Experimental study of a tracked mobile robot’s mobility performance

Journal of Terramechanics 77 (2018) 75–84

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Journal of Terramechanics journal homepage: www.elsevier.com/locate/jterra

Experimental study of a tracked mobile robot’s mobility performance Weidong Wang ⇑, Zhiyuan Yan, Zhijiang Du State Key Laboratory of Robotics and System, Harbin Institute of Technology (HIT), Harbin, Heilongjiang 150080, China

a r t i c l e

i n f o

Article history: Received 16 August 2016 Revised 25 October 2017 Accepted 6 March 2018

Keywords: Tracked mobile robot Terrain–track interaction Drawbar pull Tractive performance Experimental study

a b s t r a c t This paper proposes an experimental method of predicting the traction performance of a small tracked mobile robot. Firstly, a track-terrain interaction model based on terramechanics is built. Then, an experimental platform of the tracked robot is established, on which the measurement methods of the parameters that influencing the accuracy of the prediction model are introduced and the data post-processing are improved, including drawbar pull, slip ratio, sinkage, track deformation and so on. Based on the experimental data, several key terrain parameters are identified. With the tracked robot platform, the drawbar pull-slip ratio relationship is tested, and the effects on drawbar pull considering different kinds of terrain and the influence of the grousers are analyzed as well. The research results provide a reference for the experimental study on the traction performance of small tracked robots. Ó 2018 ISTVS. Published by Elsevier Ltd. All rights reserved.

1. Introduction Mobile robots have been widely used in unstructured outdoor environments. However the high-performance locomotion and robust uneven terrain negotiation are determined the robotterrain interaction. In order to improve the trafficability of mobile robots in complex ground environments, many scholars carried out theoretical modeling and experimental studies on the traction performance of mobile robots. There are three way to study the track-terrain interaction, namely theoretical modeling, soil bin experiments and platform field tests. Studies on the track-terrain interaction have been reported. Bekker developed a theoretical model for the track-pressure distribution relationship (Bekker, 1969). Wong improved the model, and established a sound model for the track-terrain interaction (Wong, 2008). As the rubber tracks get a large deformation in the process of interaction, a specific research on the interaction between rubber track and terrain was carried out. Okello presented a detailed mathematical model (Okello et al., 1998), dividing the trackterrain model into the load-bearing section and the non-loadbearing section, building the models respectively, and obtaining an integrated model under the force and displacement equation constraints on the connected points. It can be seen that, many track-terrain interaction models for large tracked vehicles based on terramechanics have been established, and these results ⇑ Corresponding author at: Room 210, Building C1, Science Park, Harbin Institute of Technology, Harbin 150080, China. E-mail address: [email protected] (W. Wang). https://doi.org/10.1016/j.jterra.2018.03.004 0022-4898/Ó 2018 ISTVS. Published by Elsevier Ltd. All rights reserved.

provide a foundation for the model setup of small, lightweight mobile robots. Most experimental researches about mobility performance of small tracked robots were conducted in the soil bin test equipment with a single track system. Senatore established a soil bin testing platform with a small track system, and carried out the corresponding research on traction performance (Senatore et al., 2013). On the basis of Senatore’s tests, Wong presented the theoretical modeling and simulation software, obtaining a good simulated performance (Wong et al., 2015). In the application of lunar rovers, Gao analyzed the traction performance of single wheel, multiple wheels and single track system under different terrain conditions (Gao et al., 2012). Ding and Sutoh investigated the principle of the wheels-terrain interaction (Ding et al., 2011, Sutoh et al., 2012). Another method of predicting the traction performance is to test the entire robots in the soil bin. Wang analyzed the traction performance of a tracked robot on seafloor terrain (Wang et al., 2016), and Al-Milli investigated the skid steering performance of a tracked robot based on terramechanics (Al-Milli et al., 2010). In order to match with the practical robot as better as possible, the tracked vehicles were tested in actual application environments. Park installed sensors on a tracked vehicle to measure the traction performance (Park et al., 2008), and Ray presented a measurement method of the drawbar pull-slip relationship for a differential steering wheeled robot, as well as the method of data acquisition and post-processing (Ray et al., 2009). Setterfield established the measurement and analysis method of the rover-terrain interaction (Setterfield et al., 2013).

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Besides above traction performance prediction methods based on terramechanics, Fan introduced machine learning to establish the relationship between the traction performance and the effect parameters (Fan et al., 2016), and then traction performance of tracked robots could be predicted. This is a novel method. In summary, most research focused on the wheel–terrain interaction, including theoretical modeling and the soil bin test. In this study, research emphasis is laid on the test method and data processing of drawbar pull’s influencing factors for a light tracked mobile robot in outdoor environment. Considering the terrain parameters, grouser parameters and structural parameters of the tracked robot, a small flexible track model is built. On the foundation of above models, the experimental platform and measurement method of key parameters were established, then traction performance of the small tracked robot is tested and terrain parameters identification method is carried out. The main contributions of our paper are test method of traction characteristics and identification method of terrain parameters for a light tracked robot in outdoor environment.

2.1.2. Middle track-terrain interaction The normal stress is calculated with the following empirical equations proposed by Bekker (1969):




rðzÞ ¼

ðkc =b þ k/ Þzn

z P zu

ðkc =b þ k/ Þznu  ku ðzu  zÞ z 6 zu

ð1Þ

where r is the normal stress, b is the width of the track, n, kc and k/ are the soil pressure-sinkage parameters and z is the sinkage. ku is the parameter that considers the repetitive loading effect, and zu is the maximum sinkage. The sinkage of the first road wheel z1 can be expressed as follows:

pffiffiffi ð2=ð2nþ1ÞÞ z1 ¼ ½3W 1 =½ð3  nÞðkc þ bk/ dÞ

ð2Þ

2. Track-terrain interaction

where W 1 is the vertical load on the first wheel and d is the road wheel diameter. The shape of the deflected track segment CDEF (shown in Fig. 1) between the road wheels is assumed to be a part of a circle with radius Rt . According to the model mentioned by Okello (Okello et al., 1998), the track radius of the track-terrain interaction is calculated by equations:

2.1. Model of track-terrain

Rt ¼

As tracked robots move on the ground, the track-terrain interaction causes the normal and shear stress between the track and soil which generates the drawbar pull of tracked robots. So the normal stress-sinkage and the shear stress-displacement relationship play an important role in predicting mobility.

2.1.1. Model description As shown in Fig. 1, the deflected track in contact with the terrain is divided into three sections, as follows: (1) The segment ABC is in contact with the front road wheel and terrain. (2) The segment CDEF is in contact with terrain only. (3) The segment FGH is in contact with the rear road wheel and terrain. The pressure increases from A to B due to the loading while from B to D the pressure decreases due to the unloading, and the pressure will increase again form D to G corresponding to the reloading (Okello et al., 1998). The road wheel-terrain interaction in the segment ABC and FGH are similar to the wheel-terrain model, so the robot-terrain interaction can divided into two wheel-terrain interactions and one track-terrain interaction. According to the displacement continuity and force balance in the connect points, these three segments can be connected into a whole track system by the tracks. The drawbar pull of the road wheel segments can be calculated by the Bekker’s wheel-terrain interaction model (Wong, 2008). In the following section, the middle track segment (CDEF) will be carried out.

L

ω

P ψ

H

θ22 θ21 G

F

W

D

E

θ C θ12 11 B

Rt

A

τ σ

θw 21θw12 O Fig. 1. A whole track on the deformable terrain.

z

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð X 2 þ Y 2 Þ=2 sinððh12 þ h2 Þ=2Þ

X ¼ L  cos w  r  ðsin h21 þ sin h12 Þ

ð3Þ

Y ¼ z1 R1f þ r  ðcos h21  cos h12 Þ As shown in Fig. 1, where X is the horizontal distance between points C and F, and Y is the vertical distance between points C and F. r is the radius of the driving wheels and h21 is the entrance angle of the rear wheel. R1f is the repetitive loading factor derived by Dwyer from experimental repeated plate-sinkage data and it is expressed mathematically as (Okello et al., 1998):

R1f ¼ ðzr  zu Þ=zu

ð4Þ

where zu is the sinkage when unloading begins and zr is the sinkage when reloading begins (Wong, 2008). According to the empirical equations, each entrance angle is proportional to the corresponding exit angle, and these angles will be used in Equation:

hi;2 ¼ Ai;2  hi;1 hiþ1;1 ¼ hi;2 þ 2  u

ð5Þ

The shear stress is calculated with the empirical stressdisplacement model:

s ¼ smax K r ½1 þ ½1=ðK r ð1  1=eÞÞ  1 expð1  j=K w Þ  ½1  expðj=K w Þ

ð6Þ

where K is the soil shear deformation modulus, K r is the ratio of the residual shear stress sr to the maximum shear smax , and K w is the shear displacement where smax occurs. The maximum shear stress smax is given by smax ¼ c þ rðhÞ tan /. c is the soil cohesion and / is the soil internal friction angle. The shear deformation velocity dj of any point at the track to soil interface is the tangential component of the absolute velocity. It can be written as:

dj ¼ xr  xrð1  iÞ sin h

ð7Þ

where i is the slip ratio and x is the angular velocity of the wheel. 2.1.3. Whole track-terrain interaction According to the displacement balance and force balance in the connect points, these three segments of the deflected track can be

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connected into a whole track system. The equilibrium equation of the track unit in the vertical direction is given by:

where h is the inclination angle of this section, and the pressure is shown as follows:

W ¼ W w1 þ W w2 þ W t Z hw12 W w1 ¼ rb ðsw1 ðhÞ sin h þ rw1 ðhÞ cos hÞdh þ T 1 sin hw12

F ztn ¼ bl1 r

where b is the width of the track, and l1 is the pitch length of the track. The thrust Fxn is obtained through the theory of slip-pressure:

hw11

Z

hw22

W w2 ¼ rb Z

hw21 hw12

W t ¼ Rt b

hw21

(

ðsw2 ðhÞ sin h þ rw2 ðhÞ cos hÞdh þ T 2 sin hw21

ðsðhÞ sin h  rðhÞ cos hÞdh  T 1 sin hw12  T 2 sin hw21 ð8Þ

The equations of equilibrium in the horizontal direction are given by:

DP ¼ DP w1 þ DP w2 þ DP t Z hw12 DPw1 ¼ rb ðsw1 ðhÞ cos h  rw1 ðhÞ sin hÞdh hw11

Z DPw2 ¼ rb Z DPt ¼ Rt b

hw22

hw21 hw12

hw21

ð12Þ

ð9Þ

ðsw2 ðhÞ cos h  rw2 ðhÞ sin hÞdh

ðsðhÞ cos h þ rðhÞ sin hÞdh

where W is the total vertical load of the body acted on one single track unit, and W w1 , W w2 , W t are the vertical loads of the body acted on the front wheel segment, the rear road wheel segment and the track segment respectively. T 1 , T 2 represent the tensions of the track at the point C and point F. DP denotes the drawbar pull developed by one single track unit, and DP w1 , DP w2 , DP t denote the drawbar pull produced by the front wheel segment, the rear road wheel segment and the track segment.

d

F xn ¼ ajn

jn 6 jk

F xn ¼ ðF zti cos hÞf g

jn > jk

where jk is the transitional soil compressive displacement where soil shear is failed. f g is the coefficient of friction. jn is the shear displacement of the n-th grouser. The slip displacements of the robot track at different points are different relative to the soil, and the displacements at each point can be calculated through the integration of the formula dj ¼ xr  xrð1  iÞ cos h, where a is the corresponding constant relating to the track structural parameter and the soil parameter (Grecˇenko, 2007), d is exponent related to the shape of the compression curve and dj is the shear deformation velocity of any point at the track to soil interface, which can be calculated by Eq. (7). When the tracked robot is moving at a certain slip ratio i, the slip varies under different tracked grouser. That is, the soil is in the compressed status if the slip jn < jk , while the soil is in the slip status or the shear failure status if the slip jn > jk . According to the Grecˇenko’s method, the predicted thrust–displacement diagram of a track link is developed, as shown in Fig. 3. The total drawbar pull except for the top-grouser part is obtained by adding the drawbar pull of each grouser together. Assuming the number of grousers that interacted with the ground is p, the result of the total drawbar pull except for the top-grouser part is shown as follows:

2.2. Effect of grousers In the case of straight length grouser, the track structure can be divided into two parts: the top-grouser part and the other grouser part (Grecˇenko, 2007), as shown in Fig. 2. For the top-grouser part, the sinkage, the normal and shear stress distribution and the drawbar pull are calculated by Bekker’s theory. Without considering track grouser effect, the drawbar pull DP is obtained by Eq. (9). Assuming the distance between grouser is ll, the width of single grouser is lw, then the drawbar pull generated by the top-grouser part is simplified as follows:

DP B ¼ lw=ll  DP

ð10Þ

For the other grouser part, the stress mainly consists of two parts: the pressure on the track Fztn and the thrust on the grouser Fxn. According to the force analysis as shown in Fig. 2, the thrust Fxn and the pressure Fztn both have influence on drawbar pull DP n :

DP n ¼ F xn cos h  F ztn sin h

ð11Þ

ð13Þ

DP ¼

n¼p X

DPn þ DPB

ð14Þ

n¼1

3. Experimental setup and data acquisition 3.1. Experimental platform An experimental platform was designed based on the tracked mobile robot (Wang et al., 2014). The platform consists of a tracked robot, a load-changeable box, a tension gauge to measure the drawbar pull, a fifth wheel instrument to measure the slip, an accelerometer to measure the inclination of the robot and Laser displacement sensors to measure the sinkage, and the platform is shown in Figs. 4 and 5. The swing arms are integrated in the robot system, so the robot can move in the main track locomotion, and the front/back swing arms locomotion and the all six track locomotion. The parameters

θ

ψ

Fztn

ω

P

Fxn

W

z1

Fig. 2. Model of track grouser.

2 Other grouser part

1 Top-grouser

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jk (clay)

Fig. 7 (a). When the tracked robot moves, the laser sensor scan the entire track, then the displacement of the entire track is obtained. The predicted and measured deformations of the track which is between the load wheels have a quite match as shown in Fig. 7 (b). The thin curve represents the theoretical track deformation and the thick line represents the measured track deformation. This diagram proves the correctness of the assumption that the middle track is an arc.

jk (sand)

Fig. 3. Predicted thrust–displacement diagram of a track link.

of the robot structure are 820  589  747 mm (arm folded) and 1500  589  747 mm (arm deployed) and the mass is 130 kg. The laser displacement sensor is ODSL8 of Leuze Electronic Company. Its measurement range is 20–400 mm, with 0.1 mm accuracy. The accelerometer is NAV420 GPS&MEMS combination inertia sensor of Crossbow Company. The tension gauge is HG2000. Its measurement range is up to 2000 N, with 2% error. Displacement of the robot and rotation distance of the driven wheel are measured by the encoder (HEDL 5540), whose resolution is 0.18 degree. The sampling frequency of the system is 100 Hz. The collecting and processing program are developed based on Visual C++ 2012.

3.3.2. Entrance and exist angles of load wheels The sinkage distribution of the entire track system should be analyzed in the process of model setup, and the sinkage distribution consists of the wheel sinkage and the track sinkage. The road wheel sinkage is determined by the size of the wheel, which could be calculated by the measurement results of the entrance and exist angles, as shown in Fig. 8. 3.3.3. Inclination and sinkage of the tracked robot In the experiment, it is impossible to measure the sinkage of each point of the robot, so the sinkage distribution of the wheels is studied for the convenience. Two laser sensors are mounted on the front and rear part of the robot respectively and the inclinometer inclination is mounted in the middle of the robot, as shown in Fig. 9. The sinkage of the rear wheel can be calculated as follows:

zr ¼ lr þ L sin d  lr

3.2. Test methods of drawbar pull and slip ratio (1) Drawbar pull: The drawbar pull is obtained by the tension gauge which is connected between the track robot and the payload box. By changing the weight of the box, the desired drawbar pull is obtained, as shown in Fig. 5. (2) Slip ratio: The fifth wheel instrument mounted in the front of the tracked robot is designed to measure the actual velocity and the displacement of the robot, as shown in Fig. 6. Meanwhile the theoretical velocity and displacement of the tracked robot can be calculated by the robot’s interior motor encoders. According to the actual and theoretical values, the slip ratio can be calculated, then the relationship between the drawbar pull and the slip ratio is obtained.

ð15Þ

where lf and lr are the distance measured by the front and rear sensors, d is the inclination angle, L is the distance between the two sensors. 4. Experiments and results The experiments are conducted under a variety of conditions, including terrain type (sandy or clay) and grouser effect (with or without grouser) on the drawbar pull of the robot. By changing one or two parameters of the experiment respectively, a set of contrast experiments are carried out. 4.1. Experimental data processing and discussion

3.3. Test methods of model parameters In order to verify the accuracy of the empirical model several test methods are presented, including the measurement of the deformation of middle track, the sinkage of entire robot and the platform inclination. 3.3.1. Deformation of middle track As we all know, in order to simplify the model, the track between the road wheels is assumed to be an arc when the track interacts with the ground. To confirm the hypothesis, a laser displacement sensor is employed to measure the deformation of the track. In the process of the experiment, the single point laser sensor is fixed on the ground and focused on the track, as shown in

4.1.1. Slip ratio The slip ratio is calculated by measuring actual displacement and input displacement. The robot displacement DL and the driving wheel displacement DLt can be obtained through the exterior and interior encoders respectively. So the slip ratio can be calculated by the equation i ¼ ðDLt  DLÞ=DLt , and the result is shown in Fig. 10 (d). 4.1.2. Drawbar pull The drawbar pull can be measured by the tension gauge or driving motor current. Fig. 10 show the raw data of the tension gauge and the low-pass filter data of the motor current. Both the two method can reflect the change of the drawbar pull. In our experi-

Control Unit Front laser sensor Wheel and encoder

Rear laser sensor Inclinometer

Fig. 4. Schematic diagram of the experimental platform.

Tensiometer

Payload

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W. Wang et al. / Journal of Terramechanics 77 (2018) 75–84

Tensiometer Used to test drawpull

Fifth wheel Used to test slip

Rear Laser Used to test rear sinkage

Front Laser Used to test front sinkage

Fig. 5. Experimental devices.

(B) Effects of the grouser ruts. Considering the influence of the grouser ruts, an average process of the sinkage is established, a schematic diagram of single grouser with pitch length L is shown in Fig. 13. Assuming zone 1 is the soil distribution created by the flat track system, for the track with grousers, the soil will be transferred to zone 2 by the grouser-soil interaction. So the nominal sinkage can be obtained through the volume equation of the soil, as follows:

Fifth wheel Spring Encoder

hL1 ¼ ðz  z1 ÞL

Fig. 6. Measurement method of slip ratio.

ð16Þ

z2 ¼ z1 þ h

where z is the mean sinkage or nominal sinkage. z1 is the lower peak of the sinkage, which is the sinkage of shoe edge. z2 is the upper peak in the sinkage of the measurement, which is the lower peak of the sinkage. The nominal sinkage z can be calculated as follows:

ment, the drawbar pull is obtained by the mean of the tension gauge data in the stationary segment (see Fig. 11). 4.1.3. Sinkage Preliminary data processing about the sinkage is presented to deal with the effects caused by the platform vibration and the track ruts. (A) Effects of vibration. In the process of measuring the sinkage with the front laser sensor, the collected data would involve the fluctuations caused by the robot vibration and sand particles, as shown in Fig. 12(a). The low-pass filter is conducted to eliminate the influence of vibration, as shown in Fig. 12(b). As the influence of the track ruts, the sinkage which is measured through the rear laser sensor is always fluctuating, as shown in Fig. 12(c) and (d). With the combination of the front and rear laser sensors, the sinkage of the rear wheel can be calculated by Eq. (15), as shown in Fig. 12(e).

z¼

L1 L  L1 z2 þ z1 L L

ð17Þ

Based on this calculated method, the average sinkage-drawbar pull relationship is obtained, as shown in Fig. 12(f). We can conclude that drawbar pull have a positive correlation with sinkage, the increase of drawbar pull will lead to the increase of the inclination angle and the sinkage of the robot. 4.2. Identification of terrain parameters The tracked robot can adapt to complex ground environments rather than a single terrain such as sandy land. The environments

Sinkage (m)

0.04

Theoretical Experimental

0.03 0.02 0.01 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x (m)

(a) Test method of track deformation

(b) Test results of track deformation

Fig. 7. Comparison of the theoretical and experimental results on track deformation.

0.8

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(a) Rear wheel

(b) Front wheel

Fig. 8. Entrance and exist angles of the road wheels.

(a) Inclinometer

(b) Front laser distance sensor

(c) Rear laser distance sensor

z Front laser

δ

lf

z0 z1 o

Rear laser

lr x

(d) Schematic diagram of the sinkage measurement Fig. 9. Measurement of inclination angle and sinkage of the tracked robot.

60 0.25 55

s

L (mm)

0.2 50 45

0.1

40 35 1.95

0.15

Wheel displacement Robot displacement

2

2.05

2.1

2.15

2.2

0.05 2.25

0 1.95

2

t (s)

2.05

2.1

2.15

2.2

2.25

t (s)

(a) Displacement data fitting

(b) Slip ratio calculated by displacement

Fig. 10. Data processing of slip ratio.

are likely to be the mixed types of terrain, such as mixtures of sand and soil or mixtures of gravel and soil. Obviously, it is complicated to carry out mechanical parameter measurement by sampling the soil that the robot passes through, especially for researchers without terramechanics experimental equipment. Therefore a parameter identification method is proposed to identify the soil

parameters. The soil parameters which need to be identified includes: n, kp , c, / and K. In this program, large number of experiments have been carried out for a kind of ground types. The criterion of system identification is to make the curve of the model fit with the experimental data as much as possible. Therefore, the mathematical description

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z

z1

z2

Ground

Fig. 13. Average processing of sinkage.

Fig. 11. Data processing of drawbar pull.

is that the identified parameters make the 2-norm kf ðp; XÞ  YðXÞk2 of the difference between them as small as possible. In this program, X is slip ratio, and Y is experimental data of the drawbar pull. f ðxÞ is the drawbar pull model established in section 3, and p is the T

terrain parameters ½n; c; /; K p ; K to be identified.

4.2.1. Identification of parameters of sandy land Eight sets of data were used as training group for parameters identification. According to the iterative process of each parameter, as shown in Fig. 14. The eight identification results are obtained, as shown in Table 1, and the average of eight results is ½n / kp K c = [0.9342 0.4363 1123.7 0.0451 0.975]. 4.2.2. Regression analysis of identification result The identified parameters are applied to the model. In order to verify the effect of parameters identification method. A new set of

(a) Raw data of front laser sensor

(b) Low-pass filter of collected data

(c) Grouser ruts of track

(d) Effectof ruts on measrured rear distance 25

Sinkage Z (mm)

20 15 10 5 0 -5 0

100

200

300

400

Drawbar pull DP (N)

(e) Calculated sinkage of rear wheel Fig. 12. Data processing of sinkage.

(f) Sinkage vs.drawbar pull

500

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W. Wang et al. / Journal of Terramechanics 77 (2018) 75–84 1.3

1.4

1.2

Soil cohesion c (kPa)

Exponent of terrain deformation n

1.6

1.2 1 0.8

1.1

1

0.9

0.6

0.8

0.4 0

100

200

300

400

500

0

100

200

Iteration times

300

400

500

Iteration times

(a) Iteration of exponent of terrain deformation

(b) Iteration of soil cohesion

Fig. 14. Iterations of identified parameters.

Table 1 Parameters identification of sandy land.

Group Group Group Group Group Group Group Group

I II III IV V VI VII VIII

n

/ ðoÞ

kp ðkPa=m Þ

K ðmÞ

c ðkPaÞ

1.105 1.311 0.840 0.844 0.854 0.829 0.870 0.821

40 40 20 20 20 20 20 20

1060.8 2613.3 1198.5 1000 1000 1000 117.08 1000

0.028 0.049 0.042 0.05 0.05 0.05 0.042 0.05

1.2 1.2 0.9 0.9 0.9 0.9 0.9 0.9

n

Drawbar pull DW(Experimental) (N)

Drawbar pull DP (N)

1000 Experimental Model after identification

800 600 400 200 0

0

0.2

0.4

0.6

0.8

1

800

600

400

200 100

200

300

400

500

600

700

Slip ratio

Drawbar pull DW(Theoretical) (N)

(a) Comparison Between Experiments and Mode

(b) Regression Analysis

800

900

Fig. 15. System Identification Regression Analysis.

experimental data are used to verify and carry out a regression analysis. Fig. 15 illustrates the regression result between the experimental data with the theoretical model. In regression analysis, the closer correlation coefficient r2 is to 1 or the greater the value of F is, the more pronounced the regression equation is. The figures illustrate that the correlation coefficient r2 is 0.8920, the value of F is 132.1 and the slope of the linear regression equation is 1.13, indicating that the regression effect is significant, the model data can be well fitted with the experimental data, the results can be accepted. Thus the method can be used for soil parameters identification. Similar to the parameters identification process of soil land, the identified parameters of clay terrain are obtained ½n / kp K c = [1.41 0.541 1763 0.0348 4.774].

4.3. Results and discussion The experimental platform is tested on the sand and clay environment, and the relationship between drawbar pull and slip ratio with different track types and terrain is obtained. Meanwhile, the key parameters of the theoretical model are calibrated, and the model matches the experimental results quite well. In the case of the small slip ratio, the relationship between the slip ratio and the drawbar pull is the most complex but also the most frequently applied in the practical robots, and meanwhile the most important relationship we want to obtain. So we carried out lots of experiments with small slip ratio. The contrast experiments are conducted under different ground environment and track types, as shown in Figs. 16 and 17. Fig. 16

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1200

Drawbar pull DP (N)

With grousers

1000

Without grousers

800 600 400 200 0 0

0.2

0.4

0.6

0.8

1

Slip ratio

(a) Experiments on the sand

(b) Comparison of with or without grousers

1200

1200 Experimental

Predicted

1000 800 600 400 200 0

0

0.2

0.4

0.6

0.8

Predicted

1000

Drawbar pull DP (N)

Drawbar pull DP (N)

Experimental

800 600 400 200 0

1

0

0.2

0.4

Slip

0.6

0.8

1

Slip

(c) Track with grouser on the sand

(d) Track without grouser on the sand

Fig. 16. Tractive performance test on the sand.

Drawbar pull DP (N)

1200 With grousers Without grousers

1000 800 600 400 200 0 0

0.2

0.4

0.6

0.8

1

Slip ratio

(b) Comparison of with or without grousers

1200

1200

1000

1000

Drawbar pull DP (N)

Drawbar pull DP (N)

(a) Experiments on the clay

800 600 400

Experimental Predicted

200 0 0

0.2

0.4

0.6

0.8

1

Experimental Predicted

800 600 400 200 0

0

0.2

Slip

0.4

0.6

0.8

1

Slip

(c)Track with grouser on the clay

(d) Track without grouser on the clay

Fig. 17. Tractive performance test on the clay.

shows that, under the sand environment, the 12 mm grouser has little contribution to the improvement of drawbar pull, which is enhanced from 600 N to 620 N. The reason for the failure of grouser

effect is that, the track system is under the status of large slip ratio and the sand is completely destroyed by the shear stress. That is, the flow of sand particles limits the influence of the grouser effect.

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Fig. 17 shows that, under the clay environment, the 12 mm grouser has a certain contribution to the improvement of drawbar pull, which is enhanced from 800 N to 950 N. The grouser effect is obvious for the reason that the land has a larger shear strength and a larger cohesion force after the destruction by the shear stress. That is, the effect of the grouser on the tractive force is greater on the clay than on the sandy soil. By comparing Figs. 16(b) with 17(b), it can be seen that grouser effect has a significant impact on the drawbar pull on the land, while the grouser effect fails under the sand environment. By comparing Figs. 16(d) with 17(d), we can also conclude that the type of the ground has a great impact on the drawbar pull, and the robot can get a greater drawbar pull on the clay. At last, the experimental data is a little divergent, which should be caused by the complexity of the outdoor ground, which is not as ideal as the soil bin experiment.

5. Conclusion At first, a mathematical model for the prediction tractive performance of a flexible tracked robot was developed in consideration of the primary design factors of the tracked robot and the relevant terrain characteristics. In order to improve the accuracy of the predicted model, measurement methods of the key parameters of the model are designed, and parameters identification method is developed. Then, the experiment platform for tractive performance is established, and the research on the relationship between drawbar pull and slip ratio, as well as the different track types and ground environment is studied and analyzed. This paper presents a measurement method of tractive performance for the small tracked robot, including the test method of drawbar pull, slip ratio, sinkage and deformation of middle track as well as the entrance and exist angle. Especially these methods are carried out on a real tracked mobile robot. The experimental method is provided for the theoretical analysis and the tractive performance test.

Acknowledgments This research is supported in part by the National Public Welfare Project under the Grant 201509073 and National Natural Science Foundation of China under Grant 61105088 and 61773141. The authors also would like to thank all the engineers in the laboratory for their helps during the prototyping and experiments. References Bekker, M.G., 1969. Introduction to Terrain-Vehicle Systems. University of Michigan Press, Ann Arbor, Michigan. Wong, J.Y., 2008. Theory of Ground Vehicles. John Wiley, New York. Okello, J.A., Watany, M., Crolla, D.A., 1998. A theoretical and experimental investigation of rubber track performance models. J. Agr. Eng. Res. 69 (1), 15–24. Senatore, C., Jayakumar, P., Iagnemma, K., 2013. Experimental study of lightweight tracked vehicle performance on dry granular materials. In: Proceedings of ISTVS 7th Americas Regional Conference, Tampa, FL, USA. Wong, J.Y., Senatore, C., Jayakumar, P., Iagnemma, K., 2015. Predicting mobility performance of a small, lightweight track system using the computer-aided method NTVPM. J. Terramech 61, 23–32. Gao, H., Li, W., Ding, L., Deng, Z., Liu, Z., 2012. A method for on-line soil parameters modification to planetary rover simulation. J. Terramech. 49 (6), 325–339. Ding, L., Gao, H., Deng, Z., Nagatani, K., Yoshida, K., 2011. Experimental study and analysis on driving wheels’ performance for planetary exploration rovers moving in deformable soil. J. Terramech. 48 (1), 27–45. Sutoh, M., Yusa, J., Ito, T., Nagatani, K., Yoshida, K., 2012. Traveling performance evaluation of planetary rovers on loose soil. J. Field Robot 29 (4), 648–662. Wang, M., Wu, C., Ge, T., Gu, Z.M., Sun, Y.H., 2016. Modeling, calibration and validation of tractive performance for seafloor tracked trencher. J. Terramech. 66, 13–25. Al-Milli, S., Seneviratne, L.D., Althoefer, K., 2010. Track–terrain modelling and traversability prediction for tracked vehicles on soft terrain. J. Terramech. 47 (3), 151–160. Park, W.Y., Chang, Y.C., Lee, S.S., Hong, J.H., Park, J.G., Lee, K.S., 2008. Prediction of the tractive performance of a flexible tracked vehicle. J. Terramech. 45 (1), 13–23. Ray, L.R., Brande, D.C., Lever, J.H., 2009. Estimation of net traction for differentialsteered wheeled robots. J. Terramech. 46 (3), 75–87. Setterfield, T.P., Ellery, A., 2013. Terrain response estimation using an instrumented rocker-bogie mobility system. IEEE T Robot 29 (1), 172–188. Fan, Y., Wei, S., Lin, G., Zhang, W., 2016. Prediction of military vehicle’s drawbar pull based on an improved relevance vector machine and real vehicle tests. Sensors 16 (3). Grecˇenko, A., 2007. Thrust and slip of a track determined by the compressionsliding approach. J. Terramech. 44 (6), 451–459. Wang, W., Dong, W., Su, Y., Wu, D., Du, Z., 2014. Development of search-and-rescue robots for underground coal mine applications. J. Field Robot 31 (3), 386–407.