Locomotion Performance of a Configurable Paddle-Wheel Robot overDry Sandy Terrain

Yayi Shen, Shugen Ma, Fellow, IEEE, Guoteng Zhang, Member, IEEE, and Syuya Inoue

Abstract— To access rough terrain and enhance the mobilityin sandy terrain, a configurable paddle-wheel robot was pro-posed. This report addresses the paddle terradynamics, andthe experimental verification of the locomotion performanceof the robot over dry sandy terrain. To study the interactiveforces between the paddle and the media, a terradynamicmodel is built and verified through experiments. To explorethe locomotion performance, an indoor platform that allowsthe paddle-wheel module to move freely in both horizontal andvertical directions is created. Forward locomotion speed, heightvariant, and specific resistance are evaluated with different con-figurations. The protruding paddles have successfully reducedthe slippage so as to increase the locomotion efficiency in sandyterrain. The performance of the whole robot has also beenverified in outdoor sandy terrain.

I. INTRODUCTION

When traversing outdoors, field robots face a varietyof complex terrain situations to negotiate. Based on thesubstrate properties, these terrains can be generally classifiedinto two categories. One is rigid terrain which may includerocks, gravels, stairs, or debris. Another is soft terrain wherethe substrate is deformable or flowable under extra stresses,e.g., sand, mud, soil, or snow. Soft terrain usually consistsof granular media, defined as collections of tiny discreteparticles [1]. It can exhibit behaviors between solid and fluid[2]–[4]. According to the water content, granular media canalso be separated into dry granular media and wet granularmedia. The severe difference is whether cohesion exists [5].

Many existing research of mobile robots contribute to thelocomotion on rigid substrate [6]–[8]. As for the study onsoft terrain locomotion, a majority of existing works focuson the dry granular media [9]–[15]. A typical one is theresearch done by Li et al on Sandbot. They found thatthe robot dynamics on granular media depended sensitivelyon the actuation parameters [1], [9] and a terradynamicalmodel was successfully built to predict the interaction forcebetween the substrate and locomotor [10]. The Carnegie

This work was partially supported by the project of Robotics InnovationBased on Advanced Materials under Ritsumeikan Global Innovation Re-search Organization (R-GIRO). The work of Yayi Shen was supported byChina Scholarship Council for his study in Ritsumeikan University.

Yayi Shen was with the Department of Robotics, Graduate School ofScience and Engineering, Ritsumeikan University, Shiga, Japan. He is nowwith the School of Engineering, Tokyo Institute of Technology, Tokyo,Japan. (e-mail: shen.y.af@m.titech.ac.jp)

Shugen Ma and Syuya Inoue are with the Department of Robotics,Graduate School of Science and Engineering, Ritsumeikan University,Shiga, Japan. (e-mail: shugen@se.ritsumei.ac.jp)

Guoteng Zhang was with the Ritsumeikan Global Innovation ResearchOrganization, Ritsumeikan University, Shiga, Japan. He is now with theSchool of Control Science and Engineering, Shandong University, Jinan,China. (e-mail: zhanggt@sdu.edu.cn)

Fig. 1. Robot platform with paddle-wheels in outdoor sandy terrain.

Mellon Univerisity implemented sidewinding motion on asnake robot and studied the physics of sidewinding ongranular inclines [11], [12]. Mazouchova et al created asea turtle inspired robot which used limbs and flippers topropel [13]. They studied how the limb-sand interactionaffects the locomotion performance. There are also plentyof studies concerning a wheel with lugs or grousers thatcan be applied for planetary rovers [16]–[18]. But due tothe complexity of wet granular media, in which rheologyvaries a lot along with water-solid ratio, seldom researchinvolves robotic locomotion on such substrates. Zhang et alexperimentally studied the performance of a flipper-leggedrobot in muddy terrain [19].

In this report, we focus on the locomotion performanceof a configurable paddle-wheel robot on dry sandy terrain.Different with existing platforms used in sandy terrain,the locomotor in our robot is a paddle-wheel integratedmechanism. And the configuration can be transformed toadjust to different terrain situations. In our previous work,overall tests on the robot platform (Fig. 1) in various roughterrains [20] have been conducted. However, the locomotionperformance on sandy terrain has not been well explored.Hence, this report mainly presents the paddle terradynamicsand studies how the protruding paddle affects the locomotion,so as to verify its trafficability over dry sandy terrain.

The paper is organized as follows: Section II describesthe mechanism and principle of the configurable paddle-wheel. Section III introduces the paddle terradynamics, theforce measuring setup and the experimental verification.Section IV presents the locomotion performance of bothsingle paddle-wheel unit in indoor platform and whole robotin outdoor sandy field. Section V summarizes the mainconclusions and suggests guidelines for future work.

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)October 25-29, 2020, Las Vegas, NV, USA (Virtual)

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Fig. 2. Principle of the configurable paddle-wheel: (a) front and back viewof the 3D model; (b) schematic drawing; (c) prototype picture.

II. CONFIGURABLE PADDLE-WHEEL

To enhance the mobility of conventional wheeled robots inrough terrains, a configurable paddle-wheel was proposed asshown in Fig. 2 [20]. The main components include a shell-like wheel and four paddles which can rotate freely around apaddle shaft. The paddles go through hinges that are evenlyinserted at the rim of the wheel. While the wheel is actuated,the paddles are forced to rotate around the paddle shaft. Theposition of the paddle shaft is controlled by a planetary gearsystem that consists of a sun gear (O), a planet gear (O1)and a planet carrier (OO1). To be noted that the paddleshaft (S) connects with the planetary gear system througha paddle shaft carrier (O1S). The planet gear (O1), paddleshaft carrier (O1S) and the paddle shaft (S) are fixed andrelatively static. The lengths of both planet carrier (OO1) andpaddle shaft carrier (O1S) equal the pitch circle diameter (d)of the sun/planet gear. The schematic drawing of the mainparts is depicted in Fig. 2(b). To be clear, only one paddleis shown. In total, there are three actively actuated joints inthis mechanism: the wheel rotation (θ0), the sun gear rotation(θ1), and the planet carrier rotation (θ2), they are controlledby three DC motors. The position of the paddle shaft canalso be defined by: the eccentric distance rS from the paddleshaft (S) to the wheel center (O), and the eccentric angle θS.As a result, there exists a kinematic relation from the inputs(θ0, θ1, θ2) to the outputs (θ0, rS, θS): θ0

rSθS

=

θ0

d√

2(1+ cos(2θ2−θ1))2θ2−θ1/2

(1)

which can be obtained through the mechanism kinematics.A snapshot of the paddle wheel is shown in Fig. 2(c) andthe specifications are listed in Table I.

Considering the application in rough terrains, we proposeda hybrid locomotion mode in [20], which is actually a

TABLE ISPECIFICATIONS OF THE PADDLE WHEEL

Description ValueRadius of wheel 56 mm

Width of wheel 113 mm

Paddle length 96.5 mm

Paddle width 62 mm

Paddle thickness 2 mm

Eccentric distance range -40 mm ∼ 40 mm

Fig. 3. Variable configurations of the paddle-wheel in hybrid locomotionmode with different eccentric distance of the paddle shaft.

simplified mode where the paddle shaft moves only alongZ-axis. It can realize prompt and easy transitions amongdifferent support stances to adapt to complicate terrains.According to the definition, the eccentric angle θS shouldsatisfy

θS ≡π

2(2)

As a subsequent study, this report considers the same sit-uation. In a word, the actively actuated parameters are therotation of the wheel θ0 and the eccentric distance of thepaddle shaft rS. The configuration of the paddle wheel willchange along with the eccentric distance of the paddle shaft.As shown in Fig. 3, the protruding length of the near-earthpaddle outside the wheel decreases with larger rS, so asto change the stance from wheel support to wheel-paddlehybrid support and to paddle-only support. To be mentioned,the actual contact situation with the ground depends on thespecific terrain characteristics.

III. PADDLE TERRADYNAMICS

Due to the flowability of soft soil like sand, the interac-tion between the paddle-wheel and the sand becomes morecomplex than the rigid ground. To study the locomotionperformance of the paddle-wheel robot in sandy terrain,the paddle terradynamics will be analyzed theoretically andexperimentally in this section. In both modeling and exper-iment, we consider a kind of sand (tag Sand I) with theproperties as listed in Table II.

TABLE IIPHYSICAL PROPERTIES OF SAND I

Description Unit ValueCohesion stress Pa 400

Friction angle deg 38.1

Specific weight kg/m3 1480

Scaling factor αz N/cm3 1.1

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Fig. 4. (a) Schematic drawing of the paddle wheel interacting with thesoil; (b) force analysis on the inserted paddle surface.

A. Force Model

Fig. 4(a) shows the considered situation where the wheelis set to be just contacting with the surface of the sand, whichmeans the wheel sinkage is zero. For simplification, only onepaddle is depicted in the figure and modeled. The insertinglength of paddle l is denoted as li. Since the interactionbetween the paddle-wheel and the sand only exists on theinserting length li, an enlarged drawing of li is shown in Fig.4(b). According to the terradynamics model proposed in [10],both horizontal and vertical interface stresses (σx,z) on a unitpaddle segment dl are assumed to be directly proportionalto the depth (|z|). And there exists an explicit dependence ofthe stress gains (αx,z) on the attack angle (β ) and intrusionangle (γ) of the surface. The dependence was parameterizedwith the discrete Fourier transform (DFT) coefficients [10]as:

αz(β ,γ) =1

∑p=−1

1

∑q=0

[Ap,q cos(2pβ +qγ)

+Bp,q sin(2pβ +qγ)]

αx(β ,γ) =1

∑p=−1

1

∑q=0

[Cp,q cos(2pβ +qγ)

+Dp,q sin(2pβ +qγ)]

(3)

where the DFT coefficients used nine zeroth- and first-orderterms:

M = (A0,0 A1,0 B1,1 B0,1 B−1,1 C1,1 C0,1 C−1,1 D1,0)T (4)

The DFT coefficients in vector M could be calculated bymultiplying a scaling factor with the generalized DFT coef-ficient in M0 [10]:

M0 = (0.21 0.17 0.21 0.36 0.06 −0.12 0.25 0.01 0.09)T

(5)The scaling factor is obtained though inserting a horizontalplate downward the soil and measuring the vertical stressgains, expressed as αz(0,π/2). Given the stress gains (αx,z)and the depth (|z|), stresses on segment dl can be calculatedthrough

σz,x(β ,γ,z) = αz,x(β ,γ)|z| (6)

More details on the derivation can be found in [10].Then the total interaction forces could be approximated by

linear superposition of stresses on all the paddle segments.

We then calculated the instantaneous forces (Fz,x) and the netforces (Nz,x), according to:

Fz,x =∫Ω

σz,x(β ,γ,z)ds

Nz,x =∫Θ

Fz,xdθ(7)

where ds is the area of individual paddle segment and Ω

is the total leading surface area of the inserted paddle. dθ

denotes the differential angle element between the paddleand z-axis, and Θ is the angle range of interaction duringone rotation period, which starts from the paddle contactingwith the soil surface and ends with the paddle pulling out ofthe soil. Fig. 5(a) depicts the moment the paddle contactingwith the sand surface. The maximum contacting angle (θc)varies with the eccentric distance of the paddle shaft, sodoes the maximum inserting depth of the paddle (limax).The explicit relations between the eccentric distance andthe corresponding maximum inserting depth and the contactangle can be obtained through geometric analysis, and areshown in Fig. 5(b). It is easy to see that larger eccentricdistance leads to shorter inserting depth and smaller contactangle.

Fig. 5. (a) Definition of contact angle and maximum inserting depth; (b)geometric relation among eccentric distance, maximum inserting depth andcontacting angle.

B. Experimental Verification

To verify the model, an experimental setup was built asshown in Fig. 6. A force sensor was connected with thepaddle-wheel to measure the generated forces. The wheelwas adjusted to be just contacting with the sand surface.During all the experiments, the wheel joint was actuatedto rotate at a constant slow speed of π/18 rad/s. Fig. 7shows both the simulated and experimental forces with fourdifferent eccentric distances. The experimental data havebeen denoised and smoothed. The results proved the accuracyof the force model. It was verified that smaller eccentricdistance (deeper intrusion) generates larger interaction forcesin both directions. But the large forces in vertical directionmay result in vibration of the system according to the secondlaw of motion. The difference in magnitudes of positive forceand negative force in Fz indicates that it is harder to pushthe paddle into the soil than to extract it. The asymmetry inboth Fx and Fz about the middle position (θ = 0) could beresulted from the gravity effect [10].

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Fig. 6. Experimental setup for measuring the interaction force.

Fig. 7. Comparison between the simulated and experimental interactionforces in both x-axis and z-axis with different eccentric distances: (a) rS =3cm; (b) rS = 2cm; (c) rS = 1cm; (d) rS = 0cm.

IV. LOCOMOTION PERFORMANCE

The paddle terradynamics has illuminated that the systemcan generate larger propelling soil forces with smaller ec-centric distance or longer sinkage length of the paddle. Thissection inspects the locomotion performance of both a singlepaddle-wheel module and the whole robot over sandy terrain.

A. Single Paddle-Wheel Indoor Test

1) Tests design: To explore the motion of single paddle-wheel, a platform with two degree-of-freedoms was estab-lished. As depicted in Fig. 8, the platform consists of threevertical cylindrical guides, two horizontal cylindrical guides,and a paddle-wheel unit. The paddle-wheel was actuated bythree MAXON motors and controlled by a microcontrollerunit. In total, the weight capable of moving vertically is 4.3kg, which include a paddle-wheel and the control system.While the weight capable of moving in the horizontal di-rection is 6.7 kg, including a paddle-wheel, three verticalguides, the control system, and all the vertical and horizontalslide blocks. A motion capture system (VZ4050, PTI) wasemployed to record the position of the marker that are fixedwith the tested paddle-wheel. The paddle-wheel moves in asand box which is 1150 mm long, 600 mm wide and 200mm deep. The sand properties are listed in Table II.

All the tested trials are shown in Table III. In additionto the eccentric distance, angular velocity of the wheel was

Fig. 8. Locomotion platform for single module test: (a) overall environ-ment; (b) platform details.

TABLE IIIINPUTS AND OUTPUTS IN TESTS

InputsAngular velocity ω (rad/s) 0.75, 1.5, 2.25, 3, 3.75, 4.5Eccentric distance rS (mm) 40, 30, 20, 10, 0

Outputs Forward speed, height variation, motor current, motor rpm

also varied to explore the motion. The directly recordedparameters during the experiments include the horizontallocomotion speed, the height variation, the motor torque andthe rotational speed of the motor. The motion capture systemworks at a sampling frequency of 100 Hz. Before each trial,we used a claw to homogenize the sand and a gradienter tocalibrate the height level. All the trials were conducted fivetimes to reduce the error.

2) Results: Fig. 9(a) shows the average locomotion speedsof the paddle-wheel unit under different angular velocitiesof the wheel joint. Results of five eccentric distances arepresented for comparison. It can be found that the locomotionspeeds generally go up with larger angular velocity. Longersinkage length of the paddle also comes with faster motion.However, it is noticed that the locomotion speeds tend to godown at high actuating angular velocity (ω = 4.5) in casesof rS = 40 and rS = 30 (circled in dotted line). Since rS = 40represents the wheel-only support situation and rS = 30 alsocorresponds to very short paddle sinkage length, we believeslippage happened between the wheel and the sand at highrotational speed, which could be found in the logged videoas well. The slippage also resulted in inefficiency, as seenin Fig. 9(b). In this report, we use specific resistance (SR)[21] to evaluate the efficiency of the locomotion, which isdefined as:

SR =P

Wv(8)

where W is the gravity of the system, v is the average forwardspeed of the paddle-wheel, and P is the power consumedby the motor, respectively. To be specific, small SR valuesmean high locomotion efficiency. The results show that thelocomotion in wheel-only support configuration (rS = 40)is the most inefficiency, and the value of SR reaches thehighest at 4.5rad/s. It can be concluded that the slippage

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Fig. 9. Experimental results of one paddle-wheel tests: (a) forward locomotion speed of the paddle wheel; (b) specific resistance; (c) height variant.

happening between the wheel and the soil reduces boththe forward speed and the efficiency, while the paddlesprotruding out of the wheel can effectively improve theperformance. Concerning the most efficient configuration(marked in dash line), it is found that it depends on theactuated angular velocity ω . When the angular velocity issmall (ω < 2.25rad/s), rS = 10 is the most efficient. WhilerS = 0 is comparatively more efficient at high actuatingvelocity (ω > 2.25rad/s). This phenomenon could be causedby large resistance existing at low speed when rS = 0, whichconsumes more energy to move the unit. Fig. 9(c) shows theamplitude of the height variant in vertical direction of thepaddle-wheel unit during the locomotion. When the paddle-wheel performs with the wheel-only support configuration,the height variant is nearly zero. But the values get muchlarger after the eccentric distance turns to be smaller than 30mm. This means while the configuration with small eccentricdistance can perform high speed and efficiency, vibrationsmay be caused to the system at the same time.

B. Paddle-Wheel Robot Outdoor Test

The locomotion performance of one paddle-wheel unithas been evaluated with indoor platform. To verify thelocomotion of the whole robot in outdoor field, experimentswere also conducted in the sand field as shown in Fig. 1.To be mentioned, the properties of the sand in this field (tagSand II) are different from the one that was used in indoortests (tag Sand I). The particle diameter and the density ofSand II are larger than Sand I. Besides, the sand field is notguaranteed to be even or homogeneous, which increased therandomness of the results. Though by multiple experimentswe find the results reflecting general conclusions that will beillustrated by following.

Experiments were also conducted with various configu-rations of the paddle-wheel as well as different actuatingvelocities of the wheel joint. The motor currents of threetypical cases are recorded and shown in Fig. 10 (a) to explainthe energy consumption. The selected cases include thepaddle-support (rS = 0mm), the hybrid-support (rS = 30mm)and the wheel-support (rS = 40mm). It is found that thecurrents are the largest in paddle-support configuration whileleast in the wheel-support. However, through the markedcalculated SRs in the figure, it is seen that the hybrid-support

Fig. 10. Experimental results of free walking tests: (a) motor currentsduring one rotational period (T) of 2 seconds while traversing in sand; (b)specific resistance; (c) height variant.

tends to be the most efficient, while the wheel-support is themost inefficient. This could be resulted from the slippagebetween the wheel and the sand during wheel-only supportsituation. The slippage reduced the current consumption butmeanwhile decreased the locomotion speed and lead to theinefficiency. This result also supports the conclusion in one-module test that the protruding paddle helps reduce theslippage and improve the performance.

Since the hybrid-support configuration was found to be themost efficient, we also evaluated the locomotion speed andthe specific resistance in different actuating velocities (ω).The results in Fig. 10(b) show that the locomotion speedincreases slowly at low actuating velocity (before 3rad/s).And after then the speed almost increased linearly along withthe actuating velocity. When the actuating velocity passes8rad/s the traversing speed of the robot is approaching onebody length per second. Through the specific resistance curve

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in blue line, we can see it is not efficient at low speeds. Whilealong with the traversing speed increasing, the efficiencyis getting higher. The inefficiency at low speeds could becaused by large resistance from the sandy terrain.

C. Discussion

Comparing the results between indoor one paddle-wheeland outdoor robot, we found the optimal configuration varies.In one paddle-wheel, it is found that the paddle-supportconfiguration (rS = 0mm,rS = 10mm) achieves the mostefficient locomotion in laboratory sand (Sand I). While inoutdoor field tests with Sand II, the results have shown betterefficiency in hybrid-support configuration. The reason induc-ing the difference fundamentally comes from two aspects.One is the different inertia of the system. As described inthe indoor platform, the mass that can move vertically alongthe vertical guides is 4.3kg and 6.7kg along the horizontalguides. But the mass of the robot in outdoor field tests is24kg. Another aspect is the properties of the sand used inboth tests. Compared with the Sand I, Sand II in outdoortests has larger particle size and density, which means it ismore difficult to insert the paddle into Sand II than Sand I.Both the above aspects affect the sinkage of the system inthe sand, and so as to the traction force and resistance force.Hence, we believe the optimal configuration is dependent onthe system inertia and the sand properties. For a mature robotprototype, the inertia is constant but the terrain encounteringis variable according to the environment. To achieve optimalconfiguration in various terrain situation, it is urgent to detectthe terrain or sense the interaction between the robot and theterrain, which could be a future work.

V. CONCLUSION

In this paper, the locomotion performance of a config-urable paddle-wheel robot in dry sandy terrain was studied.By adjusting the eccentric distance of the paddle shaft,protruding length of the paddles that interact with the sandyterrain could be controlled. To explore the interaction forcebetween the paddle and the sand, an existing terradynamicmodel was utilized. The predicted forces were verifiedthrough experiments that longer protruding paddle lengthcan generate larger soil thrust. To investigate the locomotionperformance of the paddle-wheel, an indoor platform wasfirstly built. The locomotion speed, efficiency and the verticalvibration were evaluated with different protruding lengths ofthe paddle and various actuating velocities of the wheel. Theresults have shown that the wheel-only support configurationis easy to get slip at high locomotion speed, resulting ininefficiency. The protruding paddle helps prevent the slippagehappening between the wheel and the soil and improved theefficiency. Combining with the robot test in outdoor sandyfield, it is found the optimal configuration depends on thesystem inertia as well as the terrain properties.

The future work involves more tests in different categoriesof sand, and development of automatic control method.

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