BLEEX Design

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Design of the Berkeley Lower Extremity Exoskeleton (BLEEX)

by

Andrew Chu

B.S. (University of California, Berkeley) 2000

M.S. (University of California, Berkeley) 2003

A dissertation submitted in partial satisfaction of the requirements for the degree of

Doctor of Philosophy

in

Engineering - Mechanical Engineering

in the

GRADUATE DIVISION

of the

UNIVERSITY OF CALIFORNIA, BERKELEY

Committee in charge:

Professor Hami Kazerooni, Chair

Professor Albert Pisano

Professor Daniel Fletcher

Spring 2005


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UMI Number: 3196589

3196589

2006

Copyright 2005 by

Chu, Andrew

UMI Microform

Copyright

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by ProQuest Information and Learning Company.


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Copyright 2005

by

Andrew Chu


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Abstract


by

Andrew Chu

Doctor of Philosophy in Engineering - Mechanical Engineering

University of California, Berkeley

Professor Hami Kazerooni, Chair

Many places in the world are too rugged or enclosed for vehicles to access. Even

today, material transport to such areas is limited to manual labor and beasts of burden.

Modern advancements in wearable robotics may make those methods obsolete. Attempts

to navigate difficult terrain via purely autonomous robotics have been only moderately

successful as highly unstructured environments have proved too unpredictable for pre-

programmed robotics with limited sensory inputs. Lower extremity exoskeletons seek to

circumvent these challenges by combining the innate intelligence, dexterity and sensory

capabilities of a human with the significant strength and endurance of a pair of wearable

robotic legs capable of supporting a payload. This dissertation outlines the development

of one such system - the Berkeley Lower Extremity Exoskeleton (BLEEX). Previous

lower extremity exoskeletons have been limited by difficulties in sensing the human

operator and power supply limitations. The BLEEX however utilizes a novel control


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architecture that estimates the forces exerted on the human by the exoskeleton structure

via measurements of only the exoskeleton itself. The BLEEX also utilizes a simplified

kinematical architecture with powered joints only in the sagittal plane to minimize power

demands. The wearer connects to the BLEEX at a pair of foot bindings and a shoulder

harness. Extensive mock-up testing was used to develop the flexible anthropomorphic

architecture. The BLEEX wearer can squat, bend, swing from side to side, twist, walk on

slopes, and traverse obstacles while carrying significant payloads with ease. Clinical Gait

Analysis (CGA) data was used to provide the framework for the design of the hydraulic

BLEEX actuation system. Six double-acting hydraulic cylinders actuate the BLEEX

ankles, knees and hips in the sagittal plane. Applying CGA motion data to the actuation

design yielded hydraulic flow and prime mover requirements. A suitable self-contained

hydraulic power supply was designed and built, making the BLEEX one of the first

energetically autonomous lower extremity exoskeletons in the world. The BLEEX

prototype has been walked, un-tethered on a treadmill at speeds of up to 1.3 m/s. The

prototype has been tested in both indoor and outdoor environments and demonstrated

short duration (~30 min) energetic autonomy.


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Dedication

To my dearest Anna, for giving me a light at the end of the tunnel…


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Table of ContentsDedication.................................................................................................................................. i

Table of Contents ...................................................................................................................... iiTable of Figures.......................................................................................................................iii

Table of Equations .....................................................................................................................vTable of Tables ........................................................................................................................ viPreface .................................................................................................................................... vii

Acknowledgements................................................................................................................viii

Introduction to the BLEEX Project ...........................................................................................1Lower Extremity Exoskeletons..............................................................................................1

Anthropomorphic Design Approach......................................................................................3

Design Implications of Basic Control Methodology .............................................................6Range of Motion and Degrees of Freedom............................................................................9

Center of Gravity Constraints ..............................................................................................12

Clinical Gait Analysis as a Design Tool..................................................................................13

Reasoning and Assumptions ................................................................................................13Joint Angles & Flexibility Requirements ............................................................................14

Joint Torques & Actuation Requirements ...........................................................................18

Instantaneous Joint Powers..................................................................................................20Actuator Selection: Double-Acting Linear Hydraulic Actuators ........................................25

Actuation Design Synthesis and Iteration............................................................................27

Torque-Angle Relationship & Actuator Kinematics ...........................................................31Detailed Hydraulic Actuation Model...................................................................................35

BLEEX Power Estimates.........................................................................................................48

Predicted System Hydraulic Flow Rates & Power Consumption........................................48

Hydraulic Throttling Losses ................................................................................................51

Alternative Actuation Schemes to Minimize Throttling Losses..........................................54Detailed Design of BLEEX Hardware.....................................................................................56

BLEEX Sizing .....................................................................................................................56BLEEX Detailed Mechanical Design ..................................................................................57

Detailed Mock-up Evaluation..............................................................................................60

BLEEX Prototype Hardware...............................................................................................65Experimental BLEEX Performance Data ................................................................................68

Recorded angle & torque plots during walking cycle..........................................................68

Discrepancies between Experimental and CGA Estimated Joint Torques ..........................71

Extrapolated Hydraulic Power Usage ..................................................................................73 Net Mass Distribution Analysis...........................................................................................73

Further Work............................................................................................................................75Shortcomings of 1

st Generation Actuation Design ..............................................................75

Out of Plane Actuation ........................................................................................................77

BLEEX Effectiveness Testing.............................................................................................78

Design Implications for Future Exoskeleton Research........................................................83References................................................................................................................................86


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Table of FiguresFigure 1: Lower Extremity Exoskeleton Concept. ....................................................................2

Figure 2: Schematic Exoskeleton Representation .....................................................................4Figure 3: Non-Anthropomorphic Exoskeleton..........................................................................5

Figure 4: Anthropomorphic Exoskeleton ..................................................................................5Figure 5: Simplified Single Stance Model of Exoskeleton/Human System..............................7Figure 6: Simplified Double-Stance Schematic of Exoskeleton/Human System......................8

Figure 7: Kinematic Mock-Up of BLEEX ..............................................................................10

Figure 8: Degrees of Freedom of 1st Generation BLEEX.......................................................11Figure 9: System CG Schematic..............................................................................................12

Figure 10: CGA Sign Conventions ..........................................................................................14

Figure 11: Typical Gait Cycle [7]............................................................................................15Figure 12: CGA Ankle Angle vs. Time ...................................................................................15

Figure 13: CGA Knee Angle vs. Time ....................................................................................16

Figure 14: CGA Hip Angle vs. Time .......................................................................................17

Figure 15: CGA Ankle Torque vs. Time .................................................................................18Figure 16: CGA Knee Torque vs. Time ..................................................................................19

Figure 17: CGA Hip Torque vs. Time .....................................................................................20

Figure 18: CGA Instantaneous Ankle Power ..........................................................................22Figure 19: CGA Instantaneous Knee Power............................................................................23

Figure 20: CGA Instantaneous Hip Power ..............................................................................24

Figure 21: Total CGA power of a 75 kg human walking over flat ground atapproximately 1.3 m/s......................................................................................................25

Figure 22: Bi-directional linear hydraulic actuator schematic.................................................26

Figure 23: Triangular configuration of a linear hydraulic actuator. ........................................26

Figure 24: 2-Position kinematical synthesis of ankle actuator placement. ..............................28

Figure 25: Maximum Potential Ankle Actuation Torque vs. Angle........................................30Figure 26: Maximum Potential Knee Actuation Torque vs. Angle.........................................30

Figure 27: Maximum Potential Hip Actuation Torque vs. Angle ...........................................31Figure 28: CGA Ankle Torque vs. Angle................................................................................32

Figure 29: CGA Knee Torque vs. Angle .................................................................................33

Figure 30: CGA Hip Torque vs. Angle....................................................................................33Figure 31: Model of 1st Generation BLEEX Prototype. ........................................................34

Figure 32: Hydraulic Actuation Schematic .............................................................................36

Figure 33: 4-Way, 3-Position Closed-Center Servovalve Diagram........................................36

Figure 34: 4-Way, 3-Position Servovalve Wheatstone Bridge Analogy.................................38Figure 35: Maximum Possible Load Flow Output of Moog Type 30, 31-Series 4-way, 3-

position Servovalves as a function of Load Ratio ...........................................................45Figure 36: CGA Valve Load Flow vs. Load Ratio for Ankle..................................................46Figure 37: CGA Valve Load Flow vs. Load Ratio for Knee...................................................47

Figure 38: CGA Valve Load Flow vs. Load Ratio for Hip .....................................................47

Figure 39: BLEEX computed instantaneous total required hydraulic flow based on CGAdata (not including leakages or losses)............................................................................49

Figure 40: BLEEX computed total hydraulic power consumption based on human CGA

data (not including leakages or losses)............................................................................50


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Figure 41: Ankle CGA and Actuation Torque vs. Angle for Single-Acting Hydraulic

Cylinder Actuation with Spring Bias...............................................................................56

Figure 42: BLEEX Spine Assembly........................................................................................58Figure 43: BLEEX Hip Assembly...........................................................................................58

Figure 44: BLEEX Thigh Assembly .......................................................................................59

Figure 45: BLEEX Shank Assembly.......................................................................................59Figure 46: BLEEX Foot & Lower Ankle Assembly ...............................................................60

Figure 47: Range-of-Motion Evaluation of BLEEX Detailed Mock-up by Natick

Ergonomics Team [18] ....................................................................................................62Figure 48: Pressure, Pain and Discomfort Ratings for Natick Evaluation of BLEEX

Detailed Mock-up [18].....................................................................................................63

Figure 49: Mobility and Range of Motion Questionaire used in Evaluation of BLEEX

Detailed Mock-up [18].....................................................................................................64Figure 50: BLEEX on Jig Stand ..............................................................................................65

Figure 51: BLEEX Hardware..................................................................................................66

Figure 52: BLEEX Testing......................................................................................................67

Figure 53: Recorded Torque vs. Angle for Ankle ...................................................................69Figure 54: Recorded Torque vs. Angle for Knee.....................................................................69

Figure 55: Recorded Torque vs. Angle for Hip .......................................................................70Figure 56: Schematic of Kinematical and Inertial Differences between BLEEX and

Wearer..............................................................................................................................72

Figure 57: Original Design Mass Distribution of 75 kg BLEEX & Payload ..........................74

Figure 58: Mass Balance of Actual 70 kg BLEEX Prototype.................................................74Figure 59: BLEEX Powered Hip Abduction/Adduction Retrofit............................................78

Figure 60: Borg Ratings of Perceived Exertion (RPE) Scale [20] ..........................................79

Figure 61: Vista VO2 Lab VO2 Measurement System ............................................................80


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Table of EquationsEquation 1: Instantaneous Joint Mechanical Power................................................................21

Equation 2: Magnitude of Maximum Extension Force from Double-Acting HydraulicCylinder ...........................................................................................................................26

Equation 3: Magnitude of Maximum Retraction Force from Double-Acting HydraulicCylinder ...........................................................................................................................26

Equation 4: Maximum Potential Actuation Joint Torque from Actuator Extension ...............27

Equation 5: Maximum Potential Actuation Joint Torque from Actuator Retraction ..............27

Equation 6: Hydraulic Flow through Double-Acting Hydraulic Cylinder ..............................35Equation 7: Valve Model Definitions & Terminology............................................................37

Equation 8: 4-way, 3-position Hydraulic Servovalve Orifice Equations Governing Flow .....38

Equation 9: Valve Modeling Assumptions & Simplifications ................................................39Equation 10: Supply Pressure as a function of Actuator Port Pressures for both Positive

and Negatively Displaced Spool......................................................................................40

Equation 11: Load Pressure Definition....................................................................................40

Equation 12: Definition of Load Flow.....................................................................................40Equation 13: Load Flow as a Function of Supply Pressure and Load Pressure for Positive

Spool Displacements........................................................................................................41

Equation 14: Load Flow as a Function of Supply Pressure and Load Pressure for Negative Spool Displacements ........................................................................................41

Equation 15: Actuator Torque as a Function of Load Pressure...............................................42

Equation 16: Maximum Possible Actuation Torque as a Function of Supply and ReturnPressures ..........................................................................................................................42

Equation 17: Definition of Load Ratio ....................................................................................42

Equation 18: Load Flow as a Function of Load Ratio and Supply Pressure for Positive

Spool Displacement.........................................................................................................43

Equation 19: Load Flow as a Function of Load Ratio and Supply Pressure for NegativeSpool Displacement.........................................................................................................43

Equation 20: No-Load Rated Flow Test..................................................................................44Equation 21: Maximum Possible Valve Load Flow as a Function of Supply Pressure and

Load Ratio........................................................................................................................44

Equation 22: Total Hydraulic Flow Required for BLEEX (not including leakages) ..............48Equation 23: Actuator Extension Flow....................................................................................48

Equation 24: Actuator Contraction Flow.................................................................................48

Equation 25: Total Hydraulic Power Consumption as a Function of Supply Pressure and

Total Hydraulic Flow.......................................................................................................49Equation 26: Power Balance of Actuator/Valve System.........................................................51

Equation 27: Mechanical Power Produced when Valve Spool Fully Displaced.....................52Equation 28: Valve Throttling Losses .....................................................................................52Equation 29: Throttling Power Loss Derivation......................................................................53

Equation 30: Energy Loss per Cycle from Throttling .............................................................53


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Table of TablesTable 1: 5-95 Percentile Height, Shank Length, and Thigh Length for U.S. Army Males

(^ [16], *[17])...................................................................................................................57

Table 2: BLEEX Critical Component Count...........................................................................77

Table 3: Modified Bruce Fitness Test (adapted from [26]).....................................................82


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Preface

This dissertation represents the culmination of almost five years of work in the

University of California, Berkeley Human Engineering Laboratory on the Berkeley

Lower Extremity Exoskeleton (BLEEX) project. This Defense Advanced Research

Projects Agency (DARPA) funded project aimed to augment the intelligence and agility

of humans with the strength and endurance of modern robotics. By supporting our work,

DARPA hoped not only to develop multi-purpose robotic load-carriage platforms to aid

U.S. infantry on long marches, but to also advance the state of human-machine interface

technology in the hopes that one day similar technologies might also allow the disabled to

walk or rescue workers to get equipment into hard to reach areas. This work was carried

out by a dedicated team of graduate students, consultants, staff engineers and sub-

contractors under the direction of Professor Hami Kazerooni.


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Acknowledgements

Special thanks to Professor Homayoon Kazerooni, the director of the Human Engineering

Laboratory at the University of California at Berkeley, for providing the opportunity to

work with such a talented team on such an innovative project.

Thanks to Dr. Ephrahim Garcia, Dr. John Main, and all the other people at the Defense

Sciences Office of the Defense Advanced Research Projects Agency for daring to support

such a risky endeavor at a public university in the hopes of advancing both science and

education.

Thanks to Adam Zoss, Jean-Louis Racine, Ryan Steger and all the other talented

researchers at the Human Engineering Laboratory at Berkeley. Without your help,

dedication, and perseverance none of this work would have been possible.


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Introduction to the BLEEX Project

Lower Extremity Exoskeletons

Material transport has been dominated by wheeled vehicles. Many environments

such as stairways however, are simply too treacherous for wheeled vehicles. Many

attempts have been made to develop legged robots capable of navigating such terrain [1].

Unfortunately, difficult terrain taxes not only the kinematical capabilities of such

systems, but also the sensory, path planning, and balancing abilities of even the most

state of the art robotics.

Lower extremity exoskeletons seek to circumnavigate the limitations of

autonomous legged robots by adding a human operator to the system. These robotic

systems consist of a wearable backpack-like frame supported by a pair of robotic legs that

also connect to the wearer at the feet, as shown in Figure 1. If the robotic mechanism can

be “slaved” to the human operator, the highly developed sensory, balancing and path

planning capabilities of the human can be combined with the large payload capacity of

the robotic system. Lower extremity exoskeleton systems thereby attempt to combine the

strength and endurance of modern robotics with the intelligence and agility of a human

operator.


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Figure 1: Lower Extremity Exoskeleton Concept.

The idea of augmenting the strength of a human with a mechanical exoskeleton is

not new. Several pneumatic and electric exoskeletons were developed at the University

of Belgrade in the 60’s and 70’s to aid paraplegics [1]. Although these early devices

were limited to predefined motions and had limited success, balancing algorithms

developed for them [1] are still used in many bipedal robots today [3]. The Hardiman

exoskeleton, developed by General Electric in the 1960’s, attempted to use human

position sensing to control motion [4]. Unfortunately, difficulties in human sensing and

system complexity kept it from ever walking. Some attempts in the 1980’s (such as the

Electric Arm Enhancers at the University of California, Berkeley) used force sensors for

control. Still others (such as the HAL-3 robot developed at the University of Tsukuba)

used EMG signals given off by the human for control [5] [6]. Whereas the specific goals,

control architecture and sensory abilities of these attempts have differed, they all suffered

from the same problems - difficulty measuring their human operators, portable power

supply limitations, and system complexity. These limitations prevented all of these

systems from ever demonstrating smooth walking with energetic autonomy.


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The Berkeley Lower Extremity Exoskeleton (BLEEX) project, funded by the

Defense Advanced Research Project Agency (DARPA), attempted to resolve the

shortcomings of previous exoskeletons by a three-pronged approach. First, a novel

control architecture was developed that estimates the forces exerted by the wearer on the

exoskeleton from only measurements of the exoskeleton itself. This eliminated

problematic sensing elements on the human while retaining operator control of the

exoskeleton via distributed physical contact. Second, a series of high specific power and

specific energy power supplies were developed that were small enough to be exoskeleton

portable. Finally, a simplified architecture that only powered sagittal joints (ankle, knee

and hip) was chosen to decrease complexity and power consumption. This paper will

focus on the development of the simplified kinematic architecture and hydraulic actuation

system.

Anthropomorp h ic Des ign Approach

In order for an exoskeleton to support the payload with minimal effort by the

wearer, a load path must exist between the load and the ground that is independent of the

wearer. A successful design would be actuated and powered such that the load would be

supported above the ground by the exoskeleton while retaining enough compliancy to be

easily maneuvered by the human operator. A simplified single degree-of-freedom

schematic of this concept is shown in Figure 2 below.


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Exo Feet

Human

Exoskeleton

Legs

Human-Machine

Backpack

Interface

Human-Machine

Foot Interface

Ground

Exoskeleton Spine

Payload G r a v i t y

Figure 2: Schematic Exoskeleton Representation

The exoskeleton is represented by a controllable actuator that supports the load.

The human is represented by a smaller, un-controlled actuator that also supports the load.

Since the device is ideally wearable (as opposed to vehicular) in nature, kinematical

correspondence must be maintained between the machine and the human operator in at

least 2 places – the back where the load is attached, and the feet where the system

contacts the ground, as shown in Figure 2 above. Thus, the human connects and

interfaces with the exoskeleton through compliant elements (represented in Figure 2 by

springs). Ideally, if the exoskeleton is properly actuated, the forces exerted on the human

through the compliant backpack and foot interfaces can be minimized and made

independent of payload.

There are two different kinematical approaches to achieving the load-bearing

architecture in Figure 2. In the non-anthropomorphic approach, a robotic system is

designed that attaches semi-compliantly to the human operator at the required places

(back and feet) while having different degrees of freedom and flexibility than the human.

The advantages of such an approach are improved mechanical advantage and increased


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design freedom. In the opposing anthropomorphic approach, a mechanism that has

approximately the same size, shape and kinematics of the operator is designed –

hopefully yielding a much less obtrusive device. Examples of each approach are detailed

in Figure 3 and Figure 4 below.

Figure 3: Non-Anthropomorphic Exoskeleton1

Figure 4: Anthropomorphic Exoskeleton2

1 http://bleex.me.berkeley.edu/elecextender.htm

2 http://fourier.vuse.vanderbilt.edu/cim/projects/exoskeleton.htm


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An anthropomorphic approach was chosen with ankle, knee and hip joints closely

matching those of the human. It was hoped that an anthropomorphic architecture would

be least obtrusive and only minimally impede the wearer.

Design Impl icat ions of Basic Contro l Methodolog y

Although the architecture laid out in Figure 2 appears relatively simple, the design

implementation of a multi-degree-of-freedom exoskeleton system is much more difficult.

One of the most challenging difficulties is determining the appropriate model for control.

Figure 5 below shows a simplified model of the exoskeleton/human operator system

when one leg is on the ground. This model is a slightly more refined version of Figure 2

that shows both legs. Each leg of the human is modeled as an actuator that behaves

independently of the exoskeleton control system. Each exoskeleton leg is modeled as a

large actuator capable of supporting the combined exoskeleton and payload mass. The

connections between the wearer and the exoskeleton are modeled as semi-compliant

springs of unknown stiffness.


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Exo Stance Foot

HumanStance Leg

Exoskeleton

Stance Leg

Human-MachineBackpackInterface

Human-MachineFoot Interface

Ground

Exo Swing Foot

Human

Swing Leg

ExoskeletonSwing Leg

Human-MachineFoot Interface

Human Torso

Exoskeleton Spine


Figure 5: Simplified Single Stance Model of Exoskeleton/Human System

A free-body analysis of Figure 5 above can be used to show that by actuating the

stance and swing legs of the exoskeleton, the forces exerted on the human through the

human-machine interfaces can be minimized. In the simple gravity compensation case

(inertial forces are ignored), static equilibrium can be maintained by generating enough

upward force with the stance leg to counter the weight of the payload, exoskeleton torso

and swing leg. Similarly, the exoskeleton swing leg needs only to provide enough

vertical lift to counter the weight of the exoskeleton foot. Any additional upward force

exerted by the human, no matter how small, will simply tend to accelerate the payload

and exoskeleton in the appropriate direction. Hence the human can lift a very large

payload with only a small force. If this concept is carried out further and the exoskeleton

appropriately instrumented and controlled, even the inertial load forces can be minimized

in a similar manner.

Unfortunately, although the single-stance model of the exoskeleton system

becomes statically determinant in the limit of human-machine forces at the back and


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swing leg going to zero, it is statically indeterminate in the double-stance case. The

double-stance model is shown in Figure 6 below.

Left Exo Foot

HumanLeft Leg

ExoskeletonLeft Leg

Human-Machine

BackpackInterface

Human-MachineLeft Foot

Interface

Ground

Right Exo Foot

HumanRight Leg

ExoskeletonRight Leg

Human-MachineRight Foot

Interface

Human Torso

Exoskeleton Spine


Figure 6: Simplified Double-Stance Schematic of Exoskeleton/Human System

When both legs are on the ground, both the human and the exoskeleton form

parallel mechanisms. The system becomes statically indeterminate and the relative load

distribution between the left and right human foot is unknown without direct sensing.

This presents a problem to exoskeleton control. In double-stance mode, there are an

infinite number of ways the load can be distributed between the left and right legs.

When one leg is lifted (single stance mode), there is only a single solution with the stance

leg supporting the mass of both payload and exoskeleton. Since the system model

changes as one leg contacts or leaves the ground, some sort of sensing is needed to

determine which model to use. In the simplest form, a set of binary contact switches

should suffice. Furthermore, unless the change in model can be anticipated by the

controller, the actuation commands can become very abrupt - manifesting to poor

performance and control instability.


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A major control challenge is to construct an algorithm for choosing the load

distribution in the double-stance case based on various system sensory inputs. Several

possible schemes include force distribution based on the relative foot and cg positions

(usually more load is concentrated on the foot closer to the cg), timing (load can be

distributed based on data from human walking), or directly sensed load distribution in the

wearer. All of these methods are currently being explored.

Range of Mot ion and Degrees of Freedom

Although the simplified conceptual exoskeletons of Figure 5 and Figure 6 can be

used to gain an understanding of how an exoskeleton should function, a successful design

must have considerably more degrees of freedom. Humans are extremely flexible and

have many degrees of freedom. A kinematic mock-up was used to help determine

preliminary degrees of freedom and ranges of motion necessary for comfortable motion.

This is shown in Figure 7 below.


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Figure 7: Kinematic Mock-Up of BLEEX

Figure 8 below shows the degrees-of-freedom chosen for the 1st generation

BLEEX prototype. This includes powered hip, knee and ankle flexion and compliant toe

flexion in the sagittal plane, un-powered hip abduction in the coronal plane, and un-

powered foot rotation in the transverse plane. The sagittal plane degrees-of-freedom are

necessary for normal walking. The hip abductions are needed for proper balance and

maneuverability. The foot rotations are necessary for turning.


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Figure 8: Degrees of Freedom of 1st Generation BLEEX

The kinematical mock-up shown in Figure 7 was also used to determine the

minimum required ranges of motion of each joint to allow sufficient maneuverability for

common tasks such as walking, stair-climbing and squatting. An average person can flex

their ankles anywhere from -38° to +35°, their knees to 159° (while kneeling), and their

hips to 113° (while prone) [11]. The required BLEEX ranges of motion were set at ±45°

ankle flexion/extension, 5° to 126° knee flexion, and 10° hip extension to 115° hip

flexion. Experiments with the mock-up showed that the increased ankle flexion/extension


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was needed in the exoskeleton to compensate for the lack of several smaller degrees of

freedom in the exoskeleton foot. Both the knee and hip ranges of motion were selected to

allow squatting.

Center of Grav i ty Constra in ts

In order for the exoskeleton system to be capable of balancing itself, the center of

Gravity (CG) of the exoskeleton must be far enough forward that the net

human/exoskeleton combined CG must fall over the footprint of the system. Should the

combined CG fall outside the footprint, the system will be incapable of balancing itself

and simply fall over. This is shown in Figure 9 below.

Figure 9: System CG Schematic


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Clinical Gait Analysis as a Design Tool

Reason ing and Assum pt ions

One of the most powerful tools available when designing a walking exoskeleton is

the enormous body of data governing human walking. If the robotic exoskeleton is

designed with similar kinematics as a human (i.e. an anthropomorphic design), and with

similar mass and inertia properties, many of the actuation and power supply requirements

can be extrapolated from Clinical Gait Analysis (CGA) data on human walking.

Although such data is not perfect, may require scaling and other manipulation, and

cannot yield precise quantification of requirements, it nonetheless can offer a 1st

order

reasonable approximation of the general behavior of a similarly scaled exoskeleton.

Human joint angles and torques for a typical walking cycle were obtained in the

form of independently collected Clinical Gait Analysis (CGA) data. CGA angle data is

typically collected via human video motion capture. CGA torque data is then calculated

by estimating limb masses and inertias and applying inverse kinematics to the motion

data. Given the variations in individual gait and measuring methods, three independent

sources of CGA data were utilized for the analysis and design of the exoskeleton [8]-[10].

The CGA data from [8], [9] and [10] was further modified to yield estimates of

exoskeleton actuation requirements as opposed to experimental observations of human

subjects. This included the linear scaling of joint torques to represent a 75kg person (the

projected weight of an exoskeleton and its payload not including its wearer) and the

addition of pelvic tilt or lower back angles (depending on data available) to the hip angle

in order to account for the reduced degrees of freedom of the exoskeleton (for simplicity


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the exoskeleton hip could provide sufficient range of motion to account for lower back

flexion and pelvic tilt). The CGA data from [8], [9] and [10] were thus adjusted to yield

estimates of required exoskeleton angle, torque and power parameters. The sign

conventions used are shown in Figure 10 below.

Figure 10: CGA Sign Conventions

Each joint angle is measured as the positive counterclockwise displacement of the

distal link from the proximal link (zero in standing position) with the person oriented as

shown. In the position shown, the hip angle is positive whereas both the knee and ankle

angles are negative. Torque is measured as positive acting counterclockwise on the distal

link.

Join t A ngles & Flex ib i l i ty Requirements

The minimum required joint angles to walk can be derived by examining joint

angles during a typical step. Figure 11 below shows a typical human gait cycle. Any

successful exoskeleton must be at least as flexible as the person shown in Figure 11.


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Figure 11: Typical Gait Cycle [7]

CGA joint angles vs. time are shown from three different sources in Figure 12,

Figure 13 and Figure 14 below. Heel strike occurs at time=0 with toe-off occurring at

~time=0.6 seconds.

0 0.2 0.4 0.6 0.8 1-25

-20

-15

-10

-5

0

5

10

TOHS STANCE SWING

time(s)

a n g l e ( d e g )

[8]

[9]

[10]

Figure 12: CGA Ankle Angle vs. Time

Figure 12 shows the adjusted CGA ankle angle data for a 75 kg person walking

on flat ground at approximately 1.3 m/s vs. time. The minimum angle (extension) is ~-


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20° and occurs just after toe-off. The maximum angle (flexion) is ~+15° and occurs in

late stance phase. Although Figure 12 shows a small range of motion while walking,

greater ranges of motion are required for other movements. In fact an average human can

flex their ankles anywhere from -38° to +35° [11]. Following range of motion

experiments using the mock-up shown in Figure 7, the BLEEX ankle was designed to

have a maximum flexibility of ±45° to account for additional flexibility in the human

foot.

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

STANCE SWINGTOHS

time(s)

a n g l e ( d e g )

[8]

[9][10]

Figure 13: CGA Knee Angle vs. Time

The knee angle in Figure 13 is characterized by a slight buckling of the knee in

early stance to absorb the impact of heel strike followed by a slight extension in mid-

stance. In late stance the knee undergoes a large flexion and followed by extension in

mid swing. The maximum knee angle is ~0° (any more would correspond to hyper

extension of the knee) whereas the minimum angle is ~-60° flexion. This knee flexion

decreases the effective length of the leg, allowing the foot to clear the ground during

forward swing. Although the required knee flexion to walk is limited to approximately


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17

70°, the human has significantly more flexibility [11]. The exoskeleton knee was thus

designed with a maximum flexion of 126° to account for the greater flexibility of the

human knee.

0 0.2 0.4 0.6 0.8 1-30

-20

-10

0

10

20

30

40STANCE SWINGTOHS

time(s)

a n g l e ( d e g )

[8]

[9]

[10]

Figure 14: CGA Hip Angle vs. Time

Figure 14 above details the estimated exoskeleton hip mobility required to walk

based on human CGA data. The hip has an approximately sinusoidal behavior with the

thigh oscillating between being flexed upward ~+30° to being extended back ~-20°. The

hip moves in a sinusoidal pattern with the hip flexed upward at heel-strike to allow the

foot to contact the ground anterior to the center-of-gravity. This is followed by an

extension of the hip through most of stance phase and a flexion through swing phase

prior to subsequent heel-strike. As with the ankle and knee joints, additional hip range of

motion may be required for other motions and was thus accounted for in the BLEEX

design.


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18

Jo in t Torques & Actua t ion Requ i rements

If both the kinematical and dynamic properties of the exoskeleton are sufficiently

similar to those of the humans analyzed in CGA data, the joint torques in the CGA data

should be a good approximation of the required actuation torques to make the

exoskeleton walk at similar speeds. Thus analysis of CGA data can provide a first order

approximation of exoskeleton actuator requirements.

0 0.2 0.4 0.6 0.8 1-120

-100

-80

-60

-40

-20

0

20TOHS

STANCESWING

time(s)

T o r q u e ( N * m )

[8][9][10]

Figure 15: CGA Ankle Torque vs. Time

Figure 15 above shows the estimated torque required by a 75 kg human (or a

similarly sized exoskeleton) to walk. Peak positive torque (flexion of the foot) is very

slight (~10 N·m) and occurs just after heel strike. Peak negative torque (extension of the

foot) is very large (~-120 N·m) and occurs in late stance phase. The ankle torque in

Figure 15 is almost entirely negative – making unidirectional actuators an ideal actuation

choice. This asymmetry also implies a preferred mounting orientation for asymmetric


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19

actuators. Conversely, if symmetric bi-directional actuators are considered, spring-

loading would facilitate the use of smaller and more efficient actuators.

In addition to the torque direction, the required duty cycle provides an important

clue to actuator design. Although ankle torques are large during stance phase (0-0.6 sec),

they are negligible during swing phase. This opens the possibility for design of a system

that disengages the ankle actuators from the exoskeleton during swing to save power.

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

0

10

20

30

40

50

60TOHS STANCE SWING

time(s)

T o r q u e ( N * m )

[8]

[9]

[10]

Figure 16: CGA Knee Torque vs. Time

Figure 16 above shows that during normal human walking the knee torque is

primarily positive, corresponding to knee extension. The knee torque is bi-directional

with an initial ~-35 N·m (flexion) spike on heel strike corresponding to impact

absorption, followed by large positive extension torques (~60 N·m) to keep knee from

buckling in stance phase. The required knee torque has both positive and negative

components, indicating the need for a bi-directional actuator. The highest peak torque is


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found in extension (~60 N·m) during early stance; hence asymmetric actuators should be

biased to provide greater extension torque.

0 0.2 0.4 0.6 0.8 1-80

-60

-40

-20

0

20

40

60

80

TOHS STANCE SWING

time(s)

T o r q u e ( N * m )

[8]

[9]

[10]

Figure 17: CGA Hip Torque vs. Time

The hip torque in Figure 17 above is relatively symmetric; hence a bi-directional

hip actuator capable of supplying the necessary -80 to +60 N·m of torque is required.

The torque is negative during early stance as the hip must provide extension torque to

carry the load on the stance leg. The torque goes positive in late stance and early swing

as the hip must exert flexion torques to propel the foot forward during swing. During late

swing the torque goes negative again as the hip provides the extension torque necessary

to decelerate the foot prior to heel-strike.

Ins tantaneous Joint Powers

Another important tool in the design of an exoskeleton actuation system is the

analysis of CGA instantaneous joint powers. Positive power indicates mechanical energy


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21

production and hence the need for actuation. Negative power indicates energy absorption

which may be achievable with dampers or brakes. Similarly, power plots with sharp

spikes indicate the need for low duty-cycle, high peak-output actuators while relatively

stable power plots may indicate high duty-cycle actuators are needed.

The instantaneous joint mechanical power required by a 75 kg human (or an

equivalently sized exoskeleton) to walk can be calculated by multiplying the

instantaneous joint torque by the rate of change of the joint angle, as shown in Equation 1

below.

( )intintint jo jo jodt

d T P θ⋅=

Equation 1: Instantaneous Joint Mechanical Power

The instantaneous ankle mechanical power is plotted in Figure 18 below. This

plot indicates that the ankle absorbs energy during the first half of the stance phase and

releases energy just before toe off. The average ankle power is also positive, indicating

that power production is required at the ankle.


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0 0.2 0.4 0.6 0.8 1-100

-50

0

50

100

150

200

250

300

TOHS STANCE SWING

time(s)

P o w e r ( W )

[8]

[9][10]

[8] average: 2.00[9] average: 20.31

[10] average: 5.25

Figure 18: CGA Instantaneous Ankle Power

Figure 18 shows a relatively low average power consumption (mechanical work

per step), but has a very pronounced peak just before toe-off. This high power spike is

indicative of the power needed to propel the human forward just before toe-off.

Instantaneous power plots such as this are typical of low duty-cycle actuators.

Figure 19 below shows the power required by at the knee by a 75 kg person while

walking.


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0 0.2 0.4 0.6 0.8 1-200

-150

-100

-50

0

50

100TOHS STANCE SWING

time(s)

P o w e r ( W )

[8]

[9][10][8] average: -10.99[9] average: -24.55[10] average: -28.50

Figure 19: CGA Instantaneous Knee Power

Figure 19 above shows that although the instantaneous mechanical power in the

knee goes both positive and negative (corresponding to power creation and absorption),

the average power is negative. Thus the knee (on average) absorbs energy. This is why

many prosthetics use small dampers to mimic knee dynamics. The increased energy

expenditure observed in wearers of passively damped knee prosthetics can be partially

explained by the small regions where positive actuation power is required. Wearers of

such devices typically swing their hips harder to compensate for the lack of knee

actuation.


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0 0.2 0.4 0.6 0.8 1-80

-60

-40

-20

0

20

40

60

80

100

120

TOHS STANCE SWING

time(s)

P o w e r ( W )

[8]

[9]

[10]

[8] average: 4.54

[9] average: 0.53

[10] average: 11.45

Figure 20: CGA Instantaneous Hip Power

Figure 20 above shows that the hip absorbs power during stance phase and injects

energy during toe-off to propel the torso forward. The average hip mechanical power is

positive, implying the need for an active hip actuator. The roughly sinusoidal shape of

the power curve precludes the use of low duty cycle actuators.

The total CGA power (PCGA) shown in Figure 21 was found by summing the

absolute values of the instantaneous CGA powers for each joint (Figure 18-Figure 20)

over both legs. An average of 127 to 210 W is required to walk. The absolute value of

the joint powers was used as a conservative measure. Since the opposite leg is phase

shifted by half a cycle, the total CGA power repeats at 2Hz – twice the original walking

cycle frequency.


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25

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300

350

400

450

500

TOHS STANCE SWING

time(s)

P o w e r ( W )

[8][9]

[10][8] average: 127[9] average: 175[10] average: 210

Figure 21: Total CGA power of a 75 kg human walking over flat ground at approximately 1.3 m/s

Actuator Select ion: Dou ble-Act ing L inear Hydraul ic A ctuators

After the initial analysis of CGA data, double-acting linear hydraulic cylinders

were chosen as the most effective form of actuation for the exoskeleton. Purely passive

elements such as dampers were ruled out after analyzing the joint mechanical power plots

from CGA data in Figure 18 - Figure 20. These plots showed that the ankle, knee and hip

joints all had periods of high mechanical power usage. Electrical actuators were ruled

out for weight and complexity reasons. The joint torques in Figure 15, Figure 16, and

Figure 17 were all of relatively large magnitude while the angular velocities in Figure 12,

Figure 13, and Figure 14 were all relatively small. This combination would require either

prohibitively large and heavy motors, or some sort of gear reduction that would be

subject to friction. Lightweight pneumatic actuators were ruled out due partly to control

restrictions (force control via. compressible air is very difficult), and partly due to power

restriction (compressing high-pressure air is very inefficient) [13], [14]. That left light-


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26

weight hydraulic actuators as a possibility. Double-acting linear hydraulic actuators in

triangular mechanisms were chosen as a light-weight simple way to achieve very high

torques with good control fidelity.

rodD

actD

push

pull

rodD

actD

push

pull

Figure 22: Bi-directional linear hydraulic actuator schematic.

The magnitudes of the maximum static pushing and pulling forces (F maxpush &

Fmaxpull) that can be applied by a bi-directional actuator are given by Equation 2 and

Equation 3 as a function of supply pressure (Psupply), actuator bore diameter (actD), and

rod diameter (rodD).

( )

4P

2

supplymax

actD F push

π⋅=

Equation 2: Magnitude of Maximum Extension Force from Double-Acting Hydraulic Cylinder

( )4

P22

supplymax

rodDactD F pull

−⋅=

π

Equation 3: Magnitude of Maximum Retraction Force from Double-Acting Hydraulic Cylinder

Distal link

P lower

P pper

Actuator

Vector

(C) Moment Arm

(R )

Proximal link

P

P

Figure 23: Triangular configuration of a linear hydraulic actuator.


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27

Figure 23 shows a linear hydraulic actuator arranged to produce a joint torque. C

is the actuator vector from the mount on the distal link (P lower ) to the proximal link

(Pupper

). The moment arm vector R is the perpendicular vector from the center of the joint

to the actuator vector. Vector expressions for the maximum possible torque from an

extending and a contracting actuator (T pus h & T pull) are given by Equation 4 and Equation

5.

( )max push pushT R F = ×r r r

Equation 4: Maximum Potential Actuation Joint Torque from Actuator Extension

( )maxull pull T R F = × −r r r

Equation 5: Maximum Potential Actuation Joint Torque from Actuator Retraction

Actuat ion Design Synthes is and Iterat ion

Figure 23, Equation 4 and Equation 5 show that the placements of the actuator

end points have a direct effect on the magnitude of the joint actuator torque. The farther

the actuator is from the joint, the larger the actuator torque and volumetric displacements

for a given motion. Similarly, actuators with larger cross-sections may produce more

force and torque, but will require larger volumetric displacements for a given angular

displacement. Larger volumetric displacements correspond to higher hydraulic flows and

increased power consumption for a given motion.

The problem of actuation design is to find a combination of actuator cross-

section, actuator endpoints, and supply pressure that minimizes the hydraulic power


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28

consumption subject to several constraints. The design must reach the required ranges of

motion determined from mock-up testing, provide sufficient torque to walk (Figure 15-

Figure 17), and maintain a minimum nominal torque at all reachable joint angles.

Actuators are limited to discrete commercially available sizes while the geometry is

limited by interference with exoskeleton links. In general there is no unique solution and

many feasible possibilities exist. Although on the surface this problem was an ideal

candidate for optimization, initial optimization studies proved difficult to implement

given the complex component geometries and preliminary results did not show enough

improvement to justify the use of optimization tools over the manual iterative method

described below.

In order to find a feasible actuator configuration, an initial actuator size (cross-

section, minimum length, and stroke), hydraulic supply pressure, and one of the end-point

positions were chosen for each joint. Using the required range of motion, a 2-Position

kinematical synthesis was used to determine the second actuator end-point position.

Figure 18 below details the graphical synthesis procedure used for the ankle joint.

Joint Axis

Moving Pivot

(Position 1)

Moving Pivot(Position 2)

Moving Pivot

(Neutral Position)

Ground Pivot

Ground Link

Moving Link

L2

L1

Joint Axis

Moving Pivot

(Position 1)

Moving Pivot(Position 2)

Moving Pivot

(Neutral Position)

Ground Pivot

Ground Link

Moving Link

L2

L1

Figure 24: 2-Position kinematical synthesis of ankle actuator placement.


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29

A linear actuator of contracted length L2 and extended length L1 was chosen.

The position of the moving pivot in the neutral position was chosen. Since the required

ranges of motion were already determined for each joint based on range of motion studies

and mock-up testing, this defined the moving pivot location at the limits of motion

(positions 1 & 2). The position of the ground pivot was found by intersecting arcs of

radii L1 and L2 centered at the moving pivot positions 1 & 2.

Once the positions of the actuator mounts were located, the available actuator

torques could be calculated as a function of joint angle from Equation 4 and Equation 5.

These results were then compared with the required torques shown in Figure 15 - Figure

17. This process was iterated with different actuator sizes and mount points until a

solution with sufficient torque minimal power consumption was found. Figure 25 -

Figure 27 below show the available actuation torque versus joint angle for the chosen

ankle, knee and hip designs. These were found by applying Equation 4 and Equation 5 to

the results of the respective ankle, knee and hip 2-position kinematical syntheses such as

that shown in Figure 24 for the ankle.


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30

-50 -40 -30 -20 -10 0 10 20 30 40 50-200

-150

-100

-50

0

50

100

150

200

angle(deg)

T o r q u e ( N * m

)

pull actuator limit

push actuator limit

Figure 25: Maximum Potential Ankle Actuation Torque vs. Angle

-140 -120 -100 -80 -60 -40 -20 0-150

-100

-50

0

50

100

150

angle(deg)

T o r q u e ( N * m ) pull actuator limit

push actuator limit

Figure 26: Maximum Potential Knee Actuation Torque vs. Angle


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31

-20 0 20 40 60 80 100 120-150

-100

-50

0

50

100

150

angle(deg)

T o r q u e ( N * m

)pull actuator limitpush actuator limit

Figure 27: Maximum Potential Hip Actuation Torque vs. Angle

Torque-Ang le Relat ionsh ip & A ctuator Kin emat ics

Although the torque vs. time plots shown in Figure 15, Figure 16 and Figure 17

provide a good baseline actuation requirement for a human-sized exoskeleton, further

information was gained by consolidating this data with CGA joint angles. Although

requiring an actuator to be capable of producing the peak required torque over all joint

angles will insure the design works, such a requirement is potentially over-constraining.

The output torque from linear actuator driven mechanisms is angle dependent and may

still be sufficient to walk despite having minimum actuation torque values far lower than

the peak required CGA torques. If the CGA data for both torque (Figure 15-Figure 17)

and angle (Figure 12-Figure 14) are re-parametrized and consolidated to eliminate time,

the resulting torque vs. angle plots can provide results much more relevant to linear

actuation selection and placement. These CGA joint torque versus angle plots can then


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32

be compared to maximum potential actuation torque versus angle plots (Figure 25 -

Figure 27 above) to evaluate potential actuation geometries.

Figure 28 below shows the CGA ankle torque vs. time for a typical step. The

outer encasing lines are identical to those in Figure 25 and show the theoretical torque

capability of the linear hydraulic actuator that was implemented in the BLEEX prototype.

This actuator sizing and placement was calculated by iteration of the graphical 2-position

kinematical synthesis shown in Figure 24 above. Note that although the minimum

negative torque output of the actuator (~-90 N-m) is less than the negative torque peak in

the CGA data (~-100 N-m), this design is still sufficient since the actuator is capable of

producing greater torques at the necessary angles.

-50 -40 -30 -20 -10 0 10 20 30 40 50-200

-150

-100

-50

0

50

100

150

200

angle(deg)

T o r q u e ( N * m )

[8][9][10]

pull actuator limit

push actuator limit

Figure 28: CGA Ankle Torque vs. Angle

Figure 29 below shows the torque vs. angle plot of CGA data of a human knee.

The choice of a linear actuator system with a decreasing moment arm at increasing knee

flexion yielded a design with very little torque output at large knee angles where it is not

needed.


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33

-140 -120 -100 -80 -60 -40 -20 0 20-150

-100

-50

0

50

100

150

angle(deg)

T o r q u e ( N * m )

[8]

[9]

[10]

pull actuator limit

push actuator limit

Figure 29: CGA Knee Torque vs. Angle

Figure 30 below shows the torque vs. angle required by the hip according to CGA

data. It also shows the maximum torque output from the linear hydraulic actuation

scheme selected for powering the exoskeleton hip.

-40 -20 0 20 40 60 80 100 120-150

-100

-50

0

50

100

150

angle(deg)

T o r q u e ( N * m ) [8]

[9][10]pull actuator limitpush actuator limit

Figure 30: CGA Hip Torque vs. Angle


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34

In addition to removing the unnecessary constraints added by designing to torque

vs. time plots alone, designing with torque vs. angle plots can also yield more energy

efficient designs. For cyclical motions such as walking, the area enclosed by clockwise

encirclements on a torque vs. angle plot represents the net mechanical work per cycle that

must by done on the system to accomplish the motion. Similarly, the areas enclosed by

the maximum torque vs. angle plots for an actuation system represent the amount of

energy that would be consumed if full power were applied to the actuator over a step.

The closer the maximum actuation torque envelopes fall to the required torques, the more

efficient the design. This will be addressed in more detail in following sections.

Figure 31 shows the linear actuator designs evaluated in Figure 28 - Figure 30

above. The ankle requires predominately negative torque (Figure 15); hence the ankle

actuator is positioned anterior to the joint whereby its greater extension force capacity

can be exploited. Similarly, the knee actuator is placed behind the knee, where it can

apply the greater required extension torques (Figure 16).

Figure 31: Model of 1st Generation BLEEX Prototype.

Hip

Actuator

Ankle

Actuator

Knee Actuator

Exoskeleton

Spine

Attachment

to Harness

Hip Joint

Knee Joint

Payload &

Power

Supply

Mount

Exoskeleton

Foot Ankle Joint


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35

Deta i led Hydraul ic A ctuat ion Model

The derivations of the actuator torques in Figure 28 - Figure 30 were for static

conditions only. Although such an analysis would guarantee that the actuators could

sufficient torque to walk in a static sense, in actual operation pressure drops across the

valve at high flows may limit torque production to much lower values. A given actuator

design will be capable of producing less torque when moving very quickly than when

stationary. In order to quantify and analyze this power limitation, a much more detailed

dynamic model of a servovalve is necessary.

The model in Figure 22 can also be used to calculate the hydraulic flows

necessary to drive each actuator. The hydraulic flow rates into and out of the cylinder

ports is calculated as a function of linear actuator speed and cylinder dimensions in

Equation 6 below. These flows are important to the exoskeleton design because they

govern both the hydraulic line sizes and the hydraulic power supply requirements.

( )

⋅−=

⋅=

dt

dL D DQ

dt

dL DQ

Q

Q

C rod boreC

C boreC

C

C

22

2

2

1

2

1

4

4

cylinder hydraulicof portsiderodof outflowratefluidHydraulic:

cylinder hydraulicof portside pistonintoflowratefluidHydraulic:

π

π

Equation 6: Hydraulic Flow through Double-Acting Hydraulic Cylinder

Figure 32 below is a schematic representation of a typical bi-directional hydraulic

cylinder driven by a 4-way, 3-position servovalve. The system is powered by a constant

high pressure source and drains to a constant low pressure reservoir.


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3-Way Closed Center

Hydraulic Servovalve

Bi-Directional

Hydraulic Cylinder

Reservoir

Hydraulic High

Pressure Source

Figure 32: Hydraulic Actuation Schematic

Figure 33 is a more detailed schematic of the internal working of a typical spool

driven 4-way, 3 position hydraulic servovalve.

Control

Port 2

(C2)

Control

Port 1

(C1)

Return Port

(R)

Supply Port

(S)

Spool

1 2 3 4xV

Q R

Q S

Q C 1

Q C 2

C1C2

R S Q 1

Q 2 Q 3

Q 4

Figure 33: 4-Way, 3-Position Closed-Center Servovalve Diagram

Spool driven hydraulic servovalves such as the on in Figure 33 work by

electromagnetically driving a spool (possibly with a dual-stage hydraulic assist). The

pressures at output ports (C1) and (C2) are controlled by changing the spool position to

modulate orifice sizes and throttling losses in the valve. Power flows into the valve in the


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37

form of high pressure fluid from the supply (S) and is regulated by throttling across

orifices to produce lower pressure flows at the outputs. By electromagnetically

displacing the spool from by some distance xv (non-dimensionalized from -1 to +1) from

its centered position, positive or negative pressure differentials can be created between

control ports. Equation 7 below lists the definitions and terminology necessary to

quantify the model.

actuator by producedtorque:T

returnof out powerhydraulic-supplyfromvalveinto powerhydraulic:W

actuator by produced powermechanical:W

orificesacrossgthrottlintodueloss power:W

densityfluid:

sideC2onactuatorof areaeffective:AsideC1onactuatorof areaeffective:A

nsectionacrossareaorrificeeffective:A

1)to(-1centerfromntdisplacemespoolvalvenormalized:x

nsectionacrossleakage)rflowrate(ofluid:Q

C2intoflowfluid:Q

C1of outflowfluid:Q

linereturntovalveof outflowfluid:Q

linesupplyfromvalveintoflowfluid:Q

C2 portat pressurefluid:P

C1 portat pressurefluid:P

portreturnat pressurefluid:P

portsupplyat pressurefluid:P

hydraulic

mech

loss

C2

C1

n

v

n

C2

C1

R

S

C2

C1

R

s

ρ

+

Equation 7: Valve Model Definitions & Terminology

A more intuitive representation of the 4-way, 3-position hydraulic valve shown in

Figure 33 above is the wheatstone bridge electrical analogy shown in Figure 34 below

[15]. Hydraulic flows are treated as electrical currents, pressure differentials as potential

differences and pressure drops as resistive elements.


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QS

Q 2

Q 3

QR

Q 4Q 1

C1 C2

R

S

QC1 Q C2

Actuator

Figure 34: 4-Way, 3-Position Servovalve Wheatstone Bridge Analogy

Figure 34 can be used to analyze a standard 4-way, 3-position hydraulic

servovalve. The spool position controls the relative values of the pressure drops across

orifices 1-4 (represented by resistive elements in Figure 34). Thus by moving the spool,

the pressure differential across the actuator can be controlled. The flows can be

calculated by standard orifice equations in Equation 8 below. The valve coefficient (Cd)

is a constant loss coefficient and the flow path cross-sectional areas (Ai) vary with spool

displacement.

( )

( )

( )

( )

ρ

ρ

ρ

ρ

RC d

C S d

C S d

RC d

P P AC Q

P P AC Q

P P AC Q

P P AC Q

−⋅=

−⋅=

−⋅=

−⋅=

244

233

122

111

2

2

2

2

Equation 8: 4-way, 3-position Hydraulic Servovalve Orifice Equations Governing Flow


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39

Several assumptions can be made to further simplify the analysis. These include

assuming negligible leakages across closed sections of the valve, conservation of fluid in

the actuator and valve, and no regeneration. These are summarized in Equation 9 below.

Note that due to the rod asymmetry of the double-acting cylinders, the fluid flow into one

actuator port does not equal the flow out of the other port, but for relatively small ratios

of rod to piston cross sectional areas, this effect can be ignored.

( )

( )

( )

1 3

2 4

1 2 3 4

1 2

1 2

1 3 2 4

1. No Leakage

0 0

0 0

0 0

2. Conservation of fluid in actuator & valve

3. No Regeneration

, 0

4. Symmetric Spool Orifice Areas

,

v

v

v

C C

S R

S C C R

S R

Assumptions

Q Q x

Q Q x

Q Q Q Q x

Q Q

Q Q

P P ,P P

Q Q

A A A A

≈ ≈ >

≈ ≈ <

≈ ≈ ≈ ≈ =

≈

≈

≥ ≥

≥

≈ ≈

5. Negligable Return Line Pressure

0 R P ≈

Equation 9: Valve Modeling Assumptions & Simplifications

Combining the simplifications of Equation 9 above and the governing equations

of Equation 8 yields the simplification that the supply pressure is approximately equal to

the sum of the actuator port pressures. This result is derived for both positive and

negative spool displacements in Equation 10 below.


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40

( ) ( )

( ) ( )

( ) ( )

( ) ( )

1 3 2 4

1 2

2 4

1 2

1 2

2 4 1 3

1 2

1 3

1 2

1 2

0

0

2 2

0

0

2 2

v

S C C R

d d

S C C R

S C C

v

C R S C

d d

C R S C

S C C

x

Q Q Q Q

P P P P C A C A

P P P P

P P P

x

Q Q Q Q

P P P P C A C A

P P P P

P P P

ρ ρ

ρ ρ

>

= = → ≈

− −⋅ ≈ ⋅

− ≈ −≈ +

<= = → ≈

− −⋅ ≈ ⋅

− ≈ −

≈ +

Equation 10: Supply Pressure as a function of Actuator Port Pressures for both Positive andNegatively Displaced Spool

In order to simplify the analysis, a mathematical construct called the load

pressure was defined as the differential pressure between actuator ports, as shown in

Equation 11 below.

1 2

:

L C C

Define

P P P = −

Equation 11: Load Pressure Definition

Similarly, the concept of a load flow was defined as the hydraulic fluid flow rate

through the actuator (positive extending, negative contracting).

( )

( )

1

2

:

0

0

L C v

L C v

Define

Q Q x

Q Q x

= >

= <

Equation 12: Definition of Load Flow


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The crux of the hydraulic valve selection process is to appropriately size the valve

so that sufficient load flow can be maintained at the necessary load pressures.

From the wheatstone bridge analogy of Figure 34, and Equation 7 - Equation 11,

the load flow can be calculated as a function of orifice parameters, fluid density load

pressure and supply pressure for both positively and negatively displaced spool positions.

( )

( )

( )

1 2

1

2

1 2 1

2

1 2

2

2

if 0

2

2

1

v

L C

S C

d

S C C C

d

S C C

d

d LS

S

x

Q Q Q

P P C A

P P P P C A

P P P C A

C A P P

P

ρ

ρ

ρ

ρ

>

= ≈

−≈ ⋅

+ + −≈ ⋅

− −≈ ⋅

⋅≈ −

Equation 13: Load Flow as a Function of Supply Pressure and Load Pressure for Positive SpoolDisplacements

( )

( )

( )

2 3

2

3

1 2 2

3

1 2

3

3

if 0

2

2

1

v

L C

S C

d

S C C C

d

S C C

d

d LS

S

x

Q Q Q

P P C A

P P P P C A

P P P

C A

C A P P

P

ρ

ρ

ρ

ρ

<

= ≈ −

−≈ − ⋅

+ + −≈ − ⋅

+ −

≈ − ⋅

⋅≈ − +

Equation 14: Load Flow as a Function of Supply Pressure and Load Pressure for Negative SpoolDisplacements


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The torque produced by an actuator will be directly proportional to the load

pressure, as shown in Equation 15. Note that the proportionality constant ? is composed

of the product of the instantaneous actuator moment arm and the effective cross-sectional

area of the actuator, thus the proportionality constant differs with actuator position and

direction of force.

{ {{

Pr tan

LTorque proportionality Load essure

cons t

T P λ≈ ⋅

Equation 15: Actuator Torque as a Function of Load Pressure

Similarly, the maximum torque that may be applied by the actuator in either

direction (Tmax) can be defined as being related to the difference between supply and

return pressures by the same constant.

{{

{ {max

Re

tan Pr Pr

S R

proportionality turn Max Supply

cons t essure Actuation essureTorque

T P P λ

≈ ⋅ −

Equation 16: Maximum Possible Actuation Torque as a Function of Supply and Return Pressures

Combining Equation 15 and Equation 16 yields the following simplification.

max

load ratio L L

S R S

T P P

T P P P = = ≈

−

Equation 17: Definition of Load Ratio

Substituting the results of Equation 17 into Equation 13 and Equation 14 yields

Equation 18 and Equation 19 below.


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43

2

max

if 0

1

v

d L S

K

x

C A T Q P

T ρ

>

⋅≈ − 123

Equation 18: Load Flow as a Function of Load Ratio and Supply Pressure for Positive SpoolDisplacement

3

max

if 0

1

v

d L S

K

x

C A T Q P

T ρ

<

⋅≈ − +

123

Equation 19: Load Flow as a Function of Load Ratio and Supply Pressure for Negative SpoolDisplacement

Equation 18 and Equation 19 define the load flow through the valve as a function

of system parameters (supply pressure Ps, fluid density ?, orifice loss coefficient Cd),

valve displacement (orifice cross-sectional areas A2 and A3 both vary with spool

displacement xv), and load ratio (T/Tmax). The valve and fluid related terms are grouped

into a multiplier term (K). Equation 18 and Equation 19 can be further simplified to yield

the maximum possible load flow that can be supported by the specific valve used (with

positive and negative spool displacements respectively) as a function of load ratio. This

can be done by first examining the results of a no-load flow test. In such a test, the valve

is commanded to remain fully open in either direction (xv = +1 or -1) with no load across

the actuator ports (PL = T = 0). The load flow across the actuator ports is measured (Qtest)

and substituted into the results of Equation 18 (or Equation 19 if negative spool

displacement is used) to solve for the constant K at full spool displacement.


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44

( )

( )

( )

( )

{

2

2

no-load rated flow test

1

0

v

L

S test

L test

d test test

K

test d

test

x imposed

P imposed

P P imposed

Q Q measured

C AQ P

P C A K

Q

ρ

ρ

= +

=

=

=

=

∴ = =

Equation 20: No-Load Rated Flow Test

The results of the no-load rated flow test in Equation 20 can be used to

experimentally determine a numerical value for constant K that can be substituted back

into the more general load-flow relationships of Equation 18 and Equation 19 to yield

expressions for the maximum possible load flow for a given valve at full positive and

negative spool displacement as a function of supply pressure and load ratio. This is

shown in Equation 21 below.

max

max

for valve fully open to push/pull

1

1

: maximum possible valve flow in each direction

:experimentally determined valve constant

:constant hydraulic supply pressure

: d

v

L S

L

S

x

K K

T Q K P

T

Q

K

P

T

T

±

±

±

±

= ±

=

= ±

m

imensionless load ratio ranging from -1 to 1+

Equation 21: Maximum Possible Valve Load Flow as a Function of Supply Pressure and Load Ratio


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45

The results of Equation 21 above are plotted as a function of the dimensionless

load ratio in Figure 35 below to graphically illustrate the operational workspace of the

chosen valve.

-1 -0.5 0 0.5 1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Load Ratio = T/Tmax = PL/PS

Q L ( L 3 / s e c )

valve limit

valve limit

Figure 35: Maximum Possible Load Flow Output of Moog Type 30, 31-Series 4-way, 3-positionServovalves as a function of Load Ratio

The shape of Figure 35 makes intuitive sense. The valve has a low positive load

flow output capacity at high positive load ratios. Thus if the actuator is required to push

with high force, it can only extend slowly. This is analogous to a peak power output

limitation. Conversely, the actuator is capable of retracting very quickly (large negative

load flow) while exerting a large extension force (high load ratio) since the valve is

purely dissipative in this mode and hence not limited by power production. There are

two curves (one for positive load flow and one for negative load flow) corresponding to

the two extreme valve spool positions (xv = +1 and xv = -1).

The dual curves in Figure 35 show the maximum load flow that can be supported

by the specific hydraulic valve chosen in each direction. The load flows that are actually


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46

required to walk can be calculated by substituting Equation 6 into Equation 12 and

plotted as a function of load ratio. The resulting plots can be compared to Figure 35 to

determine if the actuator and valve combination chosen is sufficient to meet the dynamic

load flow requirements of walking. The required load flow for the ankle, knee and hip

superimposed on plots of the maximum load flow output are shown below in Figure 36 -

Figure 38 below.

-1 -0.5 0 0.5 1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4


Q L ( L 3 / s e c )

[8]

[9]

[10]

valve limit

valve limit

Figure 36: CGA Valve Load Flow vs. Load Ratio for Ankle


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47

-1 -0.5 0 0.5 1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4


Q L ( L 3 / s e c )

[8]

[9]

[10]valve limit

valve limit

Figure 37: CGA Valve Load Flow vs. Load Ratio for Knee

-1 -0.5 0 0.5 1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4


Q L ( L 3 / s e c )

[8]

[9]

[10]

valve limit

valve limit

Figure 38: CGA Valve Load Flow vs. Load Ratio for Hip

Examination of Figure 36 - Figure 38 above indicate that the actuator sizes,

placements and valve selections for the ankle, knee and hip can all supply sufficient load

flow at the required loads.


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48

BLEEX Power Estimates

Predic ted System Hydraul ic Flow Rates & Power Consumpt ion

The total instantaneous required hydraulic flow was found by summing the

hydraulic flows from each of the actuators in the BLEEX.

int

total extensionor all jo scontraction

Q Q= ∑

Equation 22: Total Hydraulic Flow Required for BLEEX (not including leakages)

Individual actuator flows were found by multiplying the magnitude of

Documents

BLEEX Design