Colin M. Creager and Kyle A. Johnson

Glenn Research Center, Cleveland, Ohio

Mark Plant

Youngstown State University, Youngstown, Ohio

Scott J. Moreland

NASA Jet Propulsion Laboratory, Pasadena, California

Krzysztof Skonieczny

Montreal, Quebec, Canada

Push-Pull Locomotion for Vehicle Extrication

NASA/TM—2014-218431

December 2014
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Colin M. Creager and Kyle A. Johnson

Glenn Research Center, Cleveland, Ohio

Mark Plant

Youngstown State University, Youngstown, Ohio

Scott J. Moreland

NASA Jet Propulsion Laboratory, Pasadena, California

Krzysztof Skonieczny

Montreal, Quebec, Canada

Push-Pull Locomotion for Vehicle Extrication

NASA/TM—2014-218431

December 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors would like to thank Vivake Asnani for providing advice on this research and reviewing the paper. We would also like

to thank Mandar Dewoolkar and his team of students at the University of Vermont for characterizing the Fillite material.

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NASA/TM—2014-218431 1 

Push-Pull Locomotion for Vehicle Extrication 

Colin M. Creager and Kyle A. Johnson 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Mark Plant 

Youngstown State University 

Youngstown, Ohio 44555 

Scott J. Moreland 

NASA Jet Propulsion Laboratory 

Pasadena, California 91011 

Krzysztof Skonieczny 

Concordia University 

Montreal, Quebec, Canada 

Abstract 

For applications in which unmanned vehicles must traverse unfamiliar terrain, there often exists the 

risk of vehicle entrapment. Typically, this risk can be reduced by using feedback from on-board sensors 

that assess the terrain. This work addressed the situations where a vehicle has already become 

immobilized or the desired route cannot be traversed using conventional rolling. Specifically, the focus 

was on using push-pull locomotion in high sinkage granular material. Push-pull locomotion is an 

alternative mode of travel that generates thrust through articulated motion, using vehicle components as 

anchors to push or pull against. It has been revealed through previous research that push-pull locomotion 

has the capacity for generating higher net traction forces than rolling, and a unique optical flow technique 

indicated that this is the result of a more efficient soil shearing method. It has now been found that pushpull locomotion results in less sinkage, lower travel reduction, and better power efficiency in high sinkage 

material as compared to rolling. Even when starting from an “entrapped” condition, push-pull locomotion 

was able to extricate the test vehicle. It is the authors’ recommendation that push-pull locomotion be 

considered as a reliable back-up mode of travel for applications where terrain entrapment is a possibility. 

Introduction 

One of the most difficult challenges faced when driving unmanned vehicles through unfamiliar terrain 

is preventing immobilization. Manned vehicle operations have the benefit of using the driver’s 

observations to survey the terrain conditions; whereas autonomous or remotely operated vehicles rely on 

either sensor feedback or previous knowledge of the terrain to determine whether an area is safe to 

traverse. Situations where a vehicle could potentially become entrapped can be difficult to assess, 

especially in extraterrestrial locations. 

Robotic vehicles with on-board sensors can be a useful method for determining the traversability of 

an area. However, it may not become apparent that the terrain is too difficult or unsafe to drive through 

until the vehicle has already become immobilized, such as in the case of robotic exploration. For example, 

in 2009 the Mars Exploration Rover, Spirit, became embedded in a soft sandy material on Mars, a terrain 

condition that was not anticipated and could not have been predicted (Ref. 1). Typically the drivers for the 

Spirit rover would assess its wheel slip by taking photos of its tracks and observing how often certain 

tread patterns appeared in the terrain. However, this assessment could only be conducted after the 
NASA/TM—2014-218431 2 

commanded movements were completed and the photos were sent back to Earth. This challenge, coupled 

with a broken drive motor on one of the wheels, resulted in a case where the rover had simply become 

entrapped in a high sinkage material before the drivers on Earth were aware of the situation. Alternative 

modes of locomotion could provide a greater likelihood of extrication in extreme situations such as this. 

This paper addresses the challenge of traversing terrain that generally results in high sinkage and high 

wheel slip under normal all-wheel drive modes. The authors demonstrate how adding additional degrees 

of freedom to a robot significantly helps not only traverse difficult terrain, but extricate the robot from an 

immobile state. Though there are other alternative modes of locomotion that can be used to improve a 

robot’s extrication abilities, such as walking which the NASA ATHLETE robot is capable of (Ref. 2), the 

focus of this paper is on one specific mode, referred to here as “push-pull locomotion”. 

Push-Pull Locomotion 

The term push-pull locomotion is used to describe a general mode of generating thrust. Unlike 

conventional rolling where thrust is produced by a rotating implement, the thrust force for push-pull 

locomotion is generated by keeping a portion of the vehicle stationary relative to the ground and 

re-positioning another portion of the vehicle to a different location by active articulation (Ref. 3). The 

stationary portion is then re-positioned while the previously moved portion remains planted to the terrain. 

This alternating process continues resulting in a translation of the entire vehicle. During this cycle, the 

stationary implements in contact with the terrain are essentially “pushing” or “pulling” the vehicle while 

gripping the ground. Walking is a familiar form of push-pull locomotion; however systems that 

implement walking are typically complex and inefficient due to the requirement of many active degrees 

of freedom (Ref. 2). 

Scarab and “Inch-Worming” 

The specific variation of push-pull locomotion that is the focus of this research is often called 

“inching” (or “inch-worming”). It is visually similar to the method an inch-worm uses to propel itself 

forward and uses a combination of rolling wheels and vehicle articulation. The Scarab roving vehicle 

(Ref. 4), developed at Carnegie Mellon University, is a four wheel drive robotic vehicle with the ability to 

move by conventional rolling or by inching (Fig. 1). On each side, each wheel is attached to the end of an 

arm that extends out from the center of the chassis at a shoulder joint. An actuator controls the angle 

between these arms, thus creating the ability to vary the wheel base (distance between the front and rear 

wheels). When inching, the rear wheels are first held in place relative to the ground while the wheel base 

is increased and the front wheels are driven forward. Once the front wheels are in place, the back wheels 

are driven forward while the wheel base is reduced. Figure 1 shows Scarab undergoing the inching 

process starting with the largest wheel base. During this cycle, two wheels (either front or rear) are always 

stationary, relative to the ground acting as anchors from which the rest of the vehicle can push or pull 

itself into position. 

Figure 1.—Scarab going through inching procedure: (a) at its greatest wheel base, (b) mid position, and (c) smallest 

wheel base. 

(a) (b) (c) 
NASA/TM—2014-218431 3 

Previous Research Using This Technique 

The concept of inching is not unique and has been investigated in the past. At the Army Land 

Locomotion Laboratory (Ref. 5) the concept of a segmented vehicle with the ability to inch was 

introduced. It was determined through theoretical analysis that by keeping one axle stationary and 

propelling the other forward, the thrust generated by the stationary wheels would be transferred to the 

rolling wheels allowing them to better overcome the resistance on the moving axle. The stationary wheels 

would not encounter rolling resistance, thus the net resistance on the vehicle as a whole decreased while 

the thrust remained the same. In theory this would allow an inching vehicle to generate more net tractive 

force than a pure rolling vehicle, but only by an amount equal to the rolling resistance on one axle. 

Drawbar Pull Testing 

More recently, a series of drawbar pull tests were conducted at the NASA Glenn Research Center 

(GRC) that quantitatively compared the net tractive forces of inching to rolling (Ref. 3). It should be 

noted that the terms “rolling” or “conventional rolling” in this paper refer to the case where all four 

wheels are being driven at the same rotational speed. 

For these tests, the Scarab rover was driven through a simulated lunar terrain consisting of a granular 

material called GRC-1 (Ref. 6) while a drawbar pull test apparatus applied a controlled pull force to the 

vehicle in the direction opposite of travel. For both modes of travel, rigid and compliant tires were tested 

over multiple levels of pull force. A relationship between pull force and the reduction in forward speed 

was developed. It was found that inching was able to generate approximately 37 percent of the vehicle’s 

weight in drawbar pull force with the pneumatic tires, compared to only 27 percent when rolling. For 

rigid tires, the maximum pull forces were approximately 33 percent for inching and 25 percent for rolling. 

The drawbar pull force, or net tractive force, is equal to the thrust generated by the wheels minus any 

rolling resistance in the system. Therefore, if inching requires less rolling resistance as theorized by 

(Ref. 5), this could account for a higher maximum drawbar pull force as shown in the results above. To 

estimate how much effect rolling resistance typically has on a vehicle in this terrain, a cart with four rigid 

wheels mounted on bearings was towed in GRC-1. The wheels were roughly the same dimensions as the 

ones used in the drawbar pull tests, but the tire loads were approximately one third that of Scarab’s (this 

was because the cart could only handle certain loads). The maximum pulling force measured, which 

represents the total rolling resistance, was about 5 percent of the vehicle weight. For Scarab’s greater tire 

loads, this percentage could be slightly higher but likely not much. Also, it can be assumed that each axle 

only accounted for half of that resistance, approximately 2.5 percent of the vehicle weight. Because the 

increase in drawbar pull force from rolling to inching was significantly more than this, it indicates that 

inching must have produced more thrust in addition to a lower rolling resistance. 

Soil Response Beneath Wheels 

In order to understand why push-pull locomotion has a higher capacity for generating thrust than 

conventional rolling, an experiment was run that produced a visualization of soil motion beneath a wheel 

(Ref. 7). This novel method, termed “Soil Optical Flow Technique” (SOFT), was developed at Carnegie 

Mellon University through collaboration with NASA GRC (Ref. 8). The technique involved positioning a 

wheel in a soil tank up against a clear glass wall so that the soil directly beneath the wheel can be viewed 

externally (Fig. 2). The soil bin in this case had been filled with GRC-1 and prepared to a repeatable 

condition through a process of loosening, leveling, and compaction. For this experiment, a rigid wheel 

with a diameter 1/3 that of the wheels used on Scarab was placed against the glass. In order to simulate 

soil directly underneath the center of the wheel, the width of the wheel was made to be only 1/6 that of the 

full size one (instead of 1/3); in other words the glass wall was placed virtually through the center of the 

 
NASA/TM—2014-218431 4 

Figure 2.—Wheel test rig used with soil 

optical flow technique. 

wheel in the width direction. By assuming the soil response to be symmetric about the center of the wheel 

in the width direction, the glass wall was determined to have a negligible effect on the soil response as 

long as friction forces between the glass and soil were minimal (Ref. 9). It is believed that any effect of 

the glass on soil movement was not significant enough to impact the soil flow patterns beneath the wheel. 

The wheels were mounted in such a way that they could either be driven, free-rolling, or braked but 

have free motion in the vertical direction. The carriage on which the wheel and drive unit were mounted 

was also speed controlled in the horizontal direction parallel to the glass wall, and was used to simulate 

the vehicle speed. By controlling both the carriage velocity and rotational speed of the wheel, wheel slip 

was induced. A camera mounted outside of the bin took high resolution images of the soil beneath the 

surface at a constant rate. The SOFT computer software then read in these images and tracked the soil 

particle motion between frames creating velocity vector fields of the soil particles at each interval of time. 

Two specific cases were studied to better understand the increase in net traction observed from 

push-pull locomotion over conventional driving in GRC-1. In the first case, the wheel and the carriage 

were driven at rates that produced a significant amount of slippage at the wheel-terrain interface. This 

served to simulate a condition where conventional driving would generate close to the maximum amount 

of drawbar pull force possible for a given wheel and weight. As seen in the top halves of Figures 3 and 4, 

the soil particles moved at a fairly even rate along the profile of the wheel. From the directional analysis 

in Figure 4, the soil appeared to follow the edges of the wheel, moving with a downwards component at 

the leading edge and with an upwards component at the trailing edge. This type of soil response was 

defined by Bekker as “grip failure” (Ref. 10) and is typically how a driving wheel generates thrust. 
NASA/TM—2014-218431 5 

Figure 3.—Soil velocity response to rolling wheel versus pushed wheel; color indicates 

relative magnitude of soil particle velocity (Ref. 7). 

Figure 4.—Soil directional response to rolling wheel versus pushed wheel; color 

indicates direction of soil particle velocity (Ref. 7). 

In the second case, the wheel was braked to prevent rotation while the carriage was driven at a slow 

but constant rate. This essentially mimicked the maximum drawbar pull force condition of an “anchored 

wheel” using push-pull locomotion. The bottom halves of Figures 3 and 4 show the velocity and 

directional response, respectively, of the soil for this case. From these results, it is obvious that the soil 

responded differently for the two modes of driving. When the wheel was pushed or towed (braked), a 

larger mass of soil was relocated than when rolling. Of even more significance is that the direction of 

motion for the particles was more uniform; instead of following the edge of the wheel, the soil mass was 

pushed opposite the direction of travel. Since only the component of forces in the transverse direction is 

useful when driving, it appeared as though less energy was lost compared to conventional driving where 
NASA/TM—2014-218431 6 

the soil underwent more vertical displacement. Bekker described this response as “ground failure” or 

“general shear failure” (Ref. 10). Also in the case of the towed wheel, most of the soil displacement 

occurred in front of or behind the wheel, whereas with the rolling wheel case, more soil was engaged 

below the wheel. This displacement of soil beneath the wheel could be a contributing factor to sinkage. 

These findings support the notion that push-pull locomotion has a higher capacity for generating thrust 

due to the more efficient terrain response. 

Extrication Testing in the NASA GRC Sink Tank 

Description of Terrain 

The extrication research discussed here was conducted in the NASA GRC Sink Tank, a bin 12 m long 

by 3 m wide by 0.5 m deep filled with a high sinkage material. The purpose of the Sink Tank was to 

produce conditions under which most vehicles would become immobilized using conventional driving 

techniques. Though GRC-1 is a difficult material to traverse, it was never able to immobilize the Scarab 

rover, even when the vehicle was buried up to the wheel hubs. Several granular materials were 

investigated to determine the appropriate medium for the Sink Tank. The material had to have low 

bearing capacity and shear strength so that the vehicle would sink as the tires attempted forward motion. 

Its mechanical properties, such as particle size, shape, and cohesion, must be in the same realm as 

granular materials found during roving missions so that the research could have practical value. 

After considering many options, a material called Fillite (Ref. 11) was chosen as the high sinkage 

material. Fillite consists of hollow alumina-silica microspheres with a particle size distribution that is 

poorly graded (Fig. 5). Because of its low specific gravity, it is primarily used to reduce the weight of 

liquid and solid compounds such as cement or plastics. However, the shape and uniformity of the particles 

provide low shear strength when in bulk quantities because the microspheres move so freely. Typically 

when well graded granular materials get disturbed, the smaller particles fill in the voids left by the larger 

particles creating a denser and stronger bulk unit. However, because the Fillite microspheres are fairly 

homogeneous in size, the voids do not get filled in easily and the bulk density does not change 

significantly. Instead, particles flow past one another with relatively low shear resistance. This leads to 

low bearing strength and high sinkage. 

Figure 5.—View of Fillite microspheres under microscope 

(100X magnification). 

 
NASA/TM—2014-218431 7 

Some basic geotechnical properties of Fillite (Ref. 12) are listed in Table 1, along with properties for 

other granular materials, JSC-1a (Ref. 13) and GRC-1 (Ref. 6), that have been widely used by NASA for 

terramechanics research. JSC-1a consists of angular basaltic particles made to simulate the lunar soil 

driven on by Apollo astronauts. GRC-1 is a lunar strength simulant that consists of silica sand and was 

made to be slightly more challenging in terms of generating traction, as compared to JSC-1a. Though the 

other materials listed here were created to simulate specific lunar terrain properties, Fillite was chosen for 

its high sinkage properties to create a general mobility challenge. 

It should be noted that the low bulk density of the material gives it the unique ability to represent low 

gravity terrain response due to the hollow nature of the particles. When performing traction studies with 

extraterrestrial simulants on Earth, the weight of the soil particles is usually assumed to be of minimal 

importance. However for extrication studies, the weight of the soil does factor in because the tires are 

typically embedded in the terrain under a significant amount of soil which adds resistance. Figure 6 shows 

Scarab with rubber tires in Fillite after significant sinkage. 

TABLE 1.—GEOTECHNICAL PROPERTIES OF FILLITE COMPARED TO 

SIMULANTS USED FOR TRACTION TESTING 

Soil type Fillite microspheresa JSC-1Ab GRC-1c 

Description Cement/plastic filler Lunar soil simulant Lunar terrain strength analog 

Particle shape Spherical Angular Sub-angular 

Material Alumina-silica Sand/silt Sand 

D10 (mm) 0.13 0.017 0.094 

D60 (mm) 0.21 0.110 0.390 

Specific gravity 0.67 2.875 2.583 

Min bulk density (g/cc) 0.415 1.57 1.60 

Max bulk density (g/cc) 0.476 2.03 1.89 

Friction angle (deg) 32.2 (20% rel. density) 41.9 (25% rel. density) 33.4 (20% rel. density) 

Cohesion (kPa) ~0 (20% rel. density) ~0 (25% rel. density) ~0 (20% rel. density) 

a

Fillite information based on References 11 and 12 

bJSC-1A information based on Reference 13 

c

GRC-1 information based on Reference 6 

Figure 6.—Pneumatic rubber tires buried in Fillite. 

 
NASA/TM—2014-218431 8 

Typically when conducting traction tests in a granular material, the bulk density of the material is 

affected by the weight of the vehicle and the shearing that takes place beneath the tires resulting in a 

different terrain condition. For these cases, it is important to reset the terrain to its natural loosened state 

before each test and then compact the terrain if desired. However, Fillite has a narrow range of bulk 

densities and remains in a loose state even after being traversed or sheared; typically the only way to 

significantly increase the bulk density of the material is through excessive vibration and normal loading. 

The preparation instead consisted of leveling the terrain to a specific uniform height before each test run 

so that the vehicle was always driving on flat ground and sinkage measurements could be consistently 

taken with respect to the surface. 

To verify the consistency of this terrain preparation method, six identical rolling tests were run with 

pneumatic tires on Scarab. For each of these, three measurements were taken every 2 sec (the methods of 

measurement are described in the following sections): front wheel sinkage, rear wheel sinkage, and total 

forward distance traveled. The only noticeable variation occurred during the first couple of seconds when 

the vehicle was accelerating. The wheels continued to sink throughout each test. After driving for 80 sec, 

the average front wheel sinkage was 17.6 cm, the average rear wheel sinkage was 24.6 cm, and the 

average distance traveled was 1.02 m. Aside from the initial acceleration period, a standard deviation was 

calculated at each sample time for the three metrics. The maximum standard deviations were: 1.01 cm for 

front wheel sinkage, 1.22 cm for rear wheel sinkage, and 3.3 cm for distance traveled. In addition, there 

appeared to be no pattern of change from test to test indicating that the terrain was not being compacted 

by the vehicle. It was determined that the preparation method was sufficient to produce consistent and 

reliable results. 

Test Setup and Procedures 

Start Condition 

The extrication research discussed here was broken up in to two cases defined by their different 

starting conditions. The first case, which involved starting Scarab on virgin terrain, served to investigate 

how push-pull locomotion could be used to avoid becoming immobilized, and will be referred to here as 

the “free” condition. This was achieved by leveling the terrain, then lowering Scarab to the surface with a 

crane so that only sinkage due to the vehicle’s weight occurred. This resulted in sinkage less than 

15 percent of the tire radius, as seen in Figure 7(a). Both rolling and inching tests were conducted using 

this starting condition. From this starting position, the vehicle was either rolled or inched until either it 

became entrapped or successfully traversed the terrain. 

Figure 7.—The Scarab rover with rigid tires (a) before beginning driving and (b) while driving in the Fillite. 

 

(a) (b) 
NASA/TM—2014-218431 9 

The second case, referred to here as the “entrapped” condition, explored how push-pull locomotion 

could help extricate a vehicle after it has already become entrapped or immobilized. This was achieved by 

driving Scarab using conventional rolling until it reached a condition where forward velocity was near 

zero and the rear wheels had sunk to where the wheel motor hubs were almost touching the surface of the 

Fillite (Figs. 6 and 7(b)). From this position, the inching mode was initiated. 

For both the free and entrapped cases, two different tires of identical dimensions (71 cm diameter and 

18 cm width) but varying stiffness were used. Rubber pneumatic tires with very low tread were inflated to 

a pressure of 2 psi (Fig. 6). This created a highly compliant tire with a large footprint. Rigid tires of 

identical dimensions (Fig. 7) were also used that resulted in a smaller footprint and higher ground 

pressure. This contrast in footprint size and ground pressure was used to investigate the benefits of pushpull locomotion over a range of applications. The mass of the Scarab vehicle for these tests was 400 kg 

which, if taking gravity in to account, would have similar tire loads to a 1052 kg vehicle driving on Mars. 

Each test run consisted of driving the Scarab rover through the Sink Tank, starting from either a free 

or entrapped condition, until either the vehicle was making negligible forward progress or reached the end 

of the leveled terrain. For the rolling tests, a constant wheel rotational speed was commanded. The 

inching maneuver involved a combination of varying wheel speeds and wheel base in an attempt to 

achieve constant forward chassis velocity. However the chassis velocity did fluctuate throughout the cycle 

due to varying wheel slippage and transient controller errors. The rate of inching was limited by the 

maximum rotational speed of the wheel motors (approximately 0.14 rad/s or 1.3 rpm) which have been 

geared for low speed and high torque. 

Photogrammetry Technique for Tracking Vehicle Motion 

In order to measure the forward travel and sinkage of each wheel, a novel photogrammetry method 

was implemented which allowed for the tracking of numerous points on the vehicle in three-dimensions. 

A series of two-dimensional targets (in this case white circles) were placed strategically on the vehicle 

including the chassis and front and rear wheels. Coded targets were also placed next to the bin to create a 

reference plane. A pair of cameras was rigidly mounted next to the Sink Tank so that the near side of the 

vehicle could be viewed at all times during a test. Then while the vehicle was driving, the cameras were 

triggered synchronously at a rate of one image pair every 2 sec. 

The photo pairs were then uploaded to software called “Pontos”, developed by Gom (Ref. 14). Through 

a calibration procedure, the software is able to recognize the location and position of each camera relative to 

one another, and therefore used the pixel location of the targets on the vehicle to determine their actual 

three-dimensional coordinates. When grouped together, these individual sets of coordinates were used to 

compute six degree of freedom motion for specific components on the vehicle, such as for one wheel. By 

knowing the deformed radius of the tires under load as well as the vertical distance between the terrain 

surface and the reference plane outside of the bin, true sinkage was measured. 

Discussion of Experimental Results 

Metrics Used for Evaluation 

For this discussion, the metrics used to evaluate the performance of inching versus rolling were 

broken up into three categories: wheel sinkage, forward travel, and power efficiency. Wheel sinkage was 

measured for both the front and rear axles. Though forward travel is also represented here in terms of 

distance or speed as a function of time (both measured at the chassis), the metric travel reduction (TR) 

was used to normalize the results. Travel reduction quantifies the reduction in forward velocity of the 

vehicle (vactual) relative to a specific reference velocity (vref), and is defined in Equation (1). 

ref

ref actual

v

v v TR  u100% (1) 
NASA/TM—2014-218431 10 

The metric is designed to allow for different reference conditions to be used. For this study, the 

reference condition was chosen to be the self-propelled case (no external forces acting on the vehicle) on 

hard ground with the same tire load and wheel rotational speed used in the Sink Tank. It is repeatable and 

independent of terrain. This was chosen because it represents the fastest and most efficient driving 

condition for this load/tire configuration. 

It is important to note that this reference velocity was used when calculating travel reduction for both 

rolling and inching. Though inching on hard ground is significantly slower than rolling on hard ground, it 

was believed that the rolling case should still be used as a reference. This was so that the performance of 

Scarab inching could be related to the best case condition, and so that rolling and inching results could be 

compared directly in terms of speed. 

Power number (PN) was used to evaluate the power usage for both modes of operation. It is equal to 

the power (P) being used by the vehicle normalized to the vehicle weight (W) and forward velocity 

(vactual), as defined in Equation (2). 

actual W* v

P PN (2) 

Power number can also be defined in terms of energy (E) as shown in Equation (3), which is useful 

when determining the amount of total energy needed to traverse a specific distance (dactual). 

W * dactual

E PN (3) 

The power being used was recorded on the vehicle so that all vehicle actuation was taken into 

account, not just from the wheel motors. This means that hotel loads (i.e., computing, sensing, etc.) were 

also included in the final power results. Low power number values indicate the vehicle is making an 

adequate rate of progress for the amount of power being used. As the forward velocity approaches zero, 

PN approaches infinity, and if the vehicle travels backwards, PN becomes negative. Because the inching 

mechanism does not produce constant vehicle motion (there are instances during the process where the 

chassis pauses or shifts backwards for a second), power number was averaged over 6 sec intervals to 

eliminate any negative values which do not give true representation. This was done as a moving average 

using power data centered around the time stamp, so each time stamp with velocity data has a PN value 

associated with it. 

“Free” Starting Condition 

The results for the “free” starting condition tests are displayed in Figures 8 to 12, each displayed with 

respect to time. The data in Figures 8 and 9 indicate a significant decrease in sinkage for inching as 

compared to rolling (negative values represent the distance of the bottom of the tire below the terrain 

surface). The fluctuations in the inching data correspond to the inching cycles. Vehicle pitch is indicated 

by the difference in sinkage between the front and rear wheels, which is also more severe for rolling than 

inching. It is important to note that the vehicle appears to reach a steady state condition in terms of 

sinkage, implying that the sinkage of the vehicle will not get worse over time as it might with rolling. 
NASA/TM—2014-218431 11 

Figure 8.—Pneumatic tire sinkage (more negative represents deeper sinkage). 

Figure 9.—Rigid tire sinkage (more negative represents deeper sinkage). 

Ͳ40

Ͳ35

Ͳ30

Ͳ25

Ͳ20

Ͳ15

Ͳ10

Ͳ5

0

0 20 40 60 80 100 120 140 160 180 200

Wheel Sinkage (cm)

Time (sec)

FrontͲRolling FrontͲInching

RearͲRolling RearͲInching

Ͳ40

Ͳ35

Ͳ30

Ͳ25

Ͳ20

Ͳ15

Ͳ10

Ͳ5

0

0 50 100 150 200

Wheel Sinkage (cm)

Time (sec)

FrontͲRolling FrontͲInching

RearͲRolling RearͲInching

wheel radius = 35.6cm
NASA/TM—2014-218431 12 

Figure 10.—Total distance traveled as a function of time. 

Figure 11.—Vehicle travel reduction as a function of time. 

0

0.5

1

1.5

2

2.5

0 50 100 150 200

Distance Traveled (m)

Time (sec)

Pneumatic Rolling

Pneumatic Inching

Rigid Rolling

Rigid Inching

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10.00

20.00

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Travel Reduction (%)

Time (sec)

Pneumatic Rolling Pneumatic Inching

Pneumatic Inching Mean Rigid Rolling

Rigid Inching Rigid Inching Mean
NASA/TM—2014-218431 13 

Figure 12.—Power number (total power consumed normalized by vehicle weight and velocity). 

The most important takeaway from the forward travel data (Figs. 10 and 11) is the trend over time. 

For the first 90 to 100 sec of the test, the Scarab rover actually drove further while rolling. However, once 

the tires began to sink significantly, after approximately 30 to 40 sec, the forward speed of the vehicle 

dropped considerably. The data in these figures indicates that, after this initial driving period, inching 

became much faster than rolling. In fact, the average forward velocity while inching remained constant 

over time, while the rolling case approached zero forward velocity. It should be noted that the rolling tests 

were run until the wheel hubs bottomed out and contacted the surface, thus the length in time of these 

tests were much shorter than the inching ones. 

As a side note, the initial drop followed by a sudden increase in travel reduction and power number, 

as seen in Figures 11 and 12, was due to the initial acceleration of Scarab. Because these tests had to be 

started from a stand-still position, there is a brief period where the forward velocity was below the 

commanded velocity, resulting in lower TR and PN values. 

Although inching generally consumes power at a higher rate than rolling, the results for power 

number in Figure 12 indicate that inching was more power efficient when taking forward velocity into 

account in high sinkage materials such as Fillite. Again, rolling operated more efficiently in the initial 

pre-sinkage driving period but became decreasingly efficient over time, as opposed to inching where the 

power number oscillated around a constant range. This implies that to drive a specific distance beyond 

this initial driving period, rolling would actually require more total energy than inching. That is also 

assuming that the rolling vehicle is able to continue without becoming immobilized. 

It is important to note that at high sinkage, boundary effects from the bottom of the bin may have 

impacted the vehicle’s performance. Further analysis would be needed to quantify this effect; however it 

is the belief of the authors that conducting these tests in a deeper soil bin would only result in a greater 

disparity in performance between rolling and inching (if there was any change at all). If the depth of the 

soil bin is shallow enough, the bottom of the bin creates a confining effect where the particles are not able 

to move freely and the wheels are able to get a firmer grip with the terrain, resulting in higher thrust 

0.00

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Power Number (Ͳ)

Time (sec)

Pneumatic Rolling Pneumatic Inching

Pneumatic Inching Mean Rigid Rolling

Rigid Inching Rigid Inching Mean
NASA/TM—2014-218431 14 

generation. Because the vehicle underwent twice as much sinkage when rolling as when inching, the 

rolling modes should have benefitted more from the boundary effects. In a deeper tank, it is assumed that 

the rolling tests would result in a higher sinkage rate while the inching tests would maintain the same 

sinkage. 

 “Entrapped” Starting Condition 

It is evident from the results above that inching can significantly reduce the likelihood of a vehicle 

becoming immobilized in a high sinkage terrain similar to that of the GRC Sink Tank. However, a more 

critical situation would be if a vehicle has already undergone significant sinkage and is approaching or 

has reached 100 percent travel reduction (essentially entrapped). Figure 13 indicates that the inching or 

push-pull technique still proves to operate in this situation. 

The results shown in Figure 13 were collected by first driving the Scarab rover using the conventional 

rolling method for 90 sec, then engaging the inching mode. Only sinkage for the rear wheel was shown 

here because it was more pronounced than for the front wheel. Though a complete immobilized condition 

(no forward progress) was never fully reached during the 90 sec of rolling, sinkage continuously 

increased and the forward velocity approached zero. Once the vehicle began to inch, sinkage immediately 

decreased and forward velocity increased. After climbing out of the ruts created by rolling, the wheels 

drove at a fairly constant height, aside from small variations throughout the inching cycle. The average 

velocity of the vehicle also remained constant at about 0.010 m/s while inching. In addition, the power 

number continuously increased while rolling, but then fluctuated about a lower average value of 10.63 

when inching. 

Figure 13.—Results of the Scarab rover driving using conventional rolling for 90 sec, then inching. 
NASA/TM—2014-218431 15 

Conclusions 

To summarize this research, the following points were made: 

x It has been shown that push-pull locomotion can be very beneficial when high tractive forces are 

required. By moving soil in a more efficient manner, this mode of locomotion can generate 30 to 

40 percent more thrust than rolling, while reducing the amount of resistance to overcome. 

x In high sinkage material, conventional rolling resulted in continuously increasing sinkage and a 

forward velocity that continuously decreased and approached zero. By comparison, push-pull 

locomotion, specifically inch-worming, was able to travel at a constant rate with minimal 

sinkage. 

x Though less efficient on hard ground, inch-worming actually required less energy to travel a 

given distance in the high sinkage terrain than rolling. This rate of energy expenditure remained 

constant throughout its traversal as opposed to rolling which saw power usage continuously 

increase. 

x This mode of locomotion was especially useful when a vehicle had already become entrapped in 

soft soil. For a case where the vehicle was nearly immobilized (wheel sinkage approaching the 

wheel center and forward travel nearly at zero), the inch-worming method was able to drive the 

vehicle out of the ruts and traverse the terrain at a constant speed with a wheel sinkage 

approximately 50 percent that of the entrapped condition. 

x It is the authors’ recommendation that push-pull locomotion be explored as a secondary mode of 

operation on robotic vehicles. This specific type of movement (inch-worming) only requires two 

additional actuators and degrees of freedom but gives the vehicle the ability to generate 

significantly more thrust when needed. 

x It is recommended to explore methods of optimizing push-pull locomotion. This mode of travel 

could be improved by developing a system that does not require the chassis to move vertically, 

reducing the amount of power needed. More thrust could also be generated by precisely 

controlling the rotational speed of the wheels relative to the motion of the articulated joint. 

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