotsume et al. 2013; Nagaoka et al. 2016), but the effects of grouser shapes on slope traversability have not been addressed. This study experimentally investigates the effects of several grouser shapes on the traction performance of a wheeled rover. First, the fundamental performance of the grouser wheel shapes is compared through single wheel experiments on flat sand. For the evaluation of the traction performance, the results are summarized based on key indexes. Then, in order to obtain the mobility performance of the vehicle, we present slope traversal experiments using a rover testbed with grouser wheels. Based on these results, the shape effects of the grousers on the traction performance can be discussed, and thereby, possible grouser shapes are suggested for exploration rovers for the purpose of sandy terrain travel. 2. Grouser Shape Model In this study, four grouser shapes (parallel, slanted, V-shaped, and offset V-shaped) are designed and developed. The grouser models are shown in Fig. 2. The basic structure of the wheel consists of an acrylonitrile butadiene styrene (ABS) resin and is generated by 3D printing, which produces a sufficiently stiff structure for experimentation. In addition, rough sandpaper is attached to the wheel surfaces to minimize the slippage between the wheel and sand. The effects of the grousers are experimentally investigated to determine the wheeled traction performance on sandy terrain. The soil interaction of the V-shaped and offset V-shaped grousers is influenced by the rotational direction of the wheel. Herein, the rotational direction is defined as V +, V -, offset V +, and offset V - for each grouser shape, as shown in Fig. 2. In

3 (a) Parallel. (b) Slanted. (c) V-shaped. (d) Offset V-shaped. Fig. 2. Wheel grouser shapes (the top image presents a photograph of the grouser shape, and the bottom image represents the front view of the grouser shape design). addition, the circumferential angle of the slanted, V-shaped, and offset V-shaped grousers is designed as 30 for a typical case. The basic design parameters of the wheel are established: the wheel diameter (excluding the grousers) is 250 mm, the wheel width is 100 mm, the lateral-view grouser height is 25 mm, and 12 grousers are attached in the circumferential direction at equal intervals. 3. Single Wheel Performance This section discusses the single wheel experiments of the different grouser wheel shapes. The experiments provide the effects produced by the grouser shapes on the fundamental traction performance of a single wheel on flat sand. 3.1 Single Wheel Testbed Fig. 3(a) shows the layout of the single wheel testbed. This testbed includes a sandbox that is filled with Toyoura sand and has a length of 1.6 m, width of 0.3 m, and depth of 0.3 m. Regarding the coordinate system, the horizontal direction is set as the x-axis, the vertical direction is the z-axis, and the lateral direction (the direction of the wheel width) is the y-axis, as shown in Fig. 3(a). The translational (x-axis) and vertical (z-axis) motions of the wheel are unconstrained free motion, whereas the lateral (y-axis) motion is mechanically fixed. Furthermore, the various slip conditions can be simulated by applying a traction load (TL) that draws the wheel backward. A counter weight permits the adjustment of the wheel weight (vertical load). In the subsequent single wheel experiments, the wheel weight is 5 kg, and the wheel sinkage varies from 0 to 85 mm in the z-axis direction. The wheel unit, shown in Fig. 3(b), consists of the grouser wheel, wheel driving and steering motors with encoders, and a force/torque (F/T) sensor attached to the wheel axle. The wheel driving and steering motors can be controlled by the motor-controller boards to maintain a constant rotational velocity. Two linear encoders are installed to measure the vertical and horizontal wheel motion at 10 ms intervals. Their resolutions are 25 μm for the wheel sinkage and 50 μm for the horizontal distance of the wheel. The experimental data obtained by this system is calibrated and synchronized by a Robot Operating System (ROS) framework. 3.2 Forward Traveling Performance 3.2.1 Experimental Conditions and Evaluation Indexes The following conditions were set for the forward traveling experiment of the single wheel. The rotational velocity of the wheel was controlled at 10 rpm. Several slip conditions were simulated using seven traction loads: 0 kg, 0.44 kg

4 (a) Overview. Fig. 3. Single wheel testbed apparatus. (b) Wheel unit. 0.87 kg, 1.3 kg, 1.7 kg, 2.1 kg, and 2.5 kg. Prior to each trial, the sandbox was raked and flattened for the purpose of experimental reproducibility. The experiments were conducted three times for each condition, and the average value of the results was obtained. The following evaluation indexes were compared for each grouser wheel: Slip ratio of the wheel (x-axis) Sinkage of the wheel (z-axis) Driving torque of the motor for driving the wheel Side force reacting on the wheel (y-axis) The slip ratio, s, is defined as follows: s= (r+l g)ω-v x 100 (1) (r+l g )ω where r is the wheel radius, l g is the grouser height, ω is the angular velocity of the wheel rotation, and v x is the wheel traveling velocity in the horizontal direction (x-axis). This is defined such that the slip ratio of the grouser wheel becomes a positive value in the self-propelled state, i.e., 0% s 100%. Additionally, the wheel sinkage is defined as the distance from the bottom of the inter-grouser surface (z-axis direction) to the sand surface. 3.2.2 Results and Discussion Fig. 4 shows the results of the single wheel experiments. The following discussion elaborates upon the effects of the grouser shape based on the following evaluation indexes: slip ratio, sinkage, driving torque, and side force. Slip Ratio Fig. 4(a) shows the slip ratio in relation to TL. The slip ratio is plotted as the average value of the experimentally obtained slip ratios under the steady wheel motion. This result demonstrates that the slip ratio of all the grouser wheels monotonically increases with an increase in TL. The slip ratio and TL show a definite correlation. Regarding the effects of the different grouser shapes, small differences were of less than 10% were found in the slip ratio. Thus, it is concluded that the slip ratio is not largely impacted by the grouser shape for forward travel. Therefore, in the subsequent discussion, the other evaluation indexes can most likely provide an improved means of a discussion pertaining to the slip ratio. Moreover, because there is only a small difference in the slip ratios among the grouser shapes, the average slip ratio of the grouser wheels at each TL is used as the performance benchmark. That is, in order to represent the slip

5 (a) Slip ratio versus traction load. (b) Sinkage versus wheel rotation angle. (c) Driving torque versus wheel rotation angle at s = 7%. (d) Driving torque versus wheel rotation angle at s = 84%. (e) Side force versus wheel rotation angle at s = 7%. (f) Side force versus wheel rotation angel at s = 84%. Fig. 4. Results of the forward traveling experiment of a single grouser wheel. conditions, the average results of (i) s = 7% at TL = 0 [kg], (ii) s = 21% at TL = 0.87 [kg], (iii) s = 62% at TL = 1.7 [kg], and (iv) s = 84% at TL = 2.5 [kg] are subsequently compared Sinkage Fig. 4(b) shows the wheel angle history in relation to the wheel sinkage. In this experiment, the angle history is compatible with the sinkage time history due to the controlled the constant angular velocity of the wheel. From these results, the sinkage increases with an increase in the slip ratio, regardless of the grouser shape, thus, exhibiting a close correlation between the slip ratio and sinkage. Although the shape effects are small at the lower slip ratio conditions (s = 0~40%), the shape effects are notable at the increased slip ratio conditions (s = 40~100%). This is due to the directional differences produced by the grouser shapes during the digging and backward pushing of the subsoil. Moreover, the discontinuous grouser shape of the offset V-shaped grouser resulted in the largest sinkage due to the increased number of escape paths on the inter-grouser surface for the sand that is compacted by the grouser. As a result, the slip ratio does not provide adequate differentiation among the grouser shapes because the larger sinkage generates a larger soil reaction.

6 (a) Definition of β. (b) Resulting β to wheel rotation angle. Fig. 5. Direction angle, β, of the reaction force acting on the wheel with slanted grousers. However, an increase of the sinkage carries the potential risk of a stuck condition, and therefore, a smaller amount of sinkage is more desirable for the wheeled rovers. Driving Torque Figs. 4(c) and 4(d) show the angle history of the driving torque of the wheel. The results demonstrate that the driving torque increases with an increase in the slip ratio regardless of the grouser shapes. With respect to the parallel and V-shaped grousers, the torque profiles show a periodic fluctuation with the grouser spacing (the circumferential angle of the grouser attachment) at the lower slip ratio conditions; however, this fluctuation is reduced at the larger slip ratio conditions. This fluctuation is also observed in the wheel sinkage profile of Fig. 4(b), and from these results, a close correlation between the torque and sinkage is confirmed. This periodic fluctuation results from the grouser spacing of 30 and is not observed in the slanted and offset V-shaped grousers. This is because several grousers are continuously interacting with the sand, and thus, an effective soil reaction is obtained even with smaller sinkage. Therefore, this periodic fluctuation is expected to be reduced by design changes of grouser spacing. Side Force Figs. 4(e) and 4(f) show the angle history of the driving torque of the wheel. The results indicate that the slanted grousers exert a relatively larger side force, which is notable at larger slip ratios. The side force of the slanted grouser also increases with an increase in the slip ratio. In contrast, the side force profiles of the other grouser shapes do not show remarkable changes. The direction angle of the measured reaction force of the slanted grouser wheel is noted as β, which represents the resultant force of the drawbar pull and side force as illustrated in Fig. 5(a). The wheel angle history of β is shown in Fig. 5(b). The resulting β decreases with an increase in the slip ratio, and especially there is a notable periodic change in its profile at lower slip ratios. This periodic tendency is observed in the profile of the side force. Furthermore, β converges to a steady value at larger slip ratios. The range of β is 37 ~53 at s = 7% and 23 ~37 at s = 21% and converged to approximately 23 at s = 62% and 84%. Accordingly, β varies depending on the slip ratio and does not always correspond to the grouser spacing of 30. This is due to the balance between the soil thrust, which is based on the compaction properties and fluidity of the soil, and the required force for propelling the wheel forward. 4. Vehicle Performance This section presents the effects of the grouser shapes on the traction performance of a vehicle. In particular, the slope traversability of a four-wheeled skid-steering rover is experimentally investigated, as the side force exerted by the grousers affects the reduction of the side-slip during slope traversal. 4.1 Experimental Environment Fig. 6(a) shows an overview of the experimental setup. The test field contains a sandbox that is larger than the single wheel experiment, which is filled with Toyoura sand and has dimensions of 1.0 2.0 m. The sandbox can simulate

7 (a) Overview. Fig. 6. Experimental environment of the slope traversal on sand. (b) Rover testbed: MoonRaker-EM. a sandy slope through the use of a lift system to raise one end of the sandbox, as shown in Fig. 6(a). In the following experiments, the slope inclination angle is 15. The XYZ coordinate system is also fixed on the sloped sandy surface, as shown in Fig. 6(a). Through the experiments, the position and attitude of the rover were accurately measured at 60 fps by external motion tracking cameras that are capable of tracking the reflective markers attached to the rover. 4.2 Four-Wheeled Rover Testbed In the following experiments, MoonRaker-EM served as a four-wheeled skid-steering rover testbed (Yoshida et al. 2013), as shown in Fig. 6(b). The rover testbed weighs 6.1 kg and has dimensions of 0.5 m in width, 0.6 m in length, and 0.3 m in height. The rover has grouser wheels with a wheel diameter of 200 mm (excluding the grousers), a grouser height of 20 mm, and a wheel width of 40 mm. Each of the four grouser shapes, as shown in Fig. 2, is attached for the respective experiments. The rover contains an on-board computer for remote operation via Wi-Fi, and its wheel rotation speeds are controlled to maintain a constant velocity. This study focuses on seven combination patterns of grouser wheels, as illustrated in Fig. 7, which is generated from the point-of-view of the sandy surface. In the slope traversal experiments, the angular velocity of each wheel is established as 5 rpm. Thus, the wheel patterns will ideally achieve linear movement in the flat sand because the resultant side force is cancelled. 4.3 Slope Traversal Performance Fig. 8 shows the resulting trajectories for the geometric center position of the rover base in the slope traversal experiments for the XY coordinates. The initial position of the rover is defined as zero for the X- and Y-axes. The results confirm that the slanted 2 and offset V + grouser shapes result in the minimum side-slip. In contrast, the parallel configuration generates the maximum side-slip. This can be explained by the side force results of the single wheel experiments discussed in Section 3. Considering the slanted grouser wheel configurations, their trajectories are circular curves with opposite rotational directions, whereas the other configurations generate approximately linear trajectories. These circular trajectories result from the skid-steering effect produced by heading angle change of the rover, which is based on the difference between the right- and left-side traction of the wheels. This difference can be explained by the configuration having a larger weight force acting on the wheels that are located on lower portion of the slope. Consequently, the slanted 2 pattern exerts upslope traction and demonstrates improved slope traversability. In contrast, the other trajectories exhibit a steady side-slip that is proportional to the traveling distance. The difference between the linear trajectories depends upon the amount of side-slip that is suppressed by the side force exerted from each grouser. From the results of the linear trajectories, the offset V - configuration creates resistance to the side-slip on the sloped sand. Thus, the slanted 2 is a possible candidate for side-slip compensation, especially because of its increasing advantage when traveling a longer distance than that used to obtain the experimental results (600 mm in the X-axis direction).

8 (a) Parallel (b) Slanted 1 (c) Slanted 2 (d) V+ (e) V- (e) Offset V+ (e) Offset V- Fig. 7. Wheel combination patterns of the grouser wheels from the point-of-view of the sandy surface. Fig. 8. Resulting trajectories of the slope traversal experiments with an inclination angle of 15. 5. Conclusion This paper presents the effects of different wheel grouser shapes on the traction performance of a grouser wheel traveling on sandy terrain. In this study, we experimentally investigated the traction performance of four grouser shapes: parallel, slanted, V-shaped, and offset V-shaped. To evaluate the fundamental performance of each grouser wheel shape, single wheel experiments in flat sand were performed, and their results were compared based on several evaluation indexes: slip ratio, wheel sinkage, wheel driving torque, and side force. From the results, that compared the slip ratio to the TL, which is the most important indicator of mobility performance, a significant difference was not found for each grouser wheel shape. The results confirmed that the other performance indexes had a close correlation with the slip ratio. In addition, the slanted grouser wheel demonstrated a periodic performance for the driving torque and side force at lower slip ratios. This periodic performance was partially observed in some of the other grouser wheel shapes, which resulted from the number of effective the grousers that were present, depending on the amount of wheel sinkage. Likewise, the slanted grouser exerted a relatively large side force in the experiments. Since the slippage performance of the slanted grouser is comparable to that of the other grousers, this side force effect is expected to enhance the wheeled mobility performance on sandy terrain, for slope traversal. To assess the mobility performance of the vehicle, slope traversal experiments were performed using a four-wheeled rover testbed, and possible combination patterns of the grouser wheels were tested, where the rover trajectory was analyzed when traversing the sandy slope. The resulting trajectories confirmed that the slanted and offset V-shaped grousers produced lower side-slip along the slope, which was dependent upon the wheel combination pattern. Although the offset V-shaped grouser generated resistance to the side-slip, the slanted grouser wheel had improved side-slip compensation by generating a heading angle change of the rover. Summarizing the results of the two experiments, the slanted grouser served as the best candidate for exploration rovers on sandy terrain. Acknowledgments This work was supported by JKA and its promotion funds from KEIRIN RACE.

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