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Lightweight Robotic Excavation
Krzysztof Skonieczny
April 17, 2013
School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
Thesis Committee:
David Wettergreen, Co-Chair
William (Red) L. Whittaker, Co-Chair
Dimitrios ApostolopoulosKarl Iagnemma, MIT
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy.
Copyright c 2013 Krzysztof Skonieczny
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Abstract
Planetary excavators face unique and extreme engineering constraints relative to
terrestrial counterparts. In space missions mass is always at a premium because it
is the main driver behind launch costs. Lightweight operation, due to low mass and
reduced gravity, hinders excavation and mobility by reducing the forces a robot can
effect on its environment.This thesis shows that there is a quantifiable, non-dimensional threshold that
distinguishes the regimes of lightweight and heavy excavation. This threshold is
crossed at lower weights for continuous excavators (bucket-wheels, bucket chains,
etc.) than discrete excavators (loaders, scrapers, etc.). The lightweight threshold
relates payload ratio (weight of regolith payload collected to empty robot weight),
excavation resistance (force imparted on an excavator by cutting and collecting soil),
and excavation thrust (force supplied by an excavator that is available for cutting
soil).
Experiments and simulation herein show that payload ratio governs productivity
of lightweight excavators. Reducing weight (due to low mass, reduced gravity, or
both) decreases an excavators thrust to resistance ratio, especially in cohesive soils.
There is a predictable regime in the operating space where this ratio is low enough
that it limits an excavators payload ratio and, ultimately, productivity. Discrete
excavators cross into this regime more readily than continuous excavators, because
soil accumulation on their blades increases their excavation resistance.
This research introduces novel experimentation that for the first time subjects
excavators to gravity offload (a cable pulls up on the robot with 5/6 its weight, to
simulate lunar gravity) while they dig. A 300 kg excavator offloaded to 1/6 g suc-
cessfully collects 0.5 kg/s using a bucket-wheel, with no discernable effect on mobil-
ity. For a discrete excavator of the same weight, production rapidly declines as rising
excavation resistance stalls the robot; in total the discrete bucket collects less than20 kg of regolith. These experiments demonstrate that discrete excavation crosses
the lightweight threshold under conditions where continuous excavation does not.
They also suggest caution in interpreting low gravity performance predictions based
solely on testing in Earth gravity.
This work develops a novel robotic bucket-wheel excavator. It features unique
direct transfer from a bucket-wheel to a high payload ratio dump bed, as well as a
high traction and high speed mobility system. Past lightweight excavator prototypes
were too slow or carried too little regolith payload. Some used bucket-wheels or
bucket-ladders to dig continuously, but transported regolith using exposed chains or
conveyors that would not withstand harsh lunar conditions.Future research on lightweight excavation would benefit from testing in reduced
gravity flights. These provide the most representative test environment short of ac-
tually operating on a planetary surface, as excavator and regolith are both subject
to reduced gravity. Another important direction for future study is deep excavation
in the presence of submerged rocks, which pose challenges for lighweight continu-
ous and discrete excavators alike. Experiments to confirm the generality of results
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herein are recommended, including studying the scaling of excavation resistance in
cohesive soils, and comparing a broad variety of discrete and continuous excavator
tools.
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Contents
1 Introduction 1
1.1 Motivation for planetary excavation . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Load-Haul-Dump cycle at the core of excavation tasks . . . . . . . . . . . . 2
1.3 Lightweight is low mass in low gravity. . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Definitions of important terms and concepts . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Continuous vs. discrete excavators . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Payload ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4.3 Excavation thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.4 Excavation resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 The problem of distinguishing productive lightweight excavator configurations . 11
1.7 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.8 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Background and Related Work 13
2.1 Fundamental mechanics of excavation . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Gravity and cohesion forces included in all excavation models . . . . . . 14
2.1.2 Adhesion and inertial forces can usually be neglected . . . . . . . . . . . 15
2.1.3 Surcharge forces arise due to soil accumulation . . . . . . . . . . . . . . 16
2.1.4 Discrete Element Models for excavation . . . . . . . . . . . . . . . . . . 16
2.2 Experimentation for Lunar and Planetary Excavation . . . . . . . . . . . . . . . 17
2.2.1 The large impact of soil accumulation on discrete excavation . . . . . . . 17
2.2.2 Soil properties and gravity are important conditions to control . . . . . . 18
2.3 Applicability of excavation resistance models to planetary excavation . . . . . . 19
2.4 Lunar excavation trade studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Lightweight excavator prototypes. . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Soil loosening methods and mechanisms . . . . . . . . . . . . . . . . . . . . . . 23
2.7 Autonomous Earthmoving and Tele-Operation . . . . . . . . . . . . . . . . . . . 232.8 Conclusions Based on Related Work . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Hauling and Payload Ratio 27
3.1 Task-level site work modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Traction modeling (wheels) . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.2 Excavation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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3.1.3 Operations modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.4 Power modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.5 Parametric sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Experiments with a small robotic excavator . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.2 Predicted sensitivity of experimental parameters . . . . . . . . . . . . . 41
3.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Comparison of simulated and experimental results . . . . . . . . . . . . . . . . . 45
3.4 Hauling dominates task productivity . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Conclusions from sensitivy experiments and simulations . . . . . . . . . . . . . 49
4 Thrust and resistance in lightweight excavation 51
4.1 Relationship of mass and scale . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Light weight reduces excavation thrust coefficient . . . . . . . . . . . . . . . . . 53
4.3 Predicted effects of light weight on excavation resistance coefficient . . . . . . . 55
4.3.1 Effects of light weight operation on surcharge . . . . . . . . . . . . . . . 59
4.4 Excavation scaling experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4.2 Preliminary investigation of soil preparation. . . . . . . . . . . . . . . . 63
4.4.3 Soil preparation and force measurement . . . . . . . . . . . . . . . . . . 64
4.4.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Conclusions regarding thrust and resistance for lightweight resistance . . . . . . 71
5 The lightweight threshold 75
5.1 A non-dimensional Lightweight number . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Lfor continuous and discrete excavation . . . . . . . . . . . . . . . . . 775.2 Gravity offloaded excavation experiments . . . . . . . . . . . . . . . . . . . . . 79
5.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 Predicted lightweight numbers . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3 Conclusions regarding the lightweight threshold . . . . . . . . . . . . . . . . . . 86
6 Lightweight excavator development 89
6.1 Excavation tooling configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.1 Testing transverse bucket-wheels. . . . . . . . . . . . . . . . . . . . . . 92
6.2 Excavator mobility system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.3 Conclusions regarding lightweight robotic excavator development . . . . . . . . 96
7 Conclusions and future work 99
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2.1 Bringing planetary excavation missions forward. . . . . . . . . . . . . . 103
7.2.2 Establishing resources and direction for future work . . . . . . . . . . . 104
7.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
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8 Bibliography 109
A Extensions 119
A.1 Regolith shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A.2 Non-tractive excavation thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
B Soil flow imaging and grouser spacing 123
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1 Introduction
1.1 Motivation for planetary excavation
Excavation of regolith enablesin situ resource utilization(ISRU) on the Moon and Mars. ISRU
reduces the cost of exploration by producing consumables (including oxygen, water, and fuel)
from native regolith and building earthwork infrastructure (such as trenches as berms). NASA
highlights five motivations for excavation:
(1) excavation for oxygen production, (2) excavation and material handling for land-
ing pad and berm fabrication, (3) excavation for habitat protection (e.g., radiation
and micrometeoroids), (4) excavation for mission element emplacement (e.g., nu-
clear reactor burial), and (5) excavation for science (e.g., trenching for stratigraphy
evaluation). The most important task identified to date is regolith excavation and
transport for oxygen production [58].
China intends to build a lunar base for taikonauts. Russia and Japan plan to extablish robotic
lunar outposts. Early ISRU missions will be fully robotic, demonstrating ISRU and excava-
tion technology while carrying out scientific inquiry. Regolith excavation and processing will
continue to be performed robotically as the technology matures, even when supporting human
exploration.
Excavation can expose buried ice by removing overburden. Figure 1.1 shows multiple regions
at the Lunar South Pole that may harbor buried deposits of water ice. Studies suggest ice could
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Figure 1.1: The Lunar south pole has areas cold enough to sustain water ice (shown red
through blue) even in accessible areas well outside of permanently shadowed craters (outlined in
white) [23]. Excavating down to these resources can uncover them for direct scientific measure-
ment, characterization, or mining.
be found in accessible areas (outside crater rims) at depths of only tens of centimeters [ 23,59].
Excavating down to these deposits can uncover them for direct scientific measurement, charac-
terization, or mining. Characterizing and mapping these ice resources is another important goal
for ISRU [58], and Astrobotic Technology Inc. and Shackleton Energy Company intend to mine
these resources. Moon Express aims to mine platinum on the lunar surface.
The tasks requiring excavation on the Moon and Mars thus span mining, earthworking for
infrastructure, as well as direct scientific inquiry. Figure1.2 and Figure1.3 show visualizations
of some of these various excavation tasks.
1.2 The Load-Haul-Dump cycle at the core of excavation tasks
Regolith requires varying degrees of processing depending on the application. Three classes of
task are distinguished here based on this degree of processing.
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Figure 1.2: Conceptual discrete excavation robot (with a front-loading bucket) building outpost
infrastructure on the Moon
Figure 1.3: Conceptual continuous excavation robot (with a bucket-wheel) digging a trench on
the Moon, while collecting regolith
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1. Displacement. For some tasks the only requirement is moving the regolith out of the
way. These tasks (or sub-tasks) include removing overburden from buried ice, trenching
to expose stratigraphy, and digging holes to emplace mission elements.
2. Shaping. For another class of tasks - which includes building berms, covering habitats,
burying emplaced assets - the regolith is the desired material. Once moved into place, addi-
tional processing consists merely of physically shaping, molding, and perhaps compacting
or sintering the regolith.
3. Refinement. For some tasks, the desired resource makes up only a fraction of the re-
golith, and processing is required to refine and extract the resource. This includes oxygen
extraction as well as mining for ice or platinum.
Moving regolith from one place to another, in a load-haul-dump cycle, is central to the first
two of these task classes. The degree to which load-haul-dump is also central to the third depends
on where processing occurs. Options include a central processing plant designed to accept raw
regolith, a central plant that accepts beneficiated regolith (i.e. pre-processed to increase the
concentration of the desired resource), or a plant that runs entirely on the excavator. Onboard
processing introduces significant mass and extreme thermal requirements; oxygen extraction, for
example, requires heating regolith to between 900C and1600C [58]. It is assumed that, for
these reasons, onboard processing will not be incorporated into excavators themselves during
prototypical excavation missions. Load-haul-dump is thus a paradigm that encompasses the key
aspects of all relevant regolith excavation tasks.
1.3 Lightweight is low mass in low gravity
Light weight can be attributed to low robot mass, reduced gravity, or both. In any space mission,
mass is always at a premium because it is the main driver behind launch costs. Small excavators
that can achieve mission goals are preferable to larger ones. Low mass machines operating in
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Figure 1.4: Contraints of planetary excavation impose unique engineering challenges
reduced gravity (1/6 of Earth gravity on the Moon, 1/3 on Mars or Mercury) have limited weight
available to produce traction or plunge tools into regolith. Traction and plunge force are limited
to a fraction of robot weight. Figure1.4expresses how low mass and reduced gravity leads to low
traction and plunge force. Engineering challenges associated with lightweight excavation neces-
sitate a rethink of excavation configurations, possibly beyond the dozers, loaders, and excavators
typical in terrestrial applications [12].
Excavation missions started small. For example, the Surveyor, Viking, and Phoenix landers
gathered samples of a few cubic centimeters at depths of a few centimeters with scoops mounted
to relatively heavy landers (see Figure1.5). Next missions will likely escalate to excavating cubic
meters worth of regolith at depths of 10s of cms using lightweight mobile robots (e.g. digging
down to expose and collect water-ice in polar regions of the Moon). Finally, excavation will scale
up to production machines for ISRU. Having a configuration that scales well with increasing size
and mass allows subsequent missions to re-use existing technology, learn from past difficulties,
and reduce risk. This principle is exemplified in the similarities between Mars Sojourner, the
subsequent MERs, and now the Mars Science Laboratory (MSL), as seen in Fig. 1.6. Robotic
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Figure 1.5: Lunar and Martian landers to date have gathered only small samples with scoops
mounted to relatively heavy landers. Surveyor (top left) on the Moon with scoop extending right
on scissor arm; Viking (top center) model with excavation boom deployed; Phoenix (top right)
artists concept; Trenches dug by each (bottom row), respectively [NASA].
excavators with high productivity across a range of light weights are essential.
1.4 Definitions of important terms and concepts
Before addressing the problem posed by lightweight robotic excavation, a few additional con-
cepts and terms are defined.
1.4.1 Continuous vs. discrete excavators
Excavators can be classified as continuous or discrete, describing interactions with the soil while
taking multiple cuts.
Continuous excavators stay continually in contact with the soil as they take multiple cuts.
This necessitates having multiple cutting surfaces; by the time each surface or bucket has ac-
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Figure 1.6: Configurations that scale well from small initial missions reduce risks in subsequent
missions. Sojourner (center), MER (left), and MSL (right) share a common suspension configu-ration for this reason [NASA JPL].
cumulated an appreciable amount of soil it clears the ground and the next, soil-free, bucket has
already started cutting. Continuous excavators include bucket-wheels, bucket-chains, and elevat-
ing scrapers.
Discrete excavatorsare those that must break contact with the soil before starting a new cut;
between cuts, the excavator may need to dump its load or clear the cutting surface, for example.
These excavators fill one large bucket with a single cut; the cutting edge has an ever-growing
accumulation of soil as the bucket is filled. Discrete excavators include front-end loaders, dozers,
mining shovels, and open bowl scrapers.
Figure 1.7 shows examples of both continuous (left box) and discrete (right box) mobile
excavators. The taxonomy lines in the figure also note another way of subdividing the excavators,
namely into trenchers, scrapers, and front-end loaders/pushers.
In this work, a discrete excavators blade or bucket (filled directly by the act of cutting)
is assumed to be the excavators only vessel for collecting and transporting regolith. Discrete
excavators that transfer load to a secondary collection bin (i.e. a dump-bed) are considered
separately in Appendix A.
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Figure 1.7: Taxonomy of mobile excavators, with continuous excavators shown in the blue box (left), a
(right). The upper and lower rows show parallels between terrestrial and planetary machines, respectively.
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1.4.2 Payload ratio
Payload ratiois the ratio of weight of regolith payload collected to empty robot weight; it is a
measure of pound-for-pound regolith moving capacity that turns out to govern the productivity
of lightweight robotic excavators. Terrestrial loaders and scrapers attain payload ratios as high as
80% to 100% [35]. Space systems are subject to additional constraints that make it challenging
to attain payload values that high; a payload ratio of 50% is considered relatively high in this
context. In this thesis, the non-dimensional quantity payload ratio is denoted P.
1.4.3 Excavation thrust
Excavation thrust is the force supplied by an excavator that is available for cutting soil. In
this work, excavation thrust is assumed to be provided by traction, as excavator configurations
typically considered for space applications cut by driving forward. Alternate modes of providing
excavation thrust, such as resisting articulation forces using a static base or using excavator
weight directly to cut vertically down, are considered separately as extensions to this work, in
Appendix A.
A vehicles drawbar pull is the net traction available for doing work, and is dependent upon
slip (or travel reduction, a caveat explained in Chapter 4). Drawbar pull at 20% slip is a good
measure of tractive performance, as pull begins to plateau around 20% slip for many wheels (or
tracks) while negative effects such as sinkage increase [68]. A non-dimensional quantity,P20/W
(Drawbar pull at 20% slip, normalized by weight), has been used as a benchmark metric for lunar
wheel performance from the times of Apollo [24] to today [70,80].
In this thesis, excavation thrust refers to drawbar pull at 20% slip, because of the assumption
of tractive thrust; it is denoted P20. The non-dimensional ratio of excavation thrust to weight
is defined as the excavation thrust coefficient, and is denoted T. Under the tractive thrust
assumption, T =P20/W.
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1.4.4 Excavation resistance
Excavation resistanceis the force imparted on an excavator by cutting and collecting soil. Only
the forces during the cut (once the excavation blade is already in the ground) are treated explicitly.
Penetration forces are neglected but, as Blouin assumes these forces are of the same nature as
the cutting forces [11], they can be treated as analagous to cutting forces and subsumed by them.
Crucially, resistance introduced by soil accumulation at a buckets cutting edge (which increases
the force required to move additional soil into the bucket) is accounted for as part of excavation
resistance.
Excavation resistance force is denotedFex in this work. The non-dimensional ratio of exca-
vation resistance to empty excavator weight is defined as theexcavation resistance coefficient,and is denoted F =Fex/Wrobot.
1.5 Scope
This thesis considers excavation tasks that involve load-haul-dump, with some additional pro-
cessing such as shaping, compaction, and beneficiation treated as extensions to this central task.
Mining robots that fully process resources onboard are outside the scope of this work.
This work deals primarily with excavators that produce thrust for cutting by developing trac-
tion, with other sources of excavation thrust treated as extensions in Appendix A.
Excavation in gravity between 1 and 1/6 that of Earth is considered, to cover a range that
includes Earth, Mars, Mercury, and the Moon. Digging on asteroids is outside the scope of
this work. The range of robot mass considered in this work spans from 30 kg to approximately
300 kg. Larger, more massive, machines are unlikely to satisfy mass budgets of near-future
excavation missions. As machines get smaller than 30 kg or so, baseline components that do not
scale well (like computing and communications) take up an ever larger proportion of the mass,
leaving little room for productive excavation tooling. The scope of this work covers a range of
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weights that is relevant across multiple space mission scenarios.
1.6 The problem of distinguishing productive lightweight ex-
cavator configurations
Excavation using lightweight machines is problematic because light weight puts severe limits on
forces an excavator can effect for traction and plunging tools into soil. Excavators for building
infrastructure and mining resources on the Moon and Mars will necessarily be lightweight, be-
cause they will be low mass machines (in space missions mass is always at a premium) operating
in reduced gravity.
No prior methodology exists for developing or even evaluating robotic configurations that are
lightweight and yet still productive.
1.7 Thesis Statement
This thesis substantiates that continuous excavators maintain high productivity at light weights,
where productivity for discrete excavators declines. All excavators have a lightweight threshold
in the operating space, below which their productivity is limited. This threshold is crossed at
lower weights for continuous excavators than discrete excavators. The lightweight threshold is
described by a non-dimensional quantity that relates payload ratio, excavation resistance, and
excavation thrust.
1.8 Overview
The remainder of this document is organized as follows:
Chapter2presents related work in lightweight excavation. This includes excavator config-
uration trade studies and a variety of prototypes. Proposed methods for reducing excavation
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resistance, including percussion and raking, are discussed. The utility and limitations of ana-
lytical models and experimental techniques commonly used for lunar excavation research are
explored.
Chapter3shows that the haul stage of load-haul-dump cycles governs excavator productivity,
based on experiments and simulations. The resulting importance of payload ratio is discussed, as
are underlying assumptions regarding excavation thrust and resistance that underpin these results.
Excavation thrust, excavation resistance, and the relation of these terms, are the subject of
Chapter4. This chapter also discusses how excavation resistance varies during excavation de-
pending on excavator configuration (i.e. continuous vs. discrete excavation). Excavation resis-
tance due to soil accumulation is explored. Analytical models are used to extend results to low
gravity environments, and these results are compared to the limited low gravity experimental
data available.
Chapter5develops the lightweight threshold, combining the concepts from the previous
chapters. Experimental results of excavation operations below and above this threshold are pre-
sented. The limitations of performing lightweight excavation experiments on Earth are discussed.
Chapter6presents practical considerations for implementing continuous excavation in space.
This is done in the context of the development of a prototype for a novel lightweight bucket-wheel
excavator robot.
Chapter7summarizes the major conclusions and contributions of this thesis, and proposes
relevant future work.
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2 Background and Related Work
Literature related to lightweight robotic excavation research includes the principles of excavation
and attempts to model its mechanics, experimentation in analogue lunar and planetary conditions,
trade studies and prototypes of lunar excavator configurations, soil loosening methods, and au-
tomation of earthmoving and mining equipment.
2.1 Fundamental mechanics of excavation
The mechanics of excavation are based on the principles of passive earth pressure, adapted from
the design of retaining walls, as shown in Figure2.1. Reece presents the following as the funda-
mental equation of earthmoving mechanics [32]:
PEx = Ngd2 +Nccd+Nqqd +NaCad (2.1)
wherePEx is excavation resistance force per unit width, and the four terms of the summation
represent (in order) forces due to frictional shearing (i.e. gravity), cohesion, surcharge, and soil-
tool adhesion. Inertial forces are explicitly ignored, as low cutting speed is assumed. The Niare
non-dimensional coefficients pertaining to each of the four sources of force, respectively. Grav-
itational acceleration is denotedg,is soil density,d is cut depth,c is cohesion, q is surcharge
pressure, andCa is soil-tool adhesion. The equation is for cutting with a flat plate. As this is
a two-dimensional formulation, a first order estimate of excavation resistance force for a cut of
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Figure 2.1: Mechanics of excavation based on passive earth pressure [32]
finite width can be made by multipyling by said width,w:
FEx = wPEx (2.2)
A wide variety of models have been investigated for their potential applicability to planetary
excavation [26,39,73,74]. However, at their root, they are all just variations of Reeces funda-
mental equation (with the possible exception of Luth & Wismer). Models vary in which force
terms they do and dont include. Several models omit tool-soil adhesion and/or surcharge forces.
Some include inertial forces, which Reece explicitly omitted. Table2.1lists the array of models
and shows which force terms they include. Additionally, the models vary in their definitions of
theNicoefficients.
2.1.1 Gravity and cohesion forces included in all excavation models
Excavation shears soil, and a soils shear strength is governed by its internal friction angle and
cohesion. These shear strength contributions are modelled for excavation resistance by gravity
and cohesion terms, respectively. All the models listed in Table2.1 include at least some form
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Model Gravity Cohesion Surcharge Adhesion Inertia
Reece
Osman
Gill
Luth & Wismer
1
1
Godwin
Balovnev2
McKyes / Swick
Qinsen 3
Willman
Zeng 4
Table 2.1: Models vary in which force terms they include, but gravity and cohesion are always
considered. 1In Luth & Wismer, cohesion and inertia terms are multiplied by gravity terms,
rather than added to them.
2
Balovnev includes additional terms to account for sidewalls and ablunt cutting edge. 3Qinsen models a curved bulldozer blade, and explicitly models surcharge
due to soil accumulation. 4Zeng treats acceleration directly, rather than inertia.
of these two terms, implying that their contribution to total excavation resistance is of primary
importance. In fact, Wilkinson and DeGennaro show that, for the McKyes / Swick model (which
includes all five typical terms), the gravity term (referred to as the depth term in their paper)
and/or cohesion are the dominant contributions to total excavation resistance force over a very
broad range of operating conditions [73].
2.1.2 Adhesion and inertial forces can usually be neglected
Compared to gravity and cohesion, adhesion and inertial forces tend to have minimal contribution
to excavation resistance force. Hettiaratchi and Reece note that the Nacoefficient (for adhesion)
is small compared to the other Ni and that soil-tool adhesion is almost always smaller than
cohesion; they neglect inertial forces outright, arguing that cutting speeds are typically low [ 32].
Table2.1shows that adhesion and inertial terms are the two most often omitted from excavation
resistance force models.
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2.1.3 Surcharge forces arise due to soil accumulation
The surcharge term can be used to account for soil that accumulates at the front edge of the bucket
during cutting. The surcharge increases as cutting proceeds. To account for this, Shmulevich [61]
models surcharge as:
q gx (2.3)
where x is cut advance distance (and is soil density). Kobayashi [42], making different as-
sumptions about the shape of the accumulating pile, proposes: q g
dxwheredis cut depth.
In both cases, surcharge increases with cut advance distance, linearly in the former and as the
square root in the latter. In both cases, the surcharge force is assumed to be only due to the
additional weight causing increased frictional shearing.
Qinsen [57], when modeling excavation with a bulldozer blade, accounts for soil accumula-
tion directly. They model forces at steady state once soil accumulation has reached maximum
extent. The model considers not only the weight and frictional shearing of the cut soil, but also
its cohesion.
As discussed in Section1.4.1, soil accumulation is particularly notable for discrete excava-
tors such as front-end loaders and bulldozers. Section2.2.1 discusses experimental results that
demonstrate how excavation resistance increases during discrete excavation, and relates these
results to the models discussed above.
2.1.4 Discrete Element Models for excavation
Discrete Element Modeling (DEM) provides greater promise for high fidelity modeling of exca-
vation. This approach explicitly models interactions between particles, and produces resultant
flow fields and stresses for these soil particles. DEM could therefore model how soil flows and
accumulates in a bucket. The goal of current research in DEM [9,69] is to produce excavation
flow fields as well as calibrated resultant forces. Experiments providing quantified visualizations
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of excavation will drive development and validation of DEM. Bui et al [14] have performed soil
footing failure experiments in reduced gravity to provide data for tuning their DEM model for
excavation.
This modern approach is still being developed, and is not ready to incorporate into system
development optimizations, let alone online prediction and control. DEM development is a field
of research in its own right, and is outside the scope of this work.
2.2 Experimentation for Lunar and Planetary Excavation
Classical excavation experiments pull blades and buckets through soil bins, measuring how exca-
vation resistance and other variables are affected by changes in excavation parameters; a recent
example is work at NASA Glenn Research Center [2]. Controlled soil bin experiments have also
been conducted with bucket-wheels [36].
2.2.1 The large impact of soil accumulation on discrete excavation
Agui shows that horizontal excavation resistance rises approximately linearly with cut distance,as soil accumulates in a bucket [2]. These results agree with the general modeling assumptions
of Shmulevich presented in Section2.1.3.Agui also showed though, that the shape and location
of a pile accumulating in a bucket is non trivially dependent upon time as well as cut depth, cut
angle, and possibly other parameters. Modeling soil accumulation in a bucket by a continuously
changing surcharge distribution is therefore difficult, and ideally would depend on knowing how
the soil flows as it enters the bucket.
A bulldozer blade also exhibits significant increase in horizontal force as surcharge increases
with cut distance, as demonstrated by King [39]. Comparing a variety of excavation models to
their data, they conclude that Qinsens model provides the best fit. This is not entirely unex-
pected, as Qinsens model was developed specifically for bulldozing (though one of the other
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Figure 2.2: Gravity offload: a cable pulls up on an excavator with 5/6 its weight to simulate lunar
gravity
models compared against was specific to bulldozing as well).
2.2.2 Soil properties and gravity are important conditions to control
Controlled planetary excavation experiments make use of simulants that mimic the geotechnical
properties of Lunar or Martian soils. GRC-1 and GRC-3 are lunar simulants with properties
relevant for excavation [56]. JSC-1 is another lunar simulant often used for excavation experi-
ments [18,74]. JSC-1 has a particle size distribution that is similar enough to lunar regolith to
duplicate its compaction and relative density [83].
Simulating low gravity conditions is another important consideration for lightweight exca-
vation experiments. Boles [13] showed that excavation resistance in 1/6 of Earth gravity (expe-
rienced during reduced gravity flights) could be anywhere between 1/6 and 1 of the resistance
experienced in full Earth gravity. Sample data shows excavation forces in 1/6 g that average 1/3
of the resistance in full Earth gravity.
Another way to simulate low gravity conditions (at least for the excavator if not the soil) is to
use a gravity offload mechanism. No excavator testing with gravity offload has been reported in
the literature to date.
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2.3 Applicability of excavation resistance models to planetary
excavation
A common result from literature that attempts to compare excavation forces predicted by various
models (e.g. [39,73,74]) is that the models yield disparate predictions. This makes it inprudent
to rely on any one model for estimating excavation forces. As Section2.1showed, however, the
models share common fundamentals that are instructive when investigating planetary excavation.
Any estimate of excavation resistance must take into account soil weight (and thus friction) and
cohesion. Surcharge is also very important, particularly for discrete excavation; the weight, and
perhaps cohesion, of the accumulating soil comprise this surcharge.
Muff [53] reports that the Luth & Wismer model was tested against Martian telemetry from
the Viking sampling digs (a claim seemingly based on personal correspondance with those who
performed the analysis), giving this model flight heritage in a sense. The lack of published
quantitative comparisons, however, compels caution in interpreting this claim.
2.4 Lunar excavation trade studies
Trade studies have examined the applicability of various excavation robot options, specifically
for lunar outpost site work. However, these studies assume several metric tons are available for
excavation equipment; this is unlikely to be the case in the short or even medium term. The trade
studies also restrict themselves to predefined configuration options, potentially missing novel
designs that could fare better than those considered.
Boles et al. [12] compares the probable required launch mass of several construction ma-
chine suites. The study concludes that typical terrestrial excavation machines would not be as
effective as tripod cranes, sweeper leveler/excavators, and other innovative vehicles. Abu El
Samids work [1] continues along the lines of Boles, concentrating on tradeoffs between au-
tonomous and tele-operated operation and between single vehicle and team configurations. A
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Configuration options Metrics Selected option Ref.
Boom cranes, track
dozers, haulers, drills,
clamshell diggers,
sweeper excava-
tor/levelers
Launch mass All-purpose super
cranes with drilling,
excavating, level-
ing, and hauling
capabilities
[12]
Same as Boles (con-
trolled manually), or
teams of autonomous
bulldozers, bucket
loaders, or bucket
wheels
Launch mass Team of autonomous
bulldozers
[1]
Multipurpose exca-
vator, auger, bucket
ladder, bucket wheel,
dragline, overshot
loader, pneumatic
vacuum, scraper
Productivity, reliabil-
ity, dust generation,
power efficiency,
maintainability
Multipurpose excava-
tor
[51]
Table 2.2: Trade studies examining options for large-scale lunar excavation (using several metric
tons of equipment) arrive at different conclusions, demonstrating the weakness of approaching
such a complex problem with a predefined set of solutions to choose from.
team of autonomous bulldozers is recommended for the task of berm building. Mueller and
Kings study [51] scores excavator designs on a number of quantitative and qualitative metrics
and decides a multi-purpose machine with bulldozing blade and excavator arm is most appropri-
ate for lunar site work. The results of these trade studies are summarized in Table2.2.
The aforementioned trade studies restrict themselves to predefined configuration options and
compare their relative merit for lunar operations; in that sense, they espouse a top-down approach
to configuration analysis. Each of the studies arrives at different conclusions regarding robot
designs. The varying results highlight effects of differing assumptions, models, and metrics
when approaching such a complex problem with a predefined set of solutions to choose from.
Assumptions of high mass machinery, as well as wide variability of the results, limit the
relevance of past trade studies to the development of lightweight robotic excavators. Metrics for
comparison of configurations in these studies are useful to consider, but the top-down approach
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of studying a predefined set of solutions is not as useful.
2.5 Lightweight excavator prototypes
In recent years, several robot prototypes have been developed specifically for lunar excavation
and ISRU. There are tested, however, in full Earth gravity, so principles of lightweight excavation
are obscured. The taxonomy of mobile excavators introduced in Section1.4.1can be applied to
these robots as well, as seen in Figure1.7.The figure shows samples of each of the following: a
bucket-wheel excavator, a bucket-ladder scraper, an open bowl scraper, as well as a loader and a
dozer.
Bucket-wheel excavators produce low resistance forces suitable for lightweight operation [36].
A past lunar bucket-wheel excavator prototype [52] has been configured like a trencher (see Fig-
ure1.7). However, the small scale intended for the lightweight excavator made material handling
and tranfer prohibitively challenging [37]. A novel lightweight bucket-wheel excavator, with a
simplified material transfer approach, has been developed as part of this work and will be dis-
cussed in detail in Chapter 6. A Bucket-Drum Excavator, which is an adaptation of a bucket
wheel [17], has a novel regolith collection system with cutting buckets mounted directly around
the outside of the collection drum. Regolith Advanced Surface Systems Operations Robot (RAS-
SOR) has counter-rotating front and rear bucket drums, making it possible to balance horizontal
excavation forces [50]. Figure2.3shows a Bucket Drum Excavator as well as RASSOR.
Due to past difficulties encountered transferring regolith from bucket-wheel to collection
bin, bucket-ladders have gained favor [37]. Bucket-ladders use chains to move buckets along
shapeable paths, easing transfer to a collection bin. Winners of the NASA Regolith Excavation
Challenge and subsequent Lunabotics mining competitions (competitions where lightweight ex-
cavators must collect as much regolith simulant as possible in 15 to 30 minutes) have all em-
ployed bucket-ladder trenchers driven by exposed chains or flexible conveyors. However, ex-
posed chains and conveyors fare poorly in harsh lunar regolith and vacuum, making them inap-
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Figure 2.3: Adaptations of bucket-wheel excavation: Bucket Drum Excavator (left) and RAS-
SOR (right)
Figure 2.4: Juno rover with a small load-haul-dump scoop that achieves only low payload ratio.
propriate for operation on the Moon.
Cratos [16] is an open bowl scraper with a central bucket between its tracks, as seen in
Figure 1.7. It can carry a payload ratio of approximately 30% (in Earth gravity). Although
terrestrial scrapers buckets extend laterally beyond the outside of the wheel track, the central
bucket mounting is a key feature that leads to Cratos being classified as a scraper here. Juno
rovers [67] can be equipped with front-end load-haul-dump scoops, though these scoops can
carry only a small fraction of the rovers mass in regolith (see Figure2.4).
Other lunar and planetary excavator prototypes include NASAs Chariot with LANCE bull-
dozer blade and Centaur II with front-loader bucket. These machines are very high mass (on the
order of tonnes) and low payload ratio, making their relevance to lightweight excavation mis-
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sions limited. Robots that excavate by filling up with regolith as they burrow into the ground
have also been proposed [44].
2.6 Soil loosening methods and mechanisms
Lunar regolith is very strong below the top few centimeters from the surface [30]. The presence
of ice only makes this dense mass harder and more cohesive [27]. This has led researchers to
develop several methods to loosen regolith either prior to or during excavation.
Sture et al [40,66] as well as Zacny et al [18] have shown that percussive/vibratory actuation
of diggins implements reduces excavation resistance forces. Specifically, percussion reduces
the shear strength of dry soil by removing the effects of soil dilatancy from the internal friction
angle along the shear failure boundary layer [28]. To date, the advantages of percussion have
been studied for bulldozers, small narrow scoops, and helical augers.
Gertsch et al. [29] have studied the applicability of cutterhead wheels and rippers for loosen-
ing frozen and compacted regolith in preparation for excavation. Iai showed that adding ripping
reduces total excavation energy (ripping + excavation) in soils with high density and low gravel
content [34]. An important contribution of Iais work is raising awareness of the often overlooked
contribution of gravel and rock content to excavation forces.
Bernold has suggesting using small explosive charges to loosen compacted regolith [8]. The
fact that these explosives are a consumable that cannot be manufactured in situ, though, limits
their applicability to ISRU missions.
2.7 Autonomous Earthmoving and Tele-Operation
The automation and tele-operation of earthmoving machines is a research field in its own right.
Singh [62] lists a taxonomy of the fields inter-related aspects: sensing, kinematic and dynamic
modeling, soil-tool interaction modeling [45], tool trajectory planning and control, and tele-
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operation.
Dunbabin [22] investigates operating large-scale excavation machines in extra-terrestrial en-
vironments, and discusses operating modes ranging from manual, through various levels of ab-
stracted tele-operation (remote, fly-by-wire, and copilot), to autonomous. Autonomous dig and
dump cycles are demonstrated (on Earth), with the goal of shifting as much control as possible
to the robotic excavator to avoid tele-operation challenges such as dealing with latency.
A theoretical lower bound on the round trip time of communications between the Earth and
the Moon, based on the speed of light and lunar perigee, is approximately 2.5 s. Even this amount
of latency makes direct remote control a psychologically tiring task for any expert operator,
which can greatly hamper the productivity of even the most capable machines [60].
The Lunokhod rovers were commanded directly via remote tele-operation from Earth. De-
spite the taxing effects of latency, the rovers regularly drove at speeds of 1 km/hr [38]. Of course,
the remote operators did not deal with any excavation tasks as the Lunokhods were not equipped
for them.
This work investigates aspects that arise when tele-operating bucket-wheel excavators. One
of the guiding principles is that continuous excavator configurations should lead to simpler con-
trol than discrete wide bucket excavators. A generalized investigation of autonomy for earth-
moving equipment, beyond reviewing the literature, is outside the scope of this work.
2.8 Conclusions Based on Related Work
Review of literature related to lightweight robotic excavation leads to the following conclusions:
There is no consensus on appropriate excavation force modeling for lunar excavation. How-
ever, it is instructive to rise above the fray of contrasting models and focus on their commonly
shared features. Any estimate of excavation resistance must take into account soil weight (and
thus friction) and cohesion. Surcharge is also very important, particularly for discrete excava-
tion; the weight, and perhaps cohesion, of the accumulating soil comprise this surcharge. These
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common features provide a theoretical framework for broadly predicting dependence on key
variables such as soil density and cohesion as well as gravity and cut depth.
Excavation resistance varies significantly during a cut as soil accumulates in the bucket, and
classical models can only approximate this effect. They fail to capture excavation soil flows.
Modern Discrete Element Modeling (DEM) shows promise in modeling excavation soil flows.
Past experiments have studied the effects of many excavation parameters, and have shown
that bucket-wheel excavators produce low resistance forces suitable for lightweight operation.
Only preliminary efforts have been made to study excavation forces in reduced gravity. Exper-
iments with excavator prototypes simulating low gravity constitute a novel contribution to the
field of study.
The wide variability in configurations resulting from lunar excavation trade studies and proto-
type developments highlight the lack of consensus on appropriate configurations for lightweight
excavators. An anecdotal consensus is the fact that bucket-ladder trenchers have won the Regolith
Excavation Challenge and Lunabotics mining competitions each of the 4 times such competitions
were held [49].
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3 Hauling and Payload Ratio
The load-haul-dump cycle is central to lightweight robotic excavation tasks, as described in Sec-
tion1.2. This chapter will show that, for a nominally capable excavator, hauling productivity
dominates overall task performance. Payload ratio directly influences hauling productivity, mak-
ing it an important design parameter.
Section2.4showed how excavator configuration trade studies utilizing a top-down approach
(i.e. comparing a predefined set of solutions) have produced widely varying results, limiting their
usefulness.
This work explores configurations for lightweight robotic excavators from the bottom up,
starting with system parameters that figure into analytical models of excavating and driving,
synthesizing them for analysis of task-level performance metrics. This approach distinguishes
design parameters (such as driving speed, payload ratio, or number of wheels) of appropriate
excavator configurations instead of picking between configurations themselves.
3.1 Task-level site work modeling
Regolith-moving machines are commonly characterized for elemental actions like digging or
driving [73], but it is also important to measure comprehensive performance combining digging
anddriving. A task model is developed here for excavation tasks that includes digging, trans-
porting, dumping, and shuttling for recharge (See Fig. 3.1).
The REMOTE (Regolith Excavation, MObility & Tooling Environment) task simulator [65]
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Figure 3.1: Comprehensive task modeling for lunar site work that combines elemental actions of
digging and driving
, computes metrics including task completion time, production ratio (weight of regolith moved
per hour, normalized by robot weight), and production efficiency (weight of regolith moved per
unit of energy spent, normalized by robot weight), based on parameters describing the task, the
robotic system, and the environment. The novelty of comprehensive task simulation, combined
with sensitivity analysis, is that it identifies system parameters that are important for overall task
success. This determines what matters most for system design and tradeoffs.
Traction and excavation forces are modeled to determine admissible bucket geometries, and
transport and recharge times are estimated based on driving speed and power draw. Excavation
is assumed to occur on approximately flat ground (i.e. not digging on a large uphill or downhill
slope).
3.1.1 Traction modeling (wheels)
The underlying traction model is that of Bekker [7] and Wong [76], based on their empirical and
theoretical work. Net traction, also known as drawbar pull (DP), is obtained by calculating wheel
resistance and thrust.
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Wheel resistance is assumed due to soil compaction. Gravitational resistance is ignored
because of the assumption of excavating on relatively flat ground. Bulldozing resistance is also
ignored; wheel bulldozing can be avoided with careful grouser design, as shown in Appendix B.
Following Bekker, compaction resistance of a single wheel, Ri, is estimated as:
Ri= b
kcb
+k
zn+1in+ 1
Soil pressure-sinkage parameter values are based on estimates made for lunar regolith [ 30]:
kc = 1.4kN/mn+1,k = 820kN/m
n+2, andn = 1. Wheel width is denotedb, and sinkage,
zi, is estimated as:
zi=
3Ni
b(3 n)(kc/b +k)
2r
2/(2n+1)
whereNiis the normal load on a given wheel, andr is wheel radius. Slip sinkage is ignored,
for the sake of simplicity. New work in terramechanics [20] is developing modeling techniques
for slip sinkage which could be incorporated into future modeling work.
Wheel thrust, Hi, is estimated based on equations (and assumptions) presented by Bekker
and Wong:
Hi= rb
00
(c+ ((kc/b+ k)(r(cos cos 0))n)tan )
(1 exp(r/K[0 (1j)(sin 0 sin )])) cos d
wherec and are soil cohesion and internal friction angle, respectively, Kis a shear defor-
mation constant,j is wheel slip, and 0 = cos1(1 z/r)is the angle from vertical to where
the wheel rim contacts level terrain, as shown in Fig.3.2.
Within REMOTE, vehicle load is assumed to be evenly distributed between all wheels, so
drawbar pull is calculated as:
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Figure 3.2: Wheel geometry terms. Wheel width,b, is into the page.
DP =Nw(Hi Ri)
whereNw is the number of wheels.
3.1.2 Excavation models
There is no consensus excavation resistance force model for lunar excavation, as discussed in
Chapter2. REMOTE offers a choice of two underlying excavation models, Balovnev and Luth-
Wismer. Balovnevs [4] is a 3-D bucket model developed from theory. It is of the fundamental
form proposed by Reece (discussed in Section2.1). Luth-Wismer [46,75] was developed em-
pirically from separate experiments in cohesive clay and cohesionless sand. The Luth-Wismer
model represents an excavating bucket by a single plate, and may have been tested under Martian
conditions during the Viking missions [53]. The same parameters govern productivity, indepen-
dent of the choice of model, as will be shown in Section 3.1.5.
Horizontal excavation resistances modeled by Luth and Wismer for (cohesionless) sand and
(cohesive) clay are:
FH,sand = gwl1.51.73
d
d
l sin
0.77
1.05
d
w
1.1+ 1.26
v2
gl+ 3.91
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Figure 3.3: Excavation geometry terms. Bucket/plate width,w, is into the page.
FH,clay = gwl1.51.15
d
d
l sin
1.21
11.5c
gd
1.212v
3w
0.1210.055
d
w
0.78+ 0.065
+ 0.64
v2
gl
Bucket width is denotedw, cut depth isd,is the angle of the buckets cutting face (relative
to horizontal), andl is the length of cutting face interacting with the soil, as seen in Fig. 3.3. In
REMOTE, l is defined byd/ sin to avoid overconstrained geometry. The buckets horizontal
cut velocity is denotedv, and gravitational acceleration isg. Soil density is denoted, andc is
soil cohesion. Luth-Wismer does not explicitly include soil friction angle or external (soil-tool)
friction.
Balovnevs model includes typical force terms due to weight/friction, cohesion, and sur-
charge. It also includes additional terms: external friction contributes resistance on the bucket
sidewalls, and cutting edge thickness is also taken into account. The horizontal component of
excavation resistance is given by:
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FH = wd(1 + cot tan )A1
dg
2 +c cot + gq+B (d l sin )
g
1 sin 1 + sin
+ web(1 +tancot )A2ebg
2 + c cot +gq+d
g
1
sin
1 + sin
+ 2sdA3
dg
2 + c cot +gq+B (d lssin )
g
1 sin 1 + sin
+ 4 tan A4lsd
dg
2 +c cot +gq+ B (d lssin )
g
1 sin 1 + sin
Common parameters are denoted the same as on page 31. The soil internal friction angle is
denoted, andis the external (soil-tool) friction angle. Surcharge is denotedq. Bucket side
thickness is s, side length is ls, eb is blunt edge thickness, and b is blunt edge angle. Ai are
non-dimensional coefficients specific to the model [4], andB is a boolean flag indicating if the
bucket is fully buried below soil level.
Within REMOTE, excavation is assumed to occur over a short distance, so that cut depth and
cutting face length do not change substantially. By this same assumption, traction parameters
that might in reality vary with time, such as slip, also remain constant for the duration of an
excavation cut. For longer cuts, one could account for soil accumulation by making surcharge
and/or cut depth depenedent on horizontal cut progress (and thus time).
Excavation with a forward-facing bucket is assumed, meaning the excavator can generate and
sustain an excavation force no greater than its net traction, or drawbar pull. Excavation at this
stall condition is subject to:
FH=DP
This equation is solved, by defining all parameters but one (for example, bucket width), to
find an admissable bucket geometry. The bucket is assumed to be of equilateral triangular prism
shape, as seen in Fig.3.4. Combining this assumption with a bucket filling efficiency,b, gives
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Figure 3.4: Bucket geometry with equilateral triangular prism shape
the volume of soil that can be excavated in a single cut:
V =b1
2wl2 sin(/3)
To account for excavators that have secondary collection/dump beds, an overall payload ca-
pacity can be defined. In that case, several cuts may be required to reach capacity, and REMOTE
accounts for the time required for all of these cuts as well as the time for transfers from primary
bucket to collection bed.
3.1.3 Operations modeling
Traction and excavation modeling describe the dig portion of a task, but as Fig. 3.1 shows,
a general task also includes transporting and dumping regolith. To account for these aspects
of tasks, REMOTE includes operational parameters such as average distance between dig and
dump, driving speed, area and depth of the desired excavation, and operational efficiency (per-
centage of time spent actually performing work, as opposed to waiting for commands or per-
forming computations).
The number of robots performing a task, and the mass of each robot, are further system
design parameters.
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3.1.4 Power modeling
Energy is expended by both driving and excavating. There is also baseline power that is always
being dissipated in communication, computation, and other avionics tasks, even when not per-
forming physical work. Over the class of small vehicles studied (100 kg to 300 kg), this baseline
power is assumed to be the same for each vehicle. Only steady state power is considered during
each phase of a task.
Power expended during driving is modeled by:
Pdrive = KPdmgvd
Where m is vehicle mass, g is gravitational acceleration, vd is driving velocity, and KPd is a
driving power coefficient. TheKPdcoefficient captures and sums several sources of power dissi-
pation. Power required to overcome wheel rolling resistance can be estimated as a percentage of
vehicle weight [55]. Internal machine losses (in bearings, for example) are also proportional to
weight (acting as a radial load). Even undulations in the terrain can be captured by multiplying
weight by the sine of a representative terrain angle. KPd can thus be used to account for rolling
resistance, internal losses, and terrain losses.
Excavation power draw is modeled by:
Pexcav =KPexFHvex
WhereFH is excavation resistance force, vex is excavation velocity, andKPex is an excavation
power coefficient that is nominally 1. Driving power is also expended (withvd = vex) during
excavation.
Dumping power is ignored, as dumping comprises a very small portion of the overall task.
Batteries are assumed to be the primary power source for excavation robots. Each vehicle
is assumed to have a constant fraction of mass budget for batteries, meaning larger vehicles are
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able to store more energy than smaller ones. A battery charging time is included in the model.
This charge time does not include the time required to shuttle to and from the power plant, which
is accounted for separately in the same way that shuttling to and from a digging site is.
Batteries can potentially be charged during operation by additional power sources such as
onboard solar panels. Such an additional power source is modeled as a negative power draw, and
denoted within REMOTE as trickle power.
3.1.5 Parametric sensitivity analysis
As the preceding sections show, modeling excavation tasks involves a large number of parameters
(over 25). A particularly instructive application of REMOTE is in performing sensitivity analyses
that compare the relative impact of variations in these parameters on output metrics. Here it is
not so much the values themselves of the calculated metrics that are paramount, but rather how
sensitive these calculations are to changes in system, concept of operations, and environmental
parameters.
Parameters for sensitivity analysis include system parameters (such as individual robot mass,
payload ratio, wheel radius, etc.) and concept of operations parameters (operational efficiency,
distance to recharge station, etc.) that could be variables in system/mission design. Sensitivity
analysis also includes regolith parameters (bulk density, cohesion, etc.) whose values are esti-
mated within bounds. Each parameter is varied individually from its expected baseline value to
maximum and minimum values in turn. The resulting values of the metrics are calculated at each
variation. Although some parameters are not fully independent in reality, isolating each param-
eters individual contribution to productivity in this way is still a very useful guide for focusing
attention within such a broad design and operational space.
Sensitivity of production ratio to relevant parameters for an example berm building task is
presented in Figure3.5and Figure3.6. The task involves shallow digging, to a total depth of
20 cm, over a large area (50 m diameter circle). Excavated material is moved to an arc along the
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circle and dumped in a berm. Average distance between dig and dump is 25 m.
Figure3.5shows REMOTE sensitivity analysis results for the berm building task, with Luth-
Wismer as the underlying excavation resistance model. Production ratio (mass of regolith moved
per hour, normalized by rover mass) is shown on the x-axis, while parameters that can affect it
are shown on the y-axis. Changing driving speed, from its baseline value of 20 cm/s to 50 cm/s,
for example, is predicted to increase production ratio from just over 2 to a little under 4. Driving
speed, payload ratio, and operational efficiency are predicted to have the strongest effects on
productivity. Other parameters, such as number of wheels and battery characteristics, have little
effect.
Figure3.6 shows results for the same sensitivity analysis, but with the Balovnev excavation
model. Results broadly agree between the two models. Driving speed, payload ratio, and opera-
tional efficiency govern productivity. The next three most important parameters in the Balovnev
analysis are external friction angle, cohesion, and robot mass. Luth-Wismer also predicst cohe-
sion and robot mass as the next two most important parameters (Luth-Wismer does not include
external friction angle).
These results demonstrate that task-level sensitivity analyses are not particularly dependent
on the choice of underlying excavation model. In both versions of the analysis, productivity
is governed by payload ratio, driving speed, and operational efficiency. These three parameters
figure prominently in the hauling part of excavation tasks, as will be discussed in Section3.4.Co-
hesion and robot mass are also important parameters, and have been discussed in prior work [63].
In upcoming sections, additional sensitivity analysis is performed on parameters relevant to
a small robotic excavator, Lysander, and simulated results are compared to experimental data.
3.2 Experiments with a small robotic excavator
To develop effective lightweight robotic excavators, it is important to identify which design pa-
rameters have a significant effect on productivity. As described in the previous section, REMOTE
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Figure 3.5: Sensitivity analysis using Luth-Wismer excavation model shows productivity governed
and operational efficiency
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Figure 3.6: Sensitivity analysis using Balovnev excavation model shows productivity governed by driving
operational efficiency
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Figure 3.7: Lysander is a robotic platform for sitework experimentation - shown here carrying
excavated lunar regolith simulant
simulations and analyses show that payload ratio (ratio of regolith payload mass to robot mass)
and driving speed govern the productivity of small robotic excavators; operational efficiency
also significantly affects productivity. The analysis also shows that other parameters, including
number of wheels, have little effect on productivity.
A prototype excavator, Lysander, enables experimental validation of sensitivity analyses as
well as of the simulator more broadly. Lysander is a low center-of-gravity scraper, and is shown
in Fig.3.7transporting excavated lunar regolith simulant.
3.2.1 Experimental setup
Load-haul-dump experiments measure productivity of the lightweight robotic excavator, Lysander,
in controlled conditions. A sandbox was set up with an excavation area, a dump area, and ob-
stacles, as seen in Fig. 3.8. The entire experimental area was on flat ground, with a board in the
dump area to keep dumped soil separate for measurement. The setup represents a general load-
haul-dump task, and the layout provided an efficient way to incorporate all major elements of the
task, including driving approx. 6 m (roundtrip), and making turns to avoid obstacles and align
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Figure 3.8: Experimental setup for a comprehensive excavation task including digging, dumping,
and shuttling between the two
for dig and dump. The soil used in the experiments is a mixture of general-purpose play sand and
a uniformly fine silica sand. This soil is not a lunar simulant, but its granular nature allows it to
be modeled similarly to regolith. Furthermore, the soil has an internal friction angle between 39
and 42 degrees, and cohesion up to approximately 3 kPa; the values of these strength parameters
lie within the ranges measured for lunar regolith [30]. Internal friction angle and cohesion are
measured using direct shear tests (ASTM D3080). Results of these tests are shown in Fig.3.9.
The experimental setup fixes some of the parameters studied in the REMOTE simulations.
Some physical robot parameters, such as wheel radius and mass, are fixed. Battery and recharge
parameters are omitted because tethered power enables rapid repetition of experiments. Strength
parameters, i.e. internal friction angle and cohesion, are known within confidence bounds (as
described above). Soil strength parameters are kept within tight bounds with consistent soil
preparation. Between each test run, the soil conditions were reset using a technique developed
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0 50 100 1500
50
100
150
Normal Stress (kPa)
ShearStress(kPa)
Figure 3.9: Direct shear test results for soil used in Lysander experiments: Internal friction angle
of 39 to 42 degrees, cohesion of 0 to 3 kPa
at NASA Glenn Research Center. First, the soil is fully loosened by plunging a shovel approx-
imately 30 cm deep and then levering the shovel to fluff the soil to the surface; this is repeated
every 15-20 cm in overlapping rows. Next, the soil is leveled with a sand rake (first with tines,
then the flat back edge). The soil is then compacted by dropping a 10 kg tamper from a height
of approximately 15 cm; each spot of soil is tamped 3 times. Finally, the soil is lightly leveled
again for a smooth flat finish.
3.2.2 Predicted sensitivity of experimental parameters
Parameters that either varied during experiments, or were known only within bounds, are listed
on the y axis in Fig.3.10. Aside from parameters already discussed (payload ratio, driving speed,
operational efficiency, number of wheels, and soil strength parameters: cohesion and friction
angle), cutting speed, slip, and shear deformation (K) could also potentially vary. While digging,
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0 10 15 27
Number of wheels
Soil friction angle
Slip
Shear deformation
Cutting speed
Soil cohesion
Operational efficiency
Driving speed
Payload ratio
Production ratio (hr1
)
6
42 deg
90 %
2.5 cm
30 cm/s
0
80 %
28 cm/s
50 %
4
39 deg
60 %
1 cm
10 cm/s
3 kPa
65 %
18 cm/s
25 %
0 10 15 27
Number of wheels
Soil friction angle
Slip
Shear deformation
Cutting speed
Soil cohesion
Operational efficiency
Driving speed
Payload ratio
Production ratio (hr1
)
Figure 3.10: Predicted sensitivity of Lysanders productivity to candidate experimental vari-
ables [65]. Payload ratio, driving speed, and operational efficiency govern productivity. Parame-
ters that cannot be varied within experiments, such as fixed wheel radius, etc., are excluded.
soil accumulation increased excavation resistance. This higher resistance slowed progress (i.e.
cutting speed) due to increased slip. The ranges of values in cutting speed and slip account for
this variation. Shear deformation is a soil-specific parameter, which could not be measured for
these experiments. A range of possible values from 1 cm to 2.5 cm is considered, based on values
presented in literature for similar soils [33,76].
Load-haul-dump task productivity is also dependent on driving distance between dig and
dump. This distance was kept the same for all experiments, at 3 m. This is at the low end
of distances that would be required for any long-term task (e.g. mining, trenching). Longer
distances would be expected to further increase the importance of payload ratio and driving
speed, as an even higher percentage of the task would be devoted to driving and transporting
regolith, as opposed to digging or dumping.
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Figure3.10shows REMOTE sensitivity analysis results for parameters relevent to the ex-
perimentation campaign using Lysander. Production ratio (mass of regolith moved per hour,
normalized by rover mass) is shown on the x-axis, while parameters that can affect it are shown
on the y-axis. Changing Lysanders payload ratio in simulation, from its baseline value of 25% to
50%, for example, is predicted to increase production ratio from 15 to 27. As in earlier REMOTE
simulations for general lightweight excavators, payload ratio and driving speed are predicted to
have a strong effect on productivity while other parameters, such as number of wheels, are not.
3.2.3 Experimental results
The experimental campaign tested sensitivity of two high sensitivity parameters (payload ratio
and driving speed) and one low sensitivity parameter (number of wheels - on Lysander, the
two middle wheels can be removed with relative ease). Payload ratio was modified by simply
changing the amount of payload carried by the robot; this was implemented in practice by taking
either 1 or 2 cuts of soil to collect a payload ratio of 25% or 50%, respectively. Before taking a
second cut of soil, the soil from the first cut was shifted out of the way to the back of Lysanders
large bucket by tilting the bucket back. The large surface of the bucket and relatively shallow cut
angle, , kept the collected soil from sliding back to the front of the bucket during the second
cut. Clearing the cutting edge of the bucket in this fashion ensured similar excavation during
both cuts.
As operational efficiency was also predicted to be a relatively high sensitivity parameter, it
was monitored during each test. By maintaing operational efficiency within a range of 65%
and 80%, the expected effects of its variability were kept smaller than the expected effects of
varying payload ratio and driving speed, as Fig. 3.10 shows. Production ratio was measured
as the output for each test. Experimental test sets at each parameter setting were performed in
triplicate. Photos from a sample experiment are shown in Fig. 3.11,and results from all the tests
are summarized in Table3.1.
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Figure 3.11: Lysander at start location (top) and excavation area (bottom) during an experiment
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Table 3.1: Experimental data from 4 sets of tests (each set in triplicate)
Test set Speed
(cm/s)Payload
ratio
No. of wheels Operational
efficiency
Production
ratio (hr1)
Baseline
29 25% 6 73% 17.9
28 23% 6 66% 14.3
30 19% 6 72% 12.4
Low speed
18 22% 6 75% 8.7
18 25% 6 77% 10.3
18 16% 6 80% 11.0
High payload
ratio
29 51% 6 76% 28.7
28 51% 6 72% 29.3
28 51% 6 72% 26.6
4 wheels
26 26% 4 77% 14.0
24 27% 4 79% 15.2
37 25% 4 74% 13.1
High payload ratio and low speed result in statistically significant differences in production
ratio relative to the baseline test set. Applying t-tests to the test sets, high payload ratio and
low speed results in p-values of 0.002 and 0.049, respectively. Both these parameters thus affect
productivity with 95% confidence of statistical significance (meaning there is less than 5% prob-
ability of the observed difference in productivity arising by chance, as opposed to there being a
real difference). Comparison of the 4 wheel tests with the baseline (6 wheels), on the other hand,
results in a p-value of 0.679, meaning no statistically significant difference in productivity was
observed.
3.3 Comparison of simulated and experimental results
Figure 3.12 (top) shows experimental results graphically, with error bars at each setting indicating
the standard error. The top bar extends from the mean production ratio value measured during
baseline tests (which had payload ratio at 25%), on the left, to the mean production ratio value
measured during tests with 50% payload ratio, on the right. The error bar around the right edge
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represents the error in the tests with 50% payload ratio, while the error bar around the left edge
represents the error in the baseline tests. Similarly, the next bar extends from the mean production
ratio value measured during baseline tests (which had a driving speed of 28 cm/s), this time on
the right, to the mean production ratio value measured during tests with 18 cm/s driving speed,
on the left. The error bar around the baseline edge is the same as the bar above, because there
is only one set of baseline tests; these tests act as the baseline for each parameter change. For
the final parameter variation, the plot shows that not only is the mean production ratio achieved
with 4 wheels within the error for production with 6 wheels, but also the mean production ratio
achieved with 6 wheels is within the error for production with 4 wheels. This provides a visual
representation of the statistical results described in the previous section. For changes in payload
ratio and driving speed the error bars do not overlap, highlighting a stastistically significant
difference between these tests and the baseline. For changes in the number of wheels, the error
bars overlap fully and no statistically significant difference is observed.
The bottom of Fig. 3.12 shows simulated results for the same conditions as those tested
experimentally. This plot is a subsampling of Fig. 3.10, showing only payload ratio, driving
speed, and number of wheels.
The sensitivity to payload ratio, driving speed, and number of wheels observed experimen-
tally aligns consistently with the simulated results. For each of the 4 test cases, the simulated
production ratio is within the error of the corresponding experimental case.
As described in previous sections, some modeling simplifications were introduced that do
not correspond exactly with all the details of the excavation tasks. Specifically, slip sinkage
is ignored, as is the time dependency of slip, cut depth ( d) and cutting face length (l) during
digging. This makes it impossible to model the observed phenomenon of soil accumulation
(which increases effectived and l), and the subsequent increase in slip (which causes increased
sinkage and thus rolling resistance), using the current implementation of REMOTE.
The good correspondence between simulated and experimental results suggests that this mod-
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0 10 15 27
Number of wheels
Driving speed
Payload ratio
Production ratio (hr1
)
64
28 cm/s18 cm/s
50 %25 %
0 10 15 27
Number of wheels
Driving speed
Payload ratio
Production ratio (hr1
)
0 10 15 27
Number of wheels
Driving speed
Payload ratio
Production ratio (hr1
)
64
28 cm/s18 cm/s
50 %25 %
0 10 15 27
Number of wheels
Driving speed
Payload ratio
Production ratio (hr1
)
Figure 3.12: Top: Measured production ratio sensitivity to experimental variables. Bottom:
Production ratio sensitivity to experimental variables predicted by simulation. Experiments and
model show good correspondence. In both cases, payload ratio and driving speed have a signifi-
cant effect on productivity, while number of wheels does not [ 65].
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eling simplification did not diminish REMOTEs ability to predict excavator productivity for the
load-haul-dump task described in this work. Figure3.10shows that the effects of varying slip
are negligible for this specific task.
The effects of cut depth and slip on prodcutivity are somewhat more significant for trench
excavation, as simulations in prior work show [63]. This suggests that neglecting soil accumu-
lation and slip sinkage may not be appropriate for all tasks, particularly ones involving deep
digging. Before applying REMOTEs modeling framework specifically to a deep excavation
task, additional experiments and possibly additional modeling are recommended.
A significant source of variability in the experimental results was the inability, in practice,
to keep operational efficiency precisely constant. A human tele-operator cannot replicate per-
formance exactly between test runs. Errors were low enough to make clear observations, as
described above. Tighter error bounds, though, could increase the potential statistical power of
experiments. If such tighter bounds were to be required for future investigations, better control
over operational efficiency could be achieved with increased autonomy for the tests.
3.4 Hauling dominates task productivity
Experiments and simulations all show that payload ratio, driving speed, and operational effi-
ciency govern the production ratio for lightweight robotic excavators. These parameters direcly
comprise the terms for hauling productivity:
Production ratio (hauling only)= opPv/d
whereop is operational efficiency, P is payload ratio, v is driving speed, and d is hauling
distance. Note that hauling distance is not included as a parameter in above sensitivity analyses,
as it is dictated directly by a given task.
The prominence of the three hauling productivity parameters shows that hauling is the im-
portant part of load-haul-dump excavation tasks, in terms of productivity. In fact, hauling takes
up the vast majority of time in any of the tasks investigated, which is why improvements in this
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area translate into the largest overall gains. An important underlying assumption leading to this
result is that the excavators in question can achieve a nominal level of excavation capability.
If an excavator gets stuck while digging, or must regularly correct and adjust its cuts, the time
spent digging would grow relative to time spent hauling. REMOTE does not model such poten-
tial problems, and they were not encountered in the experiments performed. Ensuring that basic
excavation capability is maintained is the subject of the next chapter.
3.5 Conclusions from sensitivy experiments and simulations
Payload ratio, driving speed, and operational efficiency govern productivity of excavation tasks
by small robots.