Marc Munzer Phd

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Resolved Motion Control of MobileHydraulic Cranes

by

Marc E. Munzer

Dissertation submitted to the Faculty of Engineering & Scienceat Aalborg University

in partial fulfilment of the requirements for the degree of

Doctor of Philosophy in Electrical Engineering

Aalborg University, Denmark

Institute of Energy Technology

December, 2002


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Aalborg UniversityInstitute of Energy Technology

Pontoppidanstrde 101DK-9220 Aalborg East

Copyright cMarc E. Munzer, 2003

Printed in Denmark by Arco Grafisk A/S

First print, February 2003Second print, August 2004

ISBN 87-89179-44-7

Typeset in LATEX 2.


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Preface

This thesis is submitted to the Faculty of Engineering and Science at Aalborg Universityin partial fulfilment of the requirements for the Ph.D. degree in Electrical Engineering.The research has been conducted at the Department of Electrical Energy Conversion

which is part of the Institute of Energy Technology (IET), Aalborg University.

The project has been followed by my supervisor Peder Pedersen. I would like to thankhim for his supervision, patience, help and suggestions.

I would like to thank Sauer-Danfoss for supplying the funding to make this project pos-sible and Hjbjerg Maskin Fabrik for donating the test crane used in the experimentaltests.

I would also like to thank the technical staff for helping with the experimental setup.Especially Walter Neumayr for his patience in answering all my electrical questions

and Jan Christiansen for his help with the frequent changes necessary in the hydraulicsetups.

Also thanks to my family who gave me great support during the three years I was awayfrom home. A special thanks to my girlfriend Christina, for giving me the motivationthat I needed to actually finish this work.

Aalborg, February 2003

Marc E. [email protected]

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Abstract

This thesis deals with resolved motion control of mobile hydraulic manipulators. Withcurrently available hydraulic manipulators the operator is required to independentlycontrol the individual joints. With a resolved motion control scheme the operator

controls the tool centre directly and a computer coordinates the motion of the individualjoints. Resolved motion control is therefore also often called tool centre control, endeffector control, or coordinated motion control.

The type of manipulator discussed in this thesis has 4 degrees of freedom: a rotationabout the base, a shoulder joint, an elbow joint and a telescopic extension section.This type of manipulator typically has a range of greater than four metres and can liftloads of up to hundreds of kilograms. This type of manipulator is commonly referredto as a Large Scale Manipulator in order to differentiate it from the typical indus-trial robots. The term mobilerefers to the transportable nature of the manipulator,differentiating it from industrial robots which are usually fixed to a certain location.

The control structure used in this thesis is distributed joint control. A central con-troller coordinates the motion of the individual joints based on the operators inputand the measured state of the manipulator. The central controller sends a referencejoint velocity to the individual joint controllers mounted at each joint. The individualjoint controllers can be programmed with the flow characteristic of the valve, the ge-ometry of the joint, and a velocity control algorithm. This control structure supportsthe current trend in industry of mobile hydraulic proportional valves with embeddedmicro-controllers. The joint control algorithm can be programmed in the actual valve.Communication between the individual joint controllers and the coordinating controller

can occur over a bus system, such as CAN bus.The joint controller presented in this thesis uses a single angular position sensor forfeedback control of the joint velocity. A further sensor is added to add artificial dampingto the joint motion. Two sensor strategies are implemented, the first based on a pressuresensor, the second based on a strain gauge. Since the motion of one joint affects theother joints in the system, an analytic stability analysis was performed taking intoaccount the interaction between the joints.

The central controller presented in this thesis implements flow sharing, deflection com-pensation, gain scheduling, and redundancy control. Flow sharing means that the

reference speed is decreased if the flow demands are higher than the flow limits of the

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vi Abstract

pump. Deflection compensation estimates the deflection in the telescopic boom sec-tion and compensates for it. Gain scheduling is implemented to take care of the largeparameter changes which occur in the crane. Redundancy control determines how theextra degree of freedom of the manipulator system is utilized.

A core part of this thesis is the experimental implementation of all the ideas on a realmobile hydraulic crane.


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Dansk resume

Denne afhandling omhandler kranspids styring (tool center control) af en mobil hy-draulisk manipulator. Med de nuvrende hydrauliske manipulatorer, er det ndvendigtfor operatren at koordinere styreinput, idet hver af de enkelte bevgelser (friheds-grader) styres ved et manuelt styreinput. Med kranspids styring, kan operatren styrekranspidsen direkte, idet en computer koordinerer de enkelte frihedsgrader, saledes atden nskede bevgelse af kranspidsen opnas.

Denne type af manipulatorer, som beskrevet afhandlingen, har 4 frihedsgrader, hvo-raf de tre rotoriske frihedsgrader er et drejeled ved fundamentet, et skulderled og etalbueled. Den sidste translatoriske frihedsgrad er udformet som et udskudssystem.

Et eksempel pa denne type af manipulatorer er mobilkraner, som typisk har en rkke-

vidde pa mere end fire meter og kan lfte en last pa flere hundrede kilogram. Denneklasse af manipulator kaldes ofte teleopererede manipulatorer for at skabe kontrast tilde typiske industrielle robotter. Termen mobil beskriver at manipulatoren er flytbar ogikke fikseret til et bestemt sted. Dette indebrer, at manipulatoren typisk har sin egenmobile kraftforsyning.

I denne afhandling er behandlet et distribueret styresystem, idet hver enkelt frihedsgradudstyres med sit eget styresystem. En central styrecomputer srger for koordinerendeinput til de enkelte styresystemer. De enkelte styresystemer er programmeret underanvendelse af a priori viden om ventilkarakteristik, kinematiske bevgelses relationerog en hastighedsstyrings algoritme.

Denne Styrestruktur understttes af en ny udvikling i industrien af ventiler med ind-bygget mikrocomputer, som indebrer, at styrealgoritmen kan programmeres direktei ventilen. Kommunikation mellem de enkelte styresystemer og den centrale styrecom-puter kan ske via et bus system, som for eksempel CAN bus systemet.

Styresytemet for de enkelte frihedsgrader, som er udviklet i denne afhandling, udnyttertilbagekobling af en positionsmaling for at styre hastigheden pa de enkelte mekaniskeelementer. En ekstra sensor er endvidere indfrt for at skabe aktiv dmpning af deenkelte mekaniske bevgeelementer. To sensor strategier er undersgt med henblik paat opna den nskede dmpeeffekt. Den frste strategi er baseret pa en trykmaling,mens den anden baseret pa en strain gauge maling.

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viii Dansk resume

For at behandle den gensidige pavirkning af de enkelte styresystemer er en analytiskstabilitetsanalyse udviklet, som tager hensyn til koblingen mellem de enkelte elementer.

De centrale algoritmer, som er udviklet i denne afhandling, inkluderer en lsning af

flere problemer som volumenstrms deling (Flow Sharing), udbjnings-kompensation,forstrkningsmanipulering (gain scheduling), og redundans styring.

Volumenstrms deling betyder at operatrens input er reduceres, hvis pumpen ikke kanlevere en volumenstrm, som kan tilfredsstille det samlede behov. Udbjnings kompen-sation estimerer udbjningen af udskud systemet ved kranspidsen og kompenserer fordenne. Forstrkningsmanipulering ndrer forstrkningen i de enkelte reguleringssljfersom funktion af mobilkranens tilstands parametre. Redundans styringen bestemmer,hvorledes den overtallige frihedsgrad i systemet udnyttes.

En vsentlig del af afhandlingen er eksperimentel implementering og verifikation af

teoretisk behandlede lsningsforslag pa en rigtig mobil hydraulisk kran.


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List of abbreviations

ADC Analog to Digital Conversion

CAN Controller Area Network

DAC Digital to Analog Conversion

DSP Digital Signal Processor

FFT Fast Fourier Transform

GUI Graphical User Interface

HMF Hjb jerg Maskin Fabrik

LHV Load Holding Valve

LS Load Sensing

LSM Large Scale Manipulator

OCV Over Centre Valve

PID Proportional Integral Derivative

SMISMO Separate Meter In Separate Meter Out

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Contents

Preface iii

Abstract v

Dansk resume vii

List of abbreviations ix

Contents xi

List of Figures xiii

1 Introduction 1

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Resolved Motion Basics . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Contributions of this Work . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 Restrictions in the Scope of this Work . . . . . . . . . . . . . . . . . 13

1.6 Description of the Individual Chapters . . . . . . . . . . . . . . . . 14

2 Model Development 17

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.1 Previous Modelling Work . . . . . . . . . . . . . . . . . . . . 192.1.2 Introduction to the System . . . . . . . . . . . . . . . . . . . 20

2.1.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Hydraulic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Valve Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.2 Positive Joint Velocity . . . . . . . . . . . . . . . . . . . . . . 24

2.2.3 Negative Joint Velocity . . . . . . . . . . . . . . . . . . . . . 25

2.2.4 The Extension Beam . . . . . . . . . . . . . . . . . . . . . . . 26

2.3 Mechanical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.1 Extension Beam Length . . . . . . . . . . . . . . . . . . . . . 28

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xii Contents

2.3.2 Modelling the Flexibility . . . . . . . . . . . . . . . . . . . . . 29

2.3.3 Dynamic Model of the Structure. . . . . . . . . . . . . . . . 34

2.3.4 Connecting the Linear Cylinder and the Angular Beam . 37

2.4 The Complete Model . . . . . . . . . . . . . . . . . . . . . . . . . . 382.5 Verification of the Model . . . . . . . . . . . . . . . . . . . . . . . . 40

3 Joint Controller Design 43

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Structure of the Software Layers . . . . . . . . . . . . . . . . . . . . 47

3.3 High Level Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.3.1 Open Loop Joint Velocity Control Scheme . . . . . . . . . 48

3.3.2 Closed Loop Joint Velocity Control Scheme. . . . . . . . . 50

3.4 Low Level Control Layer . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4.1 Increased Damping via Pressure Feedback . . . . . . . . . 52

3.4.2 Increased Damping via Strain Gauge Feedback. . . . . . 62

3.4.3 Gain Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 63

4 Stability Analysis 67

4.1 Model of the Complete System . . . . . . . . . . . . . . . . . . . . 69

4.2 Kharitonovs Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3 Stability Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.3.1 Gain Scheduling Rules Used . . . . . . . . . . . . . . . . . . 74

4.3.2 Global Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5 Deflection Compensation 79

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.2 Deflection Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.3.1 Deflection Estimation . . . . . . . . . . . . . . . . . . . . . . 86

5.3.2 Deflection Compensation . . . . . . . . . . . . . . . . . . . 87

5.4 Conclusions on Deflection Compensation . . . . . . . . . . . . . . 88

6 Handling Redundancy 89

6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.1.1 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . 91

6.2 Basic Redundancy Control Concept . . . . . . . . . . . . . . . . . 92

6.2.1 Extra Utilization of the Redundancy . . . . . . . . . . . . . . 93

6.3 Different Strategies Tested . . . . . . . . . . . . . . . . . . . . . . . . 93

6.3.1 Minimum Norm in Joint Space . . . . . . . . . . . . . . . . . 93

6.3.2 Minimum Norm in Actuator Space . . . . . . . . . . . . . . 94

6.3.3 Minimum Force . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.3.4 Elbow and Extension Only Strategy . . . . . . . . . . . . . . 95


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Contents xiii

6.4 Comparing Different Strategies . . . . . . . . . . . . . . . . . . . . 96

6.4.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.4.2 Graphical Verification . . . . . . . . . . . . . . . . . . . . . . 99

6.4.3 Test Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . 996.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.5 Manual Control of the Shoulder Joint . . . . . . . . . . . . . . . . . 104

6.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.6.1 Automatic Joint Limit Avoidance Strategy . . . . . . . . . . 105

6.6.2 Manual Shoulder Joint Control . . . . . . . . . . . . . . . . . 106

6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7 Experimental Tests 109

7.1 Operator Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.1.1 Trajectory of the Tool Centre . . . . . . . . . . . . . . . . . . 112

7.1.2 Velocity of the Tool Centre . . . . . . . . . . . . . . . . . . . 113

7.1.3 Bandwidth of the Operator/Crane Combination. . . . . . 114

7.1.4 Conclusion on Operator Tests . . . . . . . . . . . . . . . . . 114

7.2 Resolved Motion Control . . . . . . . . . . . . . . . . . . . . . . . . 115

7.2.1 Rectangular Motion . . . . . . . . . . . . . . . . . . . . . . . 115

7.2.2 Triangular Motion . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.2.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . 123

7.3 Accuracy as a Function of Speed . . . . . . . . . . . . . . . . . . . 123

7.4 Gain Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

8 Conclusion 127

8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

8.2 Evaluation of the Final Strategy . . . . . . . . . . . . . . . . . . . . 131

8.3 Future Research Work . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Appendices 133

A Introduction to Current Hydraulic Systems 135A.1 Applications for Mobile Manipulators . . . . . . . . . . . . . . . . . 137

A.2 A Typical Mobile Crane . . . . . . . . . . . . . . . . . . . . . . . . . 139

A.3 System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

A.3.1 Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

A.3.2 Valves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

A.3.3 Flow and Pressure Control Valves . . . . . . . . . . . . . . . 144

A.3.4 Load Holding Valves . . . . . . . . . . . . . . . . . . . . . . . 147

A.3.5 Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

A.4 Problems with Current Industrial Systems . . . . . . . . . . . . . . . 151


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xiv Contents

A.4.1 Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

A.4.2 Flow Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 152

A.4.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

A.4.4 Environmental . . . . . . . . . . . . . . . . . . . . . . . . . . . 153A.4.5 Lack of Flexibility . . . . . . . . . . . . . . . . . . . . . . . . . 153

A.5 Differences between Mobile and Stationary Hydraulics . . . . . . 154

B Hydraulic Decoupling 157

B.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

B.2 Pump Side Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

B.3 Pressure Compensator. . . . . . . . . . . . . . . . . . . . . . . . . . 163

B.4 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . 165

C Angular Joint Actuation 167C.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

C.2 Hydraulic Actuator Control Topologies . . . . . . . . . . . . . . . . 170

C.3 Different Options for Valve-Based Control . . . . . . . . . . . . . . 173

C.3.1 Type of Orifice. . . . . . . . . . . . . . . . . . . . . . . . . . . 173

C.3.2 Valve Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . 174

C.3.3 Control Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

D Review of Different Controllers 177

D.1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179D.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

E Flow Sharing 183

E.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

E.1.1 Cylinder Velocity . . . . . . . . . . . . . . . . . . . . . . . . . 186

F Description of Laboratory Facilities 187

F.1 HMF Crane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

F.2 Development System . . . . . . . . . . . . . . . . . . . . . . . . . . 190

F.3 Tool Centre Position Measurement System . . . . . . . . . . . . . . 191

Bibliography 193


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List of Figures

1.1 Typical mobile hydraulic crane. . . . . . . . . . . . . . . . . . . . . 4

1.2 A system with a Smart valve. . . . . . . . . . . . . . . . . . . . . . 5

1.3 Typical manipulator structure with the describing variables. . . . 6

1.4 Independent joint control scheme. . . . . . . . . . . . . . . . . . . 61.5 Cylindrical coordinate system. . . . . . . . . . . . . . . . . . . . . . 7

1.6 Same tool centre position - two different manipulator configura-tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.7 Experimental test system used in this thesis. . . . . . . . . . . . . . 13

2.1 Complete Model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Reference and response for the spool position. . . . . . . . . . . . 23

2.3 Ramp and step response of the valve. . . . . . . . . . . . . . . . . 23

2.4 Flow response of the valve. . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Hydraulic set-up when raising a load. . . . . . . . . . . . . . . . . . 25

2.6 Block diagram for positive joint velocity. . . . . . . . . . . . . . . . 25

2.7 Hydraulic set-up when lowering a load. . . . . . . . . . . . . . . . 26

2.8 Block diagram of the negative joint velocity case. . . . . . . . . . 26

2.9 Hydraulic schematic of the extension beam. . . . . . . . . . . . . 27

2.10 Extension beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.11 Cylinders locked into position. . . . . . . . . . . . . . . . . . . . . . 30

2.12 Contribution of base deflection. . . . . . . . . . . . . . . . . . . . . 30

2.13 Test set-up for the deflection tests. . . . . . . . . . . . . . . . . . . . 31

2.14 Deflection versus torque at 3m extension. . . . . . . . . . . . . . . 32

2.15 Deflection of a simple beam.. . . . . . . . . . . . . . . . . . . . . . 32

2.16 Stiffness as a function of length. . . . . . . . . . . . . . . . . . . . . 33

2.17 Structure of the mechanical model. . . . . . . . . . . . . . . . . . 35

2.18 Block diagram of the coupled system. . . . . . . . . . . . . . . . . 36

2.19 Geometry of the elbow joint. . . . . . . . . . . . . . . . . . . . . . . 37

2.20 Block diagram of the complete model. . . . . . . . . . . . . . . . 38

2.21 Linear equivalent block diagram of the complete model. . . . . 39

2.22 FFT of crane motion for impulse input.. . . . . . . . . . . . . . . . . 41

2.23 Comparison of calculated and measured natural frequency. . . 42

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xvi List of Figures

2.24 Frequency estimation error. . . . . . . . . . . . . . . . . . . . . . . . 42

3.1 Proposed structure of distributed joint control. . . . . . . . . . . . 46

3.2 Actual implementation of distributed joint control.. . . . . . . . . 46

3.3 Structure of the software in the valve controller. . . . . . . . . . . 47

3.4 Open loop joint velocity control scheme. . . . . . . . . . . . . . . 48

3.5 Valve flow characteristic. . . . . . . . . . . . . . . . . . . . . . . . . 49

3.6 Hysteresis on dead-band compensation. . . . . . . . . . . . . . . 49

3.7 Basic form of the controller. . . . . . . . . . . . . . . . . . . . . . . . 50

3.8 Modified controller for constant loop gain. . . . . . . . . . . . . . 51

3.9 Position based feedback controller. . . . . . . . . . . . . . . . . . . 51

3.10 Two different forms of pressure feedback. . . . . . . . . . . . . . . 53

3.11 Effect of pressure and PDot feedback. . . . . . . . . . . . . . . . . 54

3.12 Comparison of pressure and PDot feedback. . . . . . . . . . . . . 543.13 Schematic of the positive velocity case. . . . . . . . . . . . . . . . 55

3.14 Block diagram of the positive velocity case.. . . . . . . . . . . . . 55

3.15 Stability boundary of the valve loop. . . . . . . . . . . . . . . . . . 57

3.16 Diagram of a typical overcentre valve system. . . . . . . . . . . . 57

3.17 Block diagram of typical over-centre valve system. . . . . . . . . 58

3.18 Contour plots of the coefficients of the Routh Array. . . . . . . . . 59

3.19 Experimental verification of pressure feedback. . . . . . . . . . . 60

3.20 Increasing the filter time constant of the pressure feedback. . . . 60

3.21 Effect of rate-limited motion of valve. . . . . . . . . . . . . . . . . . 613.22 Pressure feedback effect in negative velocity direction. . . . . . 62

3.23 Straingauge feedback. . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.24 Direct strain feedback. . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.25 Gain scheduling rules for the shoulder joint. . . . . . . . . . . . . . 65

3.26 Gain scheduling rules for the elbow joint. . . . . . . . . . . . . . . 66

4.1 Overall block diagram of coupled system.. . . . . . . . . . . . . . 69

4.2 Linear equivalent overall block diagram of coupled system. . . . 70

4.3 Standard coupling networks. . . . . . . . . . . . . . . . . . . . . . . 714.4 Roots of the Kharitonov polynomials. . . . . . . . . . . . . . . . . . 73

4.5 Kharitonov image set. . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.6 Gain-scheduling rules for the damping controllers. . . . . . . . . . 75

4.7 Root plot of the transfer function F11. . . . . . . . . . . . . . . . . . 76



5.1 Definition of the virtual angle. . . . . . . . . . . . . . . . . . . . . . 81

5.2 Deflection compensation. . . . . . . . . . . . . . . . . . . . . . . . 82

5.3 Feed forward deflection compensation. . . . . . . . . . . . . . . . 82


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List of Figures xvii

5.4 Location of the strain gauge and pressure transducers. . . . . . . 83

5.5 Estimation of torque . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.6 Deflection versus measured strain.. . . . . . . . . . . . . . . . . . . 85

5.7 Deflection slope versus length of extension beam. . . . . . . . . . 865.8 Deflection estimation test for 100Kg load. . . . . . . . . . . . . . . 87

5.9 Deflection estimation test for 200Kg load. . . . . . . . . . . . . . . 87

5.10 Deflection compensation results. . . . . . . . . . . . . . . . . . . . 88

6.1 Joint limit avoidance strategy. . . . . . . . . . . . . . . . . . . . . . 96

6.2 Model used to compare the redundancy strategies. . . . . . . . 97

6.3 Graphical model of the crane.. . . . . . . . . . . . . . . . . . . . . 99

6.4 Tool centre test trajectories.. . . . . . . . . . . . . . . . . . . . . . . 100

6.5 Trajectory D backwards with minimum norm strategy in joint space.101

6.6 Trajectory D backwards with minimum norm strategy in actuatorspace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.7 Trajectory D backwards with minimum force strategy. . . . . . . . 102

6.8 Trajectory D backwards for elbow and extension strategy. . . . . 102

6.9 Total energy used by the different strategies. . . . . . . . . . . . . 103

6.10 Automatic joint limit avoidance when moving towards the base. 105

6.11 Automatic joint limit avoidance when moving away from thebase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.12 Manual shoulder joint control - raising. . . . . . . . . . . . . . . . . 107

6.13 Manual shoulder joint control - Lowering . . . . . . . . . . . . . . . 107

7.1 Definition of the operator tests.. . . . . . . . . . . . . . . . . . . . . 112

7.2 Tool centre trajectory for 400kg rigidly connected load. . . . . . 112

7.3 Straightline motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.4 Tool centre velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.5 FFT of tool centre motion. . . . . . . . . . . . . . . . . . . . . . . . . 114

7.6 Rectangular path following with no load. . . . . . . . . . . . . . . 116

7.7 Rectangular path following with a 200kg load. . . . . . . . . . . . 117

7.8 Rectangular path following with a 400kg load. . . . . . . . . . . . 118

7.9 Triangular path following with no load. . . . . . . . . . . . . . . . . 120

7.10 Triangular path following with a 200kg load. . . . . . . . . . . . . . 121

7.11 Triangular path following with a 400kg load. . . . . . . . . . . . . . 122

7.12 Straightline motion at different velocities. . . . . . . . . . . . . . . 123

7.13 Controller gains tuned with beam retracted. . . . . . . . . . . . . 124

7.14 Controller gains tuned with beam extended. . . . . . . . . . . . . 124

7.15 Testing the gain scheduling algorithm. . . . . . . . . . . . . . . . . 125

A.1 Mobile manipulator as a crane. . . . . . . . . . . . . . . . . . . . . 137

A.2 Mobile manipulator with grab bucket. . . . . . . . . . . . . . . . . 138


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xviii List of Figures

A.3 Mobile manipulator with personnel basket. . . . . . . . . . . . . . 138

A.4 Mobile manipulator mounted on a forest machine. . . . . . . . . 138

A.5 Schematic diagram of laboratory crane. . . . . . . . . . . . . . . 139

A.6 Mobile hydraulic crane installed in laboratory. . . . . . . . . . . . 139A.7 Typical current actuator subsystem. . . . . . . . . . . . . . . . . . . 140

A.8 Typical hydraulic differential cylinder. . . . . . . . . . . . . . . . . . 141

A.9 Four different quadrants of operation . . . . . . . . . . . . . . . . . 142

A.10 Typical three position spool valve. . . . . . . . . . . . . . . . . . . . 142

A.11 Typical pressure vs flow characteristic for a spool valve. . . . . . . 143

A.12 Typical flow/pressure characteristic for a pressure control valve.. 144

A.13 Typical flow/pressure characteristic for a flow control valve. . . . 145

A.14 Pressure control valve . . . . . . . . . . . . . . . . . . . . . . . . . . 146

A.15 Flow control valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147A.16 Cross section of a typical load holding valve. . . . . . . . . . . . . 148

A.17 Load sensing with a pressure regulator. . . . . . . . . . . . . . . . . 150

A.18 Open center valves. . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

A.19 Variable displacement system.. . . . . . . . . . . . . . . . . . . . . 151

A.20 Efficiency of different power supplies. . . . . . . . . . . . . . . . . . 152

A.21 Figures for different applications . . . . . . . . . . . . . . . . . . . . 154

B.1 Feedback action of load sensing system and pressure compen-

sator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

B.2 Pump side module.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 160B.3 Block diagram of pump side module . . . . . . . . . . . . . . . . . 161

B.4 Block diagram of the pump side module reorganized . . . . . . . 161

B.5 Time constant of the large volume system as the operating points

are varied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

B.6 Time constant of the small volume system as the operating pointsare varied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

B.7 Pressure compensator.. . . . . . . . . . . . . . . . . . . . . . . . . . 163

B.8 Block diagram of pressure compensator.. . . . . . . . . . . . . . . 164

B.9 Reduced block diagram of pressure compensator. . . . . . . . . 164B.10 Time constant of pressure compensator system at different op-

erating points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

B.11 Comparison of the pump and load pressures. . . . . . . . . . . . 165

C.1 Rotary hydraulic actuator. . . . . . . . . . . . . . . . . . . . . . . . 170

C.2 Separate meter in separate meter out control (SMISMO).. . . . . 171

C.3 Pump based control.. . . . . . . . . . . . . . . . . . . . . . . . . . . 172

C.4 Simple seat valve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

F.1 Schematic diagram of laboratory crane. . . . . . . . . . . . . . . 189


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List of Figures xix

F.2 Mobile hydraulic crane installed in laboratory. . . . . . . . . . . . 189

F.3 Diagram of the development system setup. . . . . . . . . . . . . . 190

F.4 Tool centre position measurement system. . . . . . . . . . . . . . . 191


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xx List of Figures


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Chapter 1

Introduction

Chapter Contents

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Resolved Motion Basics . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4 Contributions of this Work . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 Restrictions in the Scope of this Work . . . . . . . . . . . . . . . . 13

1.6 Description of the Individual Chapters . . . . . . . . . . . . . . . 14

1


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1.1. Overview 3

1.1 Overview

This thesis deals with resolved motion control of mobile hydraulic manipulators. Re-

solved motion control can also be called tip control, tool centre control, end effectorcontrol, or coordinated motion control. With a resolved motion control scheme the op-erator can input the desired motion of the tip, or tool centre, of the manipulator to acontroller which then coordinates the motion of the individual joints of the manipulatorso that the tool centre of the manipulator follows the desired trajectory.

This is in contrast to the current method where the operator controls the motion of thejoints independently. In the current method of control most tasks require simultaneousmotion of two to four actuators. Since the actuators move the joints, the operator isforced to think in joint coordinates rather than world coordinates.

A simple analogy is a human arm. A human arm has a shoulder and an elbow joint.If a human being were to control his or her arm as current mobile manipulators arecontrolled, the human would have to independently control both the shoulder and theelbow joint so that the hand reaches a desired position. Instead of this inefficient modeof control, the human brain has developed its own version of resolved motion control,so that a small part of the brain automatically controls the shoulder and elbow jointdepending on a hand position reference.

The current control method of manipulator control is a complex task which requires afair amount of practise and training time before an operator is considered skilled. Evenafter an operator is considered skilled, the current control method is still stressful for theoperator because he or she constantly has to convert between the world coordinatesand the joint coordinates. With resolved motion control the manipulator controlbecomes more logical and therefore simpler for the operator. An unskilled operator isthen able to accomplish complex tasks without a large amount of time spent training.In addition, tasks can be performed with less stress.

An interesting paper on this topic is written by Oshina (1997) which presents an in-dustry perspective of the future of mobile hydraulic machines. As the author pointsout, the trend for mobile manipulators is to become multi-purpose machines designedto become an extension of the human operator. Therefore these machines should be

able to be operated in a manner which is logical for the human operator. Joint controlis not logical and disrupts the operators logical thought progression. Resolved motioncontrol on the other hand is logical and gives a seamless interface between the operatorand the machine.

The type of manipulator discussed in this thesis is a commonly available mobile hy-draulic manipulator and is shown in fig.1.1. This type of manipulator has 4 degreesof freedom: a rotation about the base, a shoulder joint, an elbow joint and anextension section. In this thesis the tip of the crane will be referred to as the toolcentre. The tool centre is usually called the end effector in the robotics literature. Theterm mobile refers to the fact that this type of manipulator is not fixed to a certainlocation, but can move from one location to another. This is in contrast to industrial


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4 Chapter 1. Introduction

robots which are usually fixed to a certain location.

Figure 1.1 Typical mobile hydraulic crane.

The terms shoulder and elbow are used to refer to the manipulator joints since theyare easy to understand. Other literature often refers to the shoulder joint as the mainjoint and the elbow joint as the jib joint.

The reader who is not very familiar with hydraulics or mobile manipulators is referredto AppendixA which presents an introduction to hydraulics and mobile manipulators.

A key requirement for doing resolved motion control is accurate control of the motion

of the individual joints. In this thesis a distributed joint control approach was taken.In a distributed joint control scheme, each joint has a local joint controller. A centralcontroller coordinates the overall motion of the manipulator by sending each jointcontroller a reference dependent on an operators input. The individual joint controllersthen control the joints so that the joints follow the reference specified by the centralcontroller.

This approach was taken due to the emergence of new mobile hydraulic valves wherea micro controller is directly embedded into the valve. Systems with the new Smartvalves will have a structure as shown in fig. 1.2. Communication between differentvalves will occur over a bus system such as CAN bus. In addition it will be possible to

connect external inputs, such as sensors, via the micro-controllers built-in Analog to


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1.2. Resolved Motion Basics 5

Digital (AD) converters.

Figure 1.2 A system with a Smart valve.

The micro-controller will have two layers of software: a low level layer and a high levellayer. The low level layer is programmed by the valve manufacturer and will include thespool position control. At some point in the future when the spool position controllerdynamics of the valves are increased then flow control or pressure control options canbe embedded in the low level layer as well.

The high level layer will be programmed by the system manufacturer. This could, forexample, be a low pass filter to eliminate high frequency reference signals input by theoperator or a hysteresis filter to eliminate unnecessary crossing of the deadband area.In this thesis, an angular velocity controller for a manipulator joint is programmedinto the high level layer. A joint velocity reference is given to the valve and based onfeedback from the sensors mounted at the joint, the joint velocity is controlled.

1.2 Resolved Motion Basics

The manipulator used in this thesis is one of the most common types of mobile manipu-lators. The manipulator was shown in fig.1.1. A schematic diagram of the manipulatorshowing the variables used to describe the position of the crane is shown in fig. 1.3.The shoulder joint angle is described by , the elbow joint angle by and the linearextension section length by L2. The shoulder beam length,L1 is fixed. Due to spacerestrictions in the laboratory, the rotation degree of freedom was locked. The toolcentre of the manipulator therefore moves in a vertical plane. The vertical motion isdescribed byy and the horizontal motion is described by x.

In this thesis, the operator specifies the desired velocity of the tool centre. This is in

contrast to traditional robotics, where the input is typically the desiredposition. Basedon the tool centre velocity reference given by the operator and the measured orientation


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of the crane, the resolved motion controller calculates the angular velocity necessaryat the individual joints in order for the manipulator to follow the operators desiredtrajectory. The function of a resolved motion rate controller is shown in fig.1.4.

Figure 1.3 Typical manipulator structure with the describing variables.

Figure 1.4 Independent joint control scheme.


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Coordinate System

The coordinate system used most frequently in robotics is the fixed Cartesian coordi-nate system. This system is based on the traditional x, y, z coordinate system and an x,y, z velocity reference is therefore input to the controller. In an industrial environmentwhere the robot is in a fixed reference frame, a Cartesian coordinate system makes themost sense.

However on many types of mobile machines the operator sits on a seat connected to thebase of the arm. As the arm rotates about the base of the manipulator, the operatorrotates with the arm. With many other mobile manipulators, the operator is not phys-ically connected to the machine and controls the manipulator from a remote positionvia a remote control device. In these two cases, the best choice for coordinate system isa cylindrical coordinate system. In this case, the operator controls the horizontal and

vertical component of the end effector in a vertical plane and then rotates the planeby rotating the arm about the base. Such a cylindrical coordinate system is shown infig.1.5.

Figure 1.5 Cylindrical coordinate system.

A cylindrical system is easier for an operator to understand when the operators ref-erence frame is constantly changing. By looking at the manipulators position, theoperator can easily see which way the manipulator will move when the tool centre isgiven a reference signal to move outwards or inwards. In a Cartesian system, the op-erator would have to keep track of the base coordinate frame in order to know whichway the tool centre will move when given an x or y velocity reference.

The type of coordinate system used in this thesis is therefore a cylindrical coordinatesystem. In this thesis the radius is described by xand the height by y.


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1.2.1 Equations of Motion

In order to implement resolved motion control, the forward kinematics equationsneed to be found. The forward kinematics equations describe the relationship betweenthe joint angles and the tool centre position. Standard techniques for finding theforward kinematics equations are available in any introductory robotics text book suchas Craig (1986). Since the typical mobile manipulator is a simple manipulator, asimplified geometric approach was used to find the forward kinematics equations.

The forward kinematics equations for the case of the typical mobile manipulator, asshown in fig.1.3, are given by equations1.1and1.2.

x = L1cos + L

2cos (+) (1.1)

y = L1sin + L2sin (+) (1.2)

Since, it is not the position that is of interest in this thesis, but the velocity, equations1.1and1.2are differentiated giving1.3and1.4.

x = L1sin L2sin (+)(+ ) + L2cos (+) (1.3)

y = L1cos + L2cos (+)(+ ) + L2sin (+) (1.4)

Writing equations1.3and1.4in matrix form gives:

x

y

=

L1sin L2sin (+) L2sin (+) cos (+)

L1cos +L2cos (+) L2cos (+) sin (+)

L2

(1.5)

The matrix in equation1.5is called the Jacobian of the manipulator. As shown in 1.5

the Jacobian is dependant on the orientation of the manipulator. A simplified form of1.5is given in1.6.

v = J(q)q (1.6)

J(q) is the Jacobian of the system, q is the vector of the joint angles and extensionlength vector, v is the tool centre velocity vector, and q is the velocity vector of thejoints and extension section.

Since it is desired to find the required joint velocities for a given tool centre velocityreference, equation1.6is solved algebraically for the joint velocities q giving equation


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1.7.

q = J1(q)v (1.7)

This simple equation is the foundation for the implementation of resolved motion con-trol. Given a desired tool centre velocity v, a required joint velocity reference q isgenerated based on the current manipulator joint angles. However, implementation ofthis equation is not that simple. Besides the obvious need for accurate joint control,the flexibility and the redundancy in the structure need to be handled in order tosuccessfully implement resolved motion control.

Flexibility in the Mechanical Structure

On most mobile manipulators, the demand for high power to weight ratios meansthat the beams of the manipulator are made as light as possible. This results in thebeams being quite flexible. In particular the extension beam on a mobile crane is veryflexible. This means that when loads are applied to the tool centre, the beam bendswhich results in a deflection of the tool centre. As an example, a 400Kg load appliedto the tool centre of the crane used in the experimental tests of this thesis will producea deflection of the tool centre of up to 0.5m. The flexibility also decreases the naturalfrequency of the system which results in oscillations in the tool centre motion.

Chapter2studies the nature of the flexibility in more detail, chapter3presents controltechniques to increase the damping in the system and chapter 5presents a scheme tocompensate for the deflection.

Redundancy

Since the manipulator is a three degree of freedom manipulator operating in a twodegree of freedom space, the tool centre can be positioned at a certain location withan infinite number of different manipulator joint angles. This is illustrated in fig. 1.6where the same tool centre position is achieved with two, of many possible, differentjoint angle configurations.

Redundancy adds extra complexity to the system but is usually considered a positivefeature of the manipulator because it introduces the possibility for optimization. Oneexample could be to optimize cylinder pressures. Since a certain tool centre positioncan be arrived at with different joint angle configurations, a controller which optimizesthe cylinder pressures can choose the joint angles which results in the lowest cylinderpressures.

Chapter6discusses redundancy in more detail and presents some different options to


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handle the redundancy.

Figure 1.6 Same tool centre position - two different manipulator configurations.

1.3 Previous Work

Resolved motion control was first applied to stationary robots. Stationary robots, orindustrial robots as they are often called, are typically powered with electric motorsat the joints, are mounted on a rigid base, and have relatively stiff links. The ideaof resolved motion control was to make it possible to control a robot in Cartesiancoordinates instead of joint coordinates. This is generally described as control inWorldSpaceinstead of control in Joint Space. This means that instead of specifying the jointangles to put the robot into a certain position, an operator specifies world coordinatesand a resolved motion controller converts those coordinates into the required jointangles.

The basics of resolved motion control were presented in section 1.2. All introductorytextbooks on basic robotics explain the theory in more details. A good example is Craig(1986). Using the geometry of the manipulator, it is possible to relate the positions andvelocities of the joints to the position and velocity of the tool centre. By manipulatingthese relationships, it is possible to find the joint motions which give a desired toolcentre motion.

The first research into resolved motion control of the type of manipulators discussedin this thesis, often called large scale manipulators, started in the late 1980s. Oneof the first references in the area was a patent granted to MacMillan Bloedel Limited

titled Articulated Arm Control, awarded to Lawrence and Ross (1991). This patentpresented a scheme for controlling the rate of the end effector using a computer. The


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1.3. Previous Work 11

strategy was meant to apply mainly to structures like an excavator with a boom andstick function. In the strategy, the operator determined an end effector velocity viaa joystick. The input signal was converted into a position requirement by integratingthe signal. The x, y, z position requirement was converted into a joint requirement

via a geometric solution to the inverse problem. No mention of how the joints werecontrolled is made in the patent.

The inventors of this particular patent worked at the University of British Columbia(UBC) and they continued their work, both through the PhD work of Nariman Sepehri(Sepehri, 1990) and through cooperation between UBC, the University of Manitoba (Uof M) and various other research groups. One reference which is of particular interestis written by Lawrence et al. (1993). This paper presents the results of some humanfactors experiments which compare the performance of log loader operators using botha traditional manual controller and a resolved motion controller. Experiments were

based on practical implementation on a real excavator. As expected, results showedthat new operators were more efficient with the resolved motion controllers than theywere with traditional controllers. More surprisingly however, results also showed thatwithin 10 hours of training on the new controller it was possible for a skilled operatorwith up to 25 years of experience on the manual controller, to match his performancewith the manual controller. These were very promising results. The controller used inthis study was the resolved mode controller presented by Lawrence and Ross (1991)where the individual joint position controllers were PD controllers with tuneable gainsfor both P and D terms.

Sepehri presented some more details of the controllers in Sepehri et al. (1994). The

strategy used is based on a feed-forward load compensating scheme. The feed-forwardcomponent is based on measurements of the hydraulic line pressures and an onlinemodel of the crane. The use of a model allows minimization of cross couplings betweenlinks, limitations in power, etc. The feed forward component is corrected via a closedloop PD controller. The work presented was based on an excavator chassis, but usedas a log loader. Further work at UBC and U of M continued with work being doneon more advanced control strategies like force feedback (Parker et al., 1993) and fuzzylogic control (Sepehri and Lawrence, 1998).

Meanwhile, other researchers were also working in the same area. Two papers (Krus

and Palmberg, 1992) (Krus and Gunnarsson, 1993) from Linkoping University in Swe-den presented some results on experiments on vector control of mobile cranes usingmobile electro-hydraulic valves. Niemela and Virvalo (1994) present Fuzzy logic as-sisted control of a hydraulic crane. In this article, a fuzzy logic control strategy ispresented which controls one degree of freedom of the crane automatically so that itfrees the operator from controlling two joysticks simultaneously. Touminen and Vir-valo (1993) presents a strategy based on distributed control of the resolved motioncontroller. In the work of Sato et al. (1993) a master slave controller for an excavatorsystem is presented.

The early strategies were all relatively simple. However as computer power increased so

did the complexity of the control algorithms used. Mattila and Virvalo (1997a) present


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a Computed Force Control scheme for mobile cranes which uses an online model tocalculate the forces on the individual joints. The controller uses the force informationto control the pressures in the individual cylinders to drive the crane. Mattila andVirvalo (2000) present a continuation of this work with more emphasis on separate

meter in separate meter out valves. Lee and Chang (2001) presents an algorithm basedon sliding mode control to control the straight-line motion of an excavator.

The Ph.D. of Elfving (1997) presents a distributed control strategy which could decou-ple the velocity and force in the actuators so that more energy efficient control couldbe realized. The strategy made use of separate meter in separate meter out valves sothat the two sides of the cylinder could be controlled independently.

Researchers have also started to apply the research work in traditional robotics incompensating for flexible links to hydraulic cranes. An example from Finland is byRouvinen and Handroos (1997) who applied neural networks to solve static deflectionof a mobile hydraulic log loader crane. Work from Sweden by Nilsson et al. (1999)uses a range sensing camera mounted in the gripper of a large scale manipulator todampen out vibrations and reduce the deflection due to flexibility in the beams of themanipulator.

The most complete work found by the author on resolved motion control was a PhDwritten by Linjama (1998) from Tampere University of Technology. This thesis dis-cusses modelling of a two DOF manipulator and resolved motion control of the manip-ulator using proportional valves. An effective controller was developed and shown tobe robust to parameter variations.

However, currently there are not many commercial implementations of resolved motionschemes. One example is a manipulator used for tree pruning around power-lines andis described by Goldenberg et al. (1995).

1.4 Contributions of this Work

This thesis builds on the previous work by presenting and implementing a resolvedmotion control scheme for a manipulator with a telescopic boom section. Most of theprevious works in the area of resolved motion control of mobile hydraulic manipulatorshave dealt with two degree of freedom structures where the beam lengths were fixed.

This thesis also introduces a gain scheduling algorithm which is based on an onlineestimation of the natural frequency of the system. The gain scheduler helps to maintainperformance and stability over the large change in the inertia of the system as thetelescopic beam changes length and the crane works with different loads.

This thesis also introduces a deflection compensation algorithm to compensate for theflexibility in the telescopic beam. In addition, two different schemes are presented to

handle the redundancy of the manipulator.


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1.5. Restrictions in the Scope of this Work 13

Furthermore, an independent joint controller is presented which can be programmeddirectly into a mobile hydraulic valve with an embedded micro controller. The con-troller uses a single angular position sensor to do the control. In order to introducedamping into the system two methods are tested, one based on pressure feedback and

one based on strain feedback. The presented joint controller can be used together witha resolved motion scheme or as a stand-alone component in a traditional manipulatorcontrol scheme.

Since the manipulator structure leads to mechanical coupling between the cylinders, astability analysis based on a parameter space approach was used to show the stabilityof the system of the coupled system over the entire parameter space. Kharitonovstheorem was used to reduce the size of the parameter space.

The final solution is implemented on the mobile crane shown in fig. 1.7. No changeswere made to the factory installed hydraulic system on the manipulator. The laboratoryset-up is described in more detail in appendix F.

Figure 1.7 Experimental test system used in this thesis.

1.5 Restrictions in the Scope of this Work

This work was limited to valve based hydraulic joint control options. The field of joint

control has so many different options that it is difficult to cover them all completely. A


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brief review of some different options is presented in AppendixC. The decision to basethe thesis on valve-based solutions was based on the emergence of commercially avail-able Smart valves. This leads to a solution which will be industrially implementablein the near future.

In order to present a stability proof, a number of assumptions needed to be made. Thebiggest assumption is that the load sensing system has no effect on the stability. Thisis the similar to many papers in the state of the art, (Linjama and Virvalo, 1999),(Mattila and Virvalo, 2000), (Honegger and Corke, 2001). Arguments for verifying thisassumption for the experimental system which has a load sensing system based on afixed displacement pump and pressure regulator are presented in appendixB. However,no mention of LS systems based on variable displacement pumps was made.

Another assumption made was that the controller knows the mass of the load. Thiscould be implemented via a strain gauge at the tool centre. In this thesis, the loadmass was manually entered by the operator via the Graphical User Interface (GUI).

A limitation was also made with regards to the length sensor of the extension beam.The laboratory crane is equipped with a length measurement on each section of thetelescopic boom. However, it was decided that a strategy which is dependant on foursensors is not economically feasible so the four independent measurements were summedtogether to give a single measurement of the length of the overall beam. This assump-tion introduces errors into the frequency estimation and the deflection estimation. How-ever, it is assumed that the increased accuracy with four sensors does not justify theadded cost.

1.6 Description of the Individual Chapters

Chapter 2 - Model DevelopmentThis chapter discusses the development of a linear model used in the design of thecontroller. The model takes into account the coupling between the different cylinders.A key feature is modelling the flexibility in the extension beam as a simple torsionspring. Static and dynamic verifications of the model are presented.

Chapter 3 - Controller DesignThis chapter presents the controller used at a single joint of the distributed joint con-troller. A structure for the software is proposed which separates the control into a lowlevel layer and a high level layer. The low level layer contains the position control ofthe spool and some optional artificial damping units. The high level layer is modifiableby the system developer. Two methods of implementing the damping units are alsopresented, one based on pressure feedback and one based on straingauge feedback.

Chapter 4 - StabilityThis chapter analyses the stability of the entire system when independent joint control

is used. A parameter space approach was used. Kharitonovs theorem was used to


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1.6. Description of the Individual Chapters 15

reduce the computational demands.

Chapter 5 - Deflection CompensationThis chapter introduces a simple method of doing deflection compensation based on a

strain gauge measurement.

Chapter 6 - Handling RedundancyThis chapter discusses how to handle the redundancy. It includes a review of theprevious work in the area, simulation of a number of different strategies, comparisonof the energy consumption of different strategies, and experimental verification of thestrategy.

Chapter 7 - Experimental TestsThis chapter presents the results of tests performed on an HMF 680 mobile crane.

Chapter 8 - ConclusionThe main contributions of this thesis are reviewed and ideas for future work are pre-sented.

Appendix A - Introdution to Mobile Manipulators and Current Hydraulic SystemsThis appendix contains an introduction to current mobile hydraulic systems, what theproblems are, and how the different components work. If the reader is new to mobilehydraulics this is a good section to read.

Appendix B - Hydraulic Decoupling AssumptionThis appendix presents the arguments for decoupling the hydraulic cylinders in the

model of the hydraulic system.

Appendix C - Options for Joint ControlThis appendix contains a discussion of different joint control topologies. The focus isnot on the controllers used, rather it is on the physical actuation of the joints, i.e. theactual actuators used and the actual control elements used.

Appendix D - Review of Different ControllersThis appendix contains a brief review of some of the controllers typically used in thecontrol of hydraulic position servos. The focus is more on the software side than thehardware side.

Appendix E - Flow SharingThis appendix contains details of the flow-sharing algorithm used.

Appendix F - Laboratory FacilitiesThis appendix contains a description of the laboratory facilities used for this Ph.D.work. The crane, the software development environment, and the tool centre positionmeasurement system are discussed.


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Chapter 2

Model Development

Chapter Contents

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.1.1 Previous Modelling Work . . . . . . . . . . . . . . . . . . . 19

2.1.2 Introduction to the System . . . . . . . . . . . . . . . . . . 20

2.1.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Hydraulic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Valve Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.2 Positive Joint Velocity . . . . . . . . . . . . . . . . . . . . . 242.2.3 Negative Joint Velocity . . . . . . . . . . . . . . . . . . . . 25

2.2.4 The Extension Beam . . . . . . . . . . . . . . . . . . . . . . 26

2.3 Mechanical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.1 Extension Beam Length . . . . . . . . . . . . . . . . . . . . 28

2.3.2 Modelling the Flexibility . . . . . . . . . . . . . . . . . . . . 29

2.3.3 Dynamic Model of the Structure. . . . . . . . . . . . . . . 34

2.3.4 Connecting the Linear Cylinder and the Angular Beam 37

2.4 The Complete Model. . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.5 Verification of the Model . . . . . . . . . . . . . . . . . . . . . . . 40

17


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2.1. Overview 19

2.1 Overview

This chapter develops a model of a standard manipulator system. In this thesis the

model should fulfill two criteria. The first criteria, is that the model can be usedto quantitatively analyse the stability of the system. The second criteria is that themodel can be programmed in a micro-controller to estimate the natural frequency ofthe system in real-time. The estimate can then be used to gain schedule a controller.

The approach taken in this chapter was to develop a linear model by analysing thedominant dynamics of the system. The dynamics included in the linear model are themechanical coupling between the shoulder and elbow cylinder, the dynamics of theover-centre valves, the dynamics of the proportional valves, the pressure dynamics inthe cylinders, and the flexibility of the structure. The main non-linear feature of thecrane system is the large variations in the system parameters such as mechanical inertia,

mechanical stiffness, flow gain, geometry, and hydraulic capacitance. The parametersare slowly changing so the dynamics of the change are not as important as the actualparameter values. Therefore the linear model is adapted to include all these effects viavariable model parameters.

This is in contrast to the traditional approach to modelling where a non linear modelof the system is developed and verified against the real system. If a linear model ofthe system is desired, the non-linear model is linearized about an operating point.However, the type of hydraulic manipulators which are discussed by this thesis arevery complex and a model which accurately captures all the dynamics becomes very

large and complex. There have been a number of student projects at The Instituteof Energy Technology, Aalborg University, which have developed realistic models ofhydraulic manipulators. A common feature of these models is high complexity andhigh computational demands.

The traditional modelling approach does not fulfill the two criteria presented above.Firstly, it is impossible to make a quantitative analysis of stability on a complex model.The only option is to simulate the system at many different operating points andthereby verify stability. However this is a time consuming process given the computa-tional demands of the model. In addition, there is a risk that a critical operating pointmight be missed from the simulation study. A linear model developed by linearizing

the non-linear model will result in a complex linear model which will suffer from thesame problems. Secondly, if the model should be implemented in real time on a mi-cro controller, a very powerful micro controller would be needed. It is unlikely thata micro controller powerful enough to run a realistic model and cheap enough to beimplemented industrially will be available in the next few years.

2.1.1 Previous Modelling Work

There have been a number of references which develop models of two degree of freedomhydraulic cranes where the beams are assumed to be stiff. Refer to Ellman et al.


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20 Chapter 2. Model Development

(1996), Sepehri et al. (1990), and Krus et al. (1991). Also a number of models havebeen developed which take the flexibility of the beams into account. Mikkola andHandroos (1996) used a combination of ADAMS and ANSYS to develop an offlinemodel of a log loader crane. Makinenet al.(1997) developed a mathematical approach

to the modelling of a single flexible beam coupled with a hydraulic system. Linjamaand Virvalo (1997) used a combination of finite elements and assumed modes coupledwith Lagrange equations to simulate the dynamics of a flexible crane in a non real-time environment. Later on Linjama and Virvalo (1999) developed a linear state spacemodel of the flexible crane so that advanced control techniques could be used.

The work which is most similar to this thesis is the thesis of Matti Linjama, fromTampere University of Technology, Linjama (1998), which also presented a linear modelof the system which took the flexibility of the beams into account.

The model presented in this chapter builds on the previous work by including botha flexible telescopic boom section and an over-centre valve on both the shoulder andelbow joints.

2.1.2 Introduction to the System

Fig.2.1 shows a schematic diagram of the complete system where the different func-tional components are shown. The system is quite complex with many interactingcomponents. Motions of one cylinder affect the other cylinders through the mechanical

structure. In addition pressure fluctuations in one cylinder affect the other cylindersthrough the load sensing system.

Figure 2.1 Complete Model.


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2.1. Overview 21

The model was split into a hydraulic model and a mechanical model. The hydraulicmodel is presented in section 2.2 and included the effects of the control valves, theover centre valves, and the cylinders. The mechanical model is presented in section2.3and included the dynamic effects of moving the mechanical structure. The connection

between the two models was made via geometric transformations.

The valves used in the model were hydraulic-mechanical flow control valves. Thespecific valves used on the manipulator in the laboratory were Sauer-Danfoss PVG32 valves with 25L/min flow capacity. The numerical examples refer to these valves,however the model can be adapted to any flow control valve.

The load sensing system discussed in this thesis is a fixed displacement pump with ahydraulic-mechanical pressure regulator. This type of Load Sensing system is charac-terized by a fast response time. If a load sensing system with variable displacementpump was to be used the model would have to be changed in order to take into accountthe slower dynamics.

The telescopic boom is modelled as a single beam whose length is controlled by a singlecylinder. The consequences of this assumption are discussed in more detail in section2.2.4and section2.3.1.

2.1.3 Assumptions

The main assumption is that the three cylinders are decoupled hydraulically. This is

based on the observation that the LS system and the pressure compensators have muchfaster dynamics than the rest of the system. Therefore the assumption is made that thepressure drop across the main spools is constant. This means that the three cylinderscan be decoupled from a hydraulic point of view. This assumption is discussed in inmore detail in appendixB.

The assumption that the load sensing system is much faster than the rest of the systemmeans that the dynamics of the LS system can be removed from the model withoutsignificantly affecting the results. This is the typical approach taken in most of thepapers on the subject of resolved motion control of hydraulic manipulators. Note that

this does not imply that the LS system is stable, rather it makes the assumption thatthe LS system is stable to being with.

The second assumption is that the extend and retract motion of the telescopic beamhas a low dynamic influence on the rest of the system. This is due to the difference inthe forces exerted by the extension cylinder and the joint cylinders. The linear motionof the extension section acts on the inertia of a mass, whereas the angular motion actson the rotational inertia of a mass at the end of a long beam. The dynamic model ofthe structure is therefore developed as a two degree of freedom model. The change inlength of the extension beam is included in the inertia matrix of the system.

A third assumption is to model the load as being rigidly attached at the tool centre.


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Typical loads are swinging loads which have dynamics of their own. However, themodel verification shows that the effect of the swinging load is not very high.

The final assumption is to describe the flexibility of the extension beam as a torsion

spring lumped at the elbow joint. This assumption is discussed in section 2.3.2.

2.2 Hydraulic Model

The hydraulic system can be split into three actuator subsystems: the shoulder system,the elbow system, and the extension system. From a functional perspective the shoulderand elbow cylinder are the same and the same model can be used for both joints.However, due to the direction dependant behaviour of the over centre valve, different

models for the lowering and raising case are presented for the shoulder and elbowsystems.

This section starts with a model of the control valve. Then the models for the shoul-der and elbow systems are presented. Finally a discussion of the extension beam ispresented.

2.2.1 Valve Model

The valve used in this study was a Sauer-Danfoss PVG 32 mobile hydraulic proportionalvalve. As is typical with valves used in mobile hydraulic systems, the valve has a largedead-band, a rate limited spool motion, and a non linear flow gain.

The dead-band is due to both a delay in the electrical actuation and the overlap onthe spool. The describing function for a dead-band shows that the gain of the systemis reduced due to dead-band. Reduced gain has a stabilizing effect on the system.Therefore for the linear stability analysis the dead-band is neglected. The rate-limitedmotion of the spool is also neglected. The effect of the rate limiter will only be noticedfor large steps. In the typical operation of the crane there wont be any large steps tothe control valves due to the filtering in the controller.

q

Vref= Kf

2ns2 + 2ns + 2n

(2.1)

The valve dynamics are approximated by a second order system with a variable gainas shown in equation2.1. Vrefis the voltage input to the valve, qis the flow output ofthe valve,Kf is the flow gain, n is the natural frequency, and is the damping ratio.The model parameters were determined by experimental analysis of the real valve. Theexperiments were performed on the crane in the laboratory. Four tests were performed.In each test the test was started with a ramp input to the valve followed by a step input


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2.2. Hydraulic Model 23

of differing magnitude. The spool reference and the measured spool position for thefour tests is shown in fig. 2.2

Figure 2.2 Reference and response for the spool position.

The speed of the valve can be determined from the lag between the spool position andthe ramp input reference. The damping can be seen from the step response. These tworesponses are enlarged in fig.2.3(a)and fig.2.3(b).

(a) Ramp response (b) Step response

Figure 2.3 Ramp and step response of the valve.

From fig. 2.3(b) it can be seen that the valve is critically damped. From fig. 2.3(a),the lag is around 80 milliseconds. From previous experiments it is known that theelectrical actuation has a delay of around 30 milliseconds, so the actual delay due to

the dynamics of the valve is around 50 milliseconds. This can be approximated by a


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critically damped second order system with a natural frequency of around 40 rads/sec.

Figure 2.4 Flow response of the valve.

The flow output of the previous four tests is shown in fig. 2.4. As can be seen fromthe figure, for large step inputs, the flow response is not as well damped as the spoolposition response due to extra dynamics in the pressure compensator and LS system.Therefore the damping ratio of the model is reduced to 0 .5. Even though large stepinputs are avoided in the real system, assuming a lower damping ratio will give a moreconservative model. It can also be seen from the flow response to the largest step, thatthe frequency is around 50 rads/sec which matches well with the ramp tests. Rememberthat a critically damped system will have a larger time lag to a ramp input than anunder-damped one.

2.2.2 Positive Joint Velocity

As was discussed in the introduction, the direction dependant behaviour of the over-centre valve means that two models need to be developed, one for positive joint velocityand one for negative joint velocity. The hydraulic diagram of the system for the posi-tive velocity case is shown in fig.2.5. Note that the hydraulic cylinder for the shoulderjoint is mounted upside down on this particular crane. However, functionally there isno effect of changing the orientation of the cylinder.

It is assumed that there is no pressure drop across the orifice connecting the top ofthe cylinder to the tank. That is to say, it is assumed that the top of the cylinder isconnected directly to tank. This is a conservative estimate since the pressure drop overthe orifice will have a damping effect on the system.

The block diagram of the hydraulic system is shown in fig. 2.6. If this model is notfamiliar refer to appendixAfor more information. The model is implemented so that


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it determines a force which is applied to the mechanical model. The mechanical modelthen returns a velocity.

Figure 2.5 Hydraulic set-up when raising a load.

Figure 2.6 Block diagram for positive joint velocity.

2.2.3 Negative Joint Velocity

When lowering the load, the flow out of the cylinder is controlled by the over-centrevalve. The hydraulic diagram is shown in fig. 2.7

The block diagram of this system is shown in fig.2.8. It is assumed that the over-centrevalve is much faster than the rest of the system. Therefore the internal dynamics of theover-centre valve can be neglected. The orifice opening of the overcentre spool is givendirectly by the pressures acting on the spool. The pressure dependant component of


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the linearized flow equation is neglected since it has a damping effect on the system.

Figure 2.7 Hydraulic set-up when lowering a load.

Figure 2.8 Block diagram of the negative joint velocity case.

2.2.4 The Extension Beam

The extension beam is a rather complex hydraulic unit of four cylinders connected inparallel. The hydraulic schematic of the system is shown in fig.2.9.

The system is connected to a regenerative over-centre valve. The function of the re-generative over-centre valve is to amplify the flow when the cylinder is extending. The


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flow from the rod side of the cylinder is fed back to the piston side. This increases thespeed of the cylinder without requiring more flow from the pump. The effect of this isa higher flow gain in the extending case.

Figure 2.9 Hydraulic schematic of the extension beam.

In order to simplify the overall system model, the extension beam dynamics wereneglected from the model. This was considered acceptable because the extension beamsection has no noticeable stability issues.

The result is not being able to verify positional control of the extension beam. However,the positional accuracy demands of the extension beam are much lower than the angularjoints. This is because the extension beam motion directly affects the tool centre. Forexample 1cm motion of the extension beam results in 1cm motion of the tool centre.The angular joints, in contrast, have a large positional gain. A 1cm motion of theshoulder joint can have up to a 28cm effect on the tool centre. Therefore it is moreimportant to control the angular joints accurately than the extension section.

The only point where the extension system has an influence is for very slow speedswhere the stiction in the cylinder and the non-linear behaviour of the over centrevalves could be noticed via limit cycles in the extension section. Limit cycles were

removed by decreasing the controller gains.

In the overall control scheme of the manipulator, the extension section position controlwas not the limiting factor. However, if a system is developed with higher positionalrequirements, it would be necessary to examine the control of the extension section inmore detail.


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2.3 Mechanical Model

There are three parts to this section. The first part discusses the effect of the telescopic

boom section. The second part presents a model of the flexibility of the extension beam.The third part models the dynamics resulting from the motion of the beams.

The flexibility is examined via static tests where different loads are applied to the beam.The dynamics are derived via a Lagrange-Euler approach.

2.3.1 Extension Beam Length

The extension beam is constructed as five hexagonal sections which slide inside each

other, much like a telescope.

(a) Innermost beam sliding first (b) Outermost beam sliding first

Figure 2.10 Extension beam

As discussed in section2.2.4, the hydraulic cylinders actuating the individual sectionsare connected together in parallel. This means that when hydraulic pressure is appliedto the extension section, all the individual sections get an equal force. The order inwhich they slide is dependant on the friction in the individual segments of the extensionsection. The friction is dependant on the amount of contamination in the section, theload being lifted, the angle of the boom, etc... This means that it is impossible topredict which extension section will slide first.

This has a large effect on how the beam behaves. For example if the thinnest beamshould slide first, as in fig.2.10(b), the stiffness would be low. If the main beam wereto slide first, as in fig. 2.10(a), the stiffness would be much higher. This means thatthere will always be an error on an estimation of the spring stiffness. This should betaken into account when using the stiffness estimation. However the error is not verylarge and can be accepted.

Another effect of not knowing how the beams slide relative to each other is that theCentre of Gravity (COG) of the beam and the rotational inertia of the beam are notable to be determined. If the little link slides first, as in fig. 2.10(b), then the COG

is closer to the joint and the rotational inertia is less. If the large link slides first, as


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2.3. Mechanical Model 29

in fig.2.10(a), then the COG moves away from the base and the rotational inertia isincreased. This will have an effect on the frequency estimation.

Having full control of the manner in which the extension beam extends would be

beneficial for more precise modelling. This would require more complex hydraulics ormore complex electronics. At the current time the cost of such extra hydraulics isnot justified by the extra positional accuracy gained. However, in the future, whenmanipulators will be used in tasks were positional accuracy is more important, thesetypes of hydraulic systems will most likely become available.

2.3.2 Modelling the Flexibility

The hypothesis proved in this section, is that the flexibility in the extension beam

can be modelled as a simple angular spring lumped at the elbow joint. The modelsproposed in the literature are difficult to use for controller design because they hide thebasic behaviour of the beam under complex mathematics. Linjama and Virvalo (1999)were one of the few to reduce a complex non linear model into a linear state space formwhich could be used for controller design. Note that the experimental results presentedin this section are specific to the crane in our laboratory, but it is expected that othermanipulators will behave in the same way.

The use of a simple angular spring model makes the controller design much moreintuitive. It also helps with implementing deflection compensation. In order to verify

the hypothesis, tests were carried out on the crane in the laboratory.An angular spring has a proportional relationship between torque and angular deflec-tion.

d = KT (2.2)

where d is the angular deflection, K is the spring constant, and T is the torque. Inorder to verify the model statically, the deflection versus torque curves at differentoperating points were found.

The defle

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