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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


4.5 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


5.3 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

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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


)

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


)

64

28 cm/s18 cm/s

50 %25 %

0 10 15 27

Number of wheels

Driving speed

Payload ratio


)

0 10 15 27

Number of wheels

Driving speed

Payload ratio


)

64

28 cm/s18 cm/s

50 %25 %

0 10 15 27

Number of wheels

Driving speed

Payload ratio


)

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.

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