1PIV ANALYSIS OF SOIL DEFORMATION BENEATH A GROUSER WHEEL
Yosuke Yamanoa, Kenji Nagaokaa, and Kazuya Yoshidaa

aTohoku University, {yamano,nagaoka,yoshida}@astro.mech.tohoku.ac.jp

Abstract
This paper presents an analysis of soil deformation beneath a grouser wheel based on particle image velocimetry (PIV).
So far, wheeled mechanism has been mainly adopted in locomotion gears of exploration rovers on lunar and planetary
surfaces because of its reliability and efficiency. Such surfaces are generally covered with fine soil such as lunar or
Martian regolith. Thus, plate-like lugs, called grousers, have been successfully attached to wheels to improve theirmobility performance. However, a reasonable model of the grouser wheel traveling on soil has not been established.
Accordingly, understanding the soil-wheel interaction including soil deformation beneath the grouser wheel is a key
approach for modeling. In this paper, we elaborate an experimental analysis of soil deformation and flow beneath agrouser wheel. We measured the wheel rotational angle, wheel sinkage, traveling distance, and consecutive images
captured by a high-resolution digital camera fixed perpendicular to a sandbox through experiments. The time histories
of flow velocity of the soil particles are calculated using a particle image velocimetry (PIV) analysis. Based on theexperimental results, we discuss the shape of the slip-line and thickness of the soil flow under several conditions ofwheel slippage and sinkage.
Keywords: PIV analysis, grouser wheel, soil deformation, exploration robots.

1. Introduction
Recently, various lunar and planetary exploration missions have been planned and operated by major development
countries. A robotic mission using mobile robots, the so-called rovers, is a possible means for advanced exploration on
the Moon and Mars. In particular, wheeled rovers have played a significant role in the past and in the ongoing Mars
missions undertaken by NASA. These rover missions have proven that unmanned rovers can contribute significantly todetailed geological investigation, and thereby provide significant scientific findings on the surfaces of extraterrestrial
bodies. In future missions, rovers are expected to accomplish more challenging exploration missions.
The lunar and planetary surfaces are covered with fine soil such as lunar regolith. Hence, wheeled rovers can easily
slip and become stuck on the soil. To avoid such critical situations, it is necessary to design, develop, and operate arover system based on wheel-soil interaction. The fundamentals of the mechanical interaction between a running gearand soil have been researched in terms of soil mechanics (Bekker 1956; Wong 2008). Most of the previous studies havefocused on relatively-larger wheels that can be modeled as simplified wheels without plate-like lugs or grousers.
Although these wheel-soil interaction models have been widely applied to terrain identification (Iagnemma andDubowsky 2004), motion control (Iagnemma and Dubowsky 2004; Ishigami et al. 2009), or prediction of tractive
limitations (Nagaoka et al. 2012), it is well-known that grousers attached to the wheel surface can enhance the mobility
performance of wheels and are essential components for traveling on loose soil. We have measured soil reaction force
acting on a grouser wheel (Higa et al. 2016), and thereby clarified that the reaction force distributions are drastically
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Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 20182

different from stress distributions acting on a grousers-less wheel, defined here as a wheel without grousers or with low
grousers as slip resistance on the wheel surface. Although our previous research reported the measurement of thisinteraction force, a reasonable model of a grouser wheel traveling on soil has not been established. In addition to theforce measurement, understanding the soil deformation characteristics beneath the grouser wheel is a key approach formodeling. With recent progression of image processing technology and computational processing capability, it has
become possible to visualize soil flow from continuous camera images without physical contact by using particle image
velocimetry (PIV). PIV-based analysis enables one to obtain the velocity of massive soil particles. PIV has been applied
to the analysis of soil deformation beneath a grouser-less wheel (Senatore et al. 2013; Skonieczny et al. 2014). However,the PIV analysis for the grouser wheel is currently lacking.
In this paper, we present a PIV analysis of soil deformation and flow beneath a grouser wheel traveling on soil.
From the PIV-based observation of soil flow, the soil deformation under interaction with the grouser wheel isquantitatively discussed using single wheel experiments. In particular, to observe soil flow without the interference ofmulti-grousers, we used a single-grouser wheel for the PIV analysis.

2. Single Wheel Testbed
Fig. 1 shows the experimental apparatus of a single-grouser wheel for the PIV-based analysis, where a multigrouser is illustrated in Fig. 1(b) for generality. The sandbox has a length, width, and depth of 1.6 m, 0.3 m, and 0.3 m,respectively, and is filled with Toyoura sand. As mentioned before, to accurately understand the characteristics of thesoil flow caused by the grouser, a single-grouser wheel was used in this study, as shown in Fig. 1(c). The specificationsof this single-grouser wheel are as follows: the wheel diameter is 200 mm, the wheel width is 100 mm, the height of thegrouser is 25 mm, the thickness of the grouser is 5 mm, and the total weight acting on the wheel is 1.6 kg. The wheel
can achieve free motion in vertical and horizontal directions, and the displacement in each direction was measured using
a linear encoder.
The single wheel testbed has a glass-walled observation window to capture the soil flow beneath the wheel using adigital camera. The position of the camera was fixed on the floor with a tripod at the height of 235 mm and distance of
320 mm from the target window, and the frame rate of the camera was set to 60 fps. In addition, to simulate various
wheel slip conditions, a traction load was applied to the wheel horizontally (see Fig. 1(b)). Throughout the experiments,
the rotational velocity of the wheel was controlled to be constant and its rotational angle was obtained using a rotary
encoder.

3. Accuracy Evaluation of PIV
Prior to the single-grouser wheel experiments, the accuracy of PIV analysis was evaluated.

3.1 Measurement Method
An evaluation experiment was carried out to compare the PIV method with ground truth values. In this experiment,
the digital camera was moved in the horizontal direction by maintaining a distance of 235 mm from the glass window ofthe sandbox. A velocity vector of the soil particle was computed based on PIV processing of the camera images. The
accuracy of the PIV-based analysis was evaluated by comparing its resulting velocity and the horizontal velocity
obtained using the linear encoder, which is a ground truth. Here, as shown in Fig. 2(a), the velocity vectors of soil flow,which is obtained in the field of view, were used for calculating the average velocity.

3.2 Results
Fig. 2 shows the experimental results of the evaluation of PIV accuracy. The processed image confirmed that thehorizontal motion was calculated based on the velocity vector as indicated by light-green-colored arrows in Fig. 2(a).
From the comparison results shown in Fig. 2(b), the velocity obtained using PIV coincides with the velocity obtained

Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018

3(b) Schematic view.

(a) Overview.

(c) Side view of single-grouser wheel.

Fig. 1. Experimental apparatus of single-grouser wheel for PIV analysis.

(a) Velocity vector in field of view.

(b) PIV vs encoder value.

Fig. 2. Experimental results of accuracy evaluation of PIV.

using the linear encoder at various velocity values. Thus, this experiment concludes that the PIV analysis is sufficiently
accurate to track the soil flow over a wide velocity range.

4. Soil Flow Analysis
4.1 Experimental Conditions
In the experiments for the analysis of soil flow, the wheel angular velocity was controlled to be 1.6 rad/s. To
simulate different wheel slip conditions, several traction loads (10, 15, 20, 25, and 30 N) were applied. As a common
initial condition, the single-grouser was set parallel to the soil surface, i.e., the traveling direction of the wheel and thewheel angle of 90°. Furthermore, a wheel angle is defined as a wheel rotational angle. Thus, when the wheel angle is 0°,
the single-grouser is located immediately beneath the wheel and the line connecting the wheel axle with the grouser isvertical.
Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018

4Thus, to evaluate the slip state of the grouser wheel, the slip ratio, S, is defined as follows:
S=(r + l ) − v(r + l )

(1)

where v is the actual velocity in the horizontal direction, ω is the angular velocity of the grouser wheel, r is the radius of
the wheel, and l is the height of the grouser. The flow vector of the soil particles is indicated by a red-colored arrow in
the images captured by the camera.

4.2 Results and Discussion
4.2.1 Velocity Vector of Soil Particles
Fig. 4 shows the experimental results of visualization of the soil flow at S = 21.5% and 81.3%, where the results forthe wheel angles of 40°, 30°, 20°, and 10° are shown. The results confirm that the soil flow is generated opposite to thedirection of the motion of the grouser. Moreover, from the results for the wheel angles of 40° and 30° at S = 21.5%, thesoil velocity is low compared with that under the other conditions. The range of the slip-line field (i.e., soil failureregion) varies with a change in the wheel angle and slip. This change in the slip-line field depends on the wheel motion.

4.2.2 Shape of Slip Line
Given that the velocity vectors in the x (horizontal) and y (vertical) directions are u and v, respectively, a streamline
as a two-dimensional steady flow can be expressed as follows:
dx dy
=uv

(2)

Based on Eq. (2), we can depict the slip-line so that the velocity vector becomes a tangent line at each curved point,where the initial position of the slip-line is set on the grouser tip.
Fig. 5 shows the results of superimposing the identified slip-line on the PIV-processed images where the wheel
angles are 20° and 10° at S = 52.4%. Reasonable slip-lines can be tracked in each condition using the streamline
analysis given in Eq. (2). Furthermore, Fig. 6 shows the slip-line shape under various slip ratios, where the initialposition of the slip-line is commonly set to (X, Y) = (0, 0). The resulting plots confirm that most slip-line fields (soilfailure regions) are generated up to a depth greater than the depth of the grouser tip position. When the wheel angle issmall, the soil failure region becomes small, and shear failure is caused in a shallow region. In contrast, when the wheel
angle is large, the slip-line shape becomes a relatively large arc.

4.2.3 Thickness of Sand Flow Field
The distance from the grouser tip to the deepest point of the slip-line and the angle of the maximum flow thickness
are respectively defined as the maximum flow thickness and λ, where λ is the angle formed by the line connecting thewheel axle and the point farthest from the slip line and the y-axis, as shown in Fig. 7.
Furthermore, as the sampling rate of the linear encoders is different from that of the digital camera, timesynchronization was performed using a linear interpolation as follows:y=yi+1 − yiy −yt + yi − i+1 i ti
ti+1 − titi+1 − ti(3)where yi is the traveling distance or sinkage at time t, and ti is the increment value of 1/60 s. From Eq. (3), the angle
between the wheel axle and the maximum flow thickness can be calculated.

Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018

540deg

40deg

30deg

30deg

20deg

20deg

10deg

10deg

0deg

0deg

(a) S = 21.5%(b) S = 81.3%

Fig. 4. Angle histories of soil flow beneath the single-grouser wheel based on PIV analysis.

Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018

6(a) Wheel angle of 20°(b) Wheel angle of 10°

Fig. 5. Resulting slip line at S = 52.4%

Fig. 6. Resulting slip-lines normalized in XY coordinates.

Fig. 8 shows the thickness of the soil flow field, where the upward direction of the y-axis is positive. From theresults, the soil flow thickness increases with an increase in the wheel angle. In particular, when the slip ratio is large,
the thickness monotonically increases. Fig. 9 shows the angle λ shown in Fig. 7. The results confirm that the maximum
soil flow thickness is observed in the approximately same direction at each slip ratio.

Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018

7Fig. 7. Diagram illustrating the relationship between the slip line and a grouser wheel

Fig.8. Thickness of soil flow field.

Fig.9. Angle of thickness of soil flow field.

4.2.4 Soil Failure Angle
The soil failure angle is defined as shown in Fig. 7, where µ represents the angle between the soil surface according
to the theory of soil mechanics and is given follows:
=4−2(4)where  is the internal friction angle of soil. Comparison between the soil failure angles of the experiments and thetheory is shown in Fig. 10. Hence, the theoretical value of µ can be calculated as 26°, where the value of µ is given indegrees for ease of understanding. From Fig. 10, however, the soil failure angle is much larger than 26° at each tractionload. This difference suggests that soil failure caused by the grouser wheel is not a typical soil failure state, and remodeling of the soil failure is required depending on the wheel motion.

5. Conclusion
In this paper, we presented an analysis of soil deformation beneath a grouser wheel based on PIV and showed theresulting soil flow beneath a single-grouser wheel under various slip conditions. From the results, one of the soil
deformation characteristics, i.e., the soil slip-line, is discussed under several slip conditions. In addition to thecomparison of the shapes of the slip-line and the flow velocities on it under various slip ratios, the thickness of the soil
failure field is discussed. In particular, unlike conventional soil failure theory, the soil failure angle changes dependingon the wheel motion. This is a key aspect for modeling the grouser wheel. Based on the results of this study, we willaddress the PIV-based analysis and modeling of the wheel with multi-grousers in the future.
Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018

8Fig. 10. Comparison of soil failure angle.

Acknowledgments
This work was supported by JKA and its promotion funds from KEIRIN RACE.

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Proceedings of the 10th Asia-Pacific Conference of the ISTVS, Kyoto, July 11–13, 2018