rotary elastic actuator - core

ROTARY ELASTIC ACTUATOR

CHAI MIN-WUI EDDIE(B.Eng(Hons.),Adelaide)

A THESIS SUBMITTED

FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2004

Acknowlegdements

I would like to thank my supervisor, Assoc. Prof Marcelo H. Ang Jr. for his continual

guidance and support to improve my actuator, and his faith that this actuator will

work.

I would also like to thank those who have helped over the year. I have appreciated

discussions with Dr Lu Tien Fu from Adelaide University and fellow uni-mates Eddie

Choong, Chua Kian Ti and Sosodoro. I won’t have come so far without them!

The lab technicians, Mr. Zhang, Mrs. Ooi, Ms. Tshin and Mdm. Hamidah have

all been very helpful indeed. I could not have done so much without their assistance

with all the paperwork and hard labour.

Thanks to my family and friends who have been there all the while, to give me

support.

ii

Table of Contents

Acknowlegdements ii

Table of Contents iii

Summary vi

List of Tables vii

List of Figures viii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Scope of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Review of Thesis Content . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Related Work 6

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Interactions between robots and environments . . . . . . . . . . . . . 7

2.2.1 Passive Compliant . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Active Control . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Recent Developments in Elastic Actuator . . . . . . . . . . . . . . . . 10

2.3.1 Electro-magnetic (EM) . . . . . . . . . . . . . . . . . . . . . . 11

2.3.2 Hydraulic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.3 Pneumatic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Recent development in position control . . . . . . . . . . . . . . . . . 16

3 Modelling and Control 18

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Model of Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

iii

3.2.1 Rigid Actuator(RA) . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.2 Elastic Actuator(EA) . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3.1 Position Control of Rigid Actuator(RA) . . . . . . . . . . . . 24

3.3.2 Position Control of Rotary Elastic Actuator(REA) . . . . . . 24

3.3.3 Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.4 Force Control: Contact Start . . . . . . . . . . . . . . . . . . 27

3.3.5 Force Control: Moving to Contact . . . . . . . . . . . . . . . . 29

4 Actuator Design 33

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 The Power-train System . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3 Elastic Flywheel Design . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 Characteristic of Elastic Flywheel . . . . . . . . . . . . . . . . . . . . 41

4.5 Sensor System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.1 Method of Sensing . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.2 Choice of Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.6 Testing of Elastic Flywheel . . . . . . . . . . . . . . . . . . . . . . . . 44

4.7 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Simulation and Experiment Results 49

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.3 Dynamic Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3.1 Static Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3.2 Dynamic Friction and Inertia . . . . . . . . . . . . . . . . . . 56

5.4 Position Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.4.1 Position Control: Step Response . . . . . . . . . . . . . . . . . 57

5.4.2 Position Control: Trajectory Response . . . . . . . . . . . . . 60

5.5 Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.6 Force Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.6.1 Contact Start . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.6.2 Moving to Contact . . . . . . . . . . . . . . . . . . . . . . . . 68

6 Conclusions 73

6.1 Summary of Work Done . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Bibliography 76

iv

A Technical Drawings 79

A.1 Part List of Rotary Elastic Actuator (REA) . . . . . . . . . . . . . . 80

A.2 Part List of Elastic Flywheel . . . . . . . . . . . . . . . . . . . . . . . 81

A.3 Part Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.3.1 Center Bearing Housing . . . . . . . . . . . . . . . . . . . . . 83

A.3.2 Motor Hub . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

A.3.3 Motor Flywheel . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.3.4 Output Flywheel . . . . . . . . . . . . . . . . . . . . . . . . . 86

A.3.5 Middle Shaft . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

A.3.6 Spring Slider . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.3.7 Dummy Weight - Main . . . . . . . . . . . . . . . . . . . . . . 89

A.3.8 Dummy Weight - Level . . . . . . . . . . . . . . . . . . . . . . 90

A.3.9 Dummy Weight - Bolt . . . . . . . . . . . . . . . . . . . . . . 91

A.3.10 Slider Washer . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.3.11 Motor Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B Controller Code Part I - Calibration and Position Control 94

B.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

B.1.1 Calibration - Header File . . . . . . . . . . . . . . . . . . . . . 95

B.1.2 Calibration - Main File . . . . . . . . . . . . . . . . . . . . . . 96

B.2 Position Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.2.1 Position Control - Header File . . . . . . . . . . . . . . . . . . 102

B.2.2 Position Control - Main File . . . . . . . . . . . . . . . . . . . 103

C Controller Code Part II - Torque Control 108

C.1 Torque Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

C.1.1 Torque Control - Header File . . . . . . . . . . . . . . . . . . 109

C.1.2 Torque Control - Main File . . . . . . . . . . . . . . . . . . . 110

D Controller Code Part III - Force Control 116

D.1 Force Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

D.1.1 Force Control - Header File . . . . . . . . . . . . . . . . . . . 117

D.1.2 Force Control - Main File . . . . . . . . . . . . . . . . . . . . 118

E Suppliers 127

v

Summary

This thesis presents a rotary elastic actuator, which is capable of torque control and

improves the performances of a robotic system. The main motivations of this thesis

is to reduce the effort of achieving a good position control method without going

through the tedious dynamic identification process. Furthermore, it also provide an

alternative method to force/torque control while adding elasticity into the robotic

links especially when the system is coming in contact with working environment e.g.

bipedal walking. The elastic flywheel which is coupled between the motor drive system

and the output load provides torque feedback for the control loop. By introducing

inner loop torque control into a typical position control loop, the performances of

the actuator are found to be improved, while its elasticity adds flexibility [1] into

the robotic structure. The flexibility contributes to better impact load tolerance [2]

and “softens” the contact between the actuator and its working surface. The details

of the mechanical designs of the rotary elastics actuator and its rigid model will be

explained. The performances of the elastic actuator will be compared against its rigid

counterpart using both computer simulated and experimental results.

vi

List of Tables

4.1 Specification of Panasonic Servo Motor MSDA043A1A . . . . . . . . 35

4.2 Specification of ZF PG50/100-040 Gearbox . . . . . . . . . . . . . . . 35

4.3 Definition of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Characteristic of Extension Spring . . . . . . . . . . . . . . . . . . . . 41

4.5 Characteristic of Elastic Flywheel. . . . . . . . . . . . . . . . . . . . . 41

5.1 Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Characteristic of Rotary Elastic Actuator. . . . . . . . . . . . . . . . 51

5.3 Characteristic of Rotary Elastic Actuator for ∆θEF ≤ (∆θEF )max. . . 55

5.4 Characteristic of Rotary Elastic Actuator for ∆θEF > (∆θEF )max. . . 55

5.5 Frictions and Inertia of Rigid Actuator. . . . . . . . . . . . . . . . . . 56

5.6 The Gains and Dynamic Compensation for Step Position Control. . . 59

5.7 The Gains and Dynamic Compensation for Trajectory Position Control

for step input. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.8 The Gains for PID Torque Controller. . . . . . . . . . . . . . . . . . . 63

5.9 The Gains and Dynamic Compensation for Force Control. . . . . . . 68

5.10 The Gains and Dynamic Compensation for Hybrid Speed/Force Control. 69

vii

List of Figures

2.1 Honda Biped.[7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Block Diagram of Series Elastic Actuator(SEA).[1] . . . . . . . . . . . 13

2.3 Picture of Series Elastic Actuator(SEA).[1] . . . . . . . . . . . . . . . 13

2.4 Hydraulic Series Elastic Actuator(SEA).[1] . . . . . . . . . . . . . . . 14

2.5 Mckibben Muscles.[22] . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1 Rigid Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Model of Rigid Actuator . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Modelling of Rigid Actuator using SimuLink . . . . . . . . . . . . . . 21

3.4 Rotary Elastic Actuator . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.5 Model of Rotary Elastic Actuator . . . . . . . . . . . . . . . . . . . . 22

3.6 Modelling of Rotary Elastic Actuator using SimuLink . . . . . . . . . 23

3.7 Position Control Architecture of Rigid Actuator . . . . . . . . . . . . 25

3.8 Position Control Architecture of Rotary Elastic Actuator . . . . . . . 26

3.9 Torque Control Architecture of Rotary Elastic Actuator . . . . . . . . 27

3.10 Force Control Architecture of Rigid Actuator in Contact with Surface. 28

3.11 Force Control Architecture of Rotary Elastic Actuator in Contact with

Surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.12 Force Control Architecture of Rigid Actuator Moving to Contact. . . 31

3.13 Force Control Architecture of Rotary Elastic Actuator Moving to Con-

tact. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1 A photograph of Rotary Elastic Actuator . . . . . . . . . . . . . . . . 34

viii

4.2 Front View and Isometric View of Elastic Flywheel . . . . . . . . . . 37

4.3 Schematic Diagram of a Quarter of the Elastic Flywheel before and

After the Transmission of Torque . . . . . . . . . . . . . . . . . . . . 37

4.4 The Configuration of Angular Limiters Between the Flywheels. . . . . 40

4.5 The Exploded View of The Spring-slider Configuration. . . . . . . . . 40

4.6 The Schematic Layout of Rotary Elastic Actuator (REA). . . . . . . 44

4.7 The Layout of the Test for Elastic Flywheel. . . . . . . . . . . . . . . 45

4.8 Measured Torque against Actual Torque. . . . . . . . . . . . . . . . . 46

4.9 The Block Diagram of Experiment Setup. . . . . . . . . . . . . . . . 47

4.10 Servotogo Data Acquisition Card . . . . . . . . . . . . . . . . . . . . 48

5.1 The Relationship between the Applied Torque and the angle of deflec-

tions for ∆θEF ≤ (∆θEF )max.. . . . . . . . . . . . . . . . . . . . . . . 52

5.2 The Relationship between the Applied Torque and the angle of deflec-

tions for ∆θEF ≤ (∆θEF )max. and ∆θEF > (∆θEF )max.. . . . . . . . . 54

5.3 Simulation Results of Step Position Control. . . . . . . . . . . . . . . 58

5.4 Experimental Results of Step Position Control. . . . . . . . . . . . . . 59

5.5 Simualtion Results of Trajectory Position Control. . . . . . . . . . . . 61

5.6 Experimental Results of Trajectory Position Control. . . . . . . . . . 62

5.7 Torque Control: Step Response of REA. . . . . . . . . . . . . . . . . 64

5.8 Torque Control: Trajectory Response of REA. . . . . . . . . . . . . . 65

5.9 Simulation Results of Force Control Start With Contact. . . . . . . . 66

5.10 Experimental Results of Force Control Start With Contact. . . . . . . 67

5.11 Experimental Results of Force Control Moving To Contact. . . . . . . 70

5.12 Experimental Results of Force Control Moving To Contact (Magnified). 71

5.13 Reflected Torque of Actuators. . . . . . . . . . . . . . . . . . . . . . . 72

A.1 Part List of Rotary Elastic Actuator. . . . . . . . . . . . . . . . . . . 80

A.2 Part List of Elastic Flywheel. . . . . . . . . . . . . . . . . . . . . . . 81

A.3 Center Bearing Housing. . . . . . . . . . . . . . . . . . . . . . . . . . 83

ix

A.4 Motor Hub. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

A.5 Motor Flywheel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.6 Output Flywheel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

A.7 Middle Shaft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

A.8 Spring Slider. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.9 Dummy Weight - Main. . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.10 Dummy Weight - Main. . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.11 Dummy Weight - Bolt. . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.12 Slider Washer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.13 Motor Bracket. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.1 Calibration - Header File. . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2 Calibration - Main File Page 1. . . . . . . . . . . . . . . . . . . . . . 96





B.7 Position Control - Header File. . . . . . . . . . . . . . . . . . . . . . . 102

B.8 Position Control - Main File Page 1. . . . . . . . . . . . . . . . . . . 103





C.1 Torque Control - Header File. . . . . . . . . . . . . . . . . . . . . . . 109

C.2 Torque Control - Main File Page 1. . . . . . . . . . . . . . . . . . . . 110





x


D.1 Force Control: Header File. . . . . . . . . . . . . . . . . . . . . . . . 117

D.2 Force Control: Main File Page 1. . . . . . . . . . . . . . . . . . . . . 118









xi

Chapter 1

Introduction

This chapter describes briefly why force/torque control is important in robotic manip-

ulations. It then explains how torque control can be used to improve the traditional

position control method in an easy and modular way. A new torque controlled actua-

tor with series elasticity, which is capable of force/torque control as well as improving

the performance of the robotic manipulation is introduced

1.1 Background

Over the past two decades, there has been a great increase in interest for research in

robotics. Robotic technologies have advanced from simple, semi-autonomous robots

to multi degree of freedom, fully autonomous robots which are normally self-contained.

Traditionally, robots are very successful at performing tasks that only require move-

ments in free space or in known environments under position control. Tasks such as

pick and place of rigid components, spray painting of vehicles and parts assembly are

some examples of position controlled manipulations. These tasks can be performed

with great success if there are no unexpected obstacles or irregularities in the com-

ponents during their operations. This is because these robots are preprogrammed to

1

Chapter 1: Introduction 2

do repetitive tasks without taking into considerations of interacting with the working

surfaces within kinematics constraints.

As development in robotics continues to progress, position control by itself is found

to be inadequate or worse, it might caused damages to its working environment.

Position controlled actuators are somewhat rigid and only actuate the robot to a

certain position regardless of the torque/force it outputs. On the other hand, an

actuator that is force sensitive will also actuate the robot to a precise position but a

known force is generated to enable the interactions between the robotic system and

the work space are under kinematics constraints. Indeed, force control is preferred

over position control in robotic manipulations.

Traditionally, force controls are just simply force sensors installed in the end-

effectors which provide a force feedback. Although a stiff manipulator allows high

bandwidth force control and precise position control, but force controls are made

difficult or worse impossible due to its stiffness. A stiff manipulator will output a high

force for a small joint displacement as its high bandwidth value suggested. Thus, this

will also contribute to large force error and overshoot. Although these actuators are

capable of force control, they are still too rigid in certain applications, for example,

where there is an impact force between the end-effectors and the working surface. The

impact force can sometimes overload the transmission system. Furthermore, upon

the impact, the robotics system might vibrate and cause uneven force distribution at

the end-effectors, which results in an unsatisfactory control system. Thus, elasticity

is needed to provide compliance into the robotic system in order to maintain the

stability of robotic manipulations. By introducing elasticity into the manipulator,

the effective stiffness of the robotic system will be reduced. At the same time, it has


the effect of making the force control easier as larger deformations of the joint are

needed to output a force of same proportion as a stiff manipulator. Since the output

force is proportional to the deflection of the elastic element, elasticity turns the force

control problem into a position control one. On the other hand, the elasticity also

limits the bandwidth that the manipulator can achieve. But, low bandwidth control

is found sufficient in most robotic application such as dynamic walking, assembly and

polishing.

Another advantage of including a torque sensor into an actuator is that an inner

loop torque control is made possible in this case. A typical position manipulation

is controlled by Computed Torque Control. This controller will command a certain

torque profile to the manipulator to achieve a certain output position. Ideally, a

robotic system is designed to be frictionless but this is not possible as gearbox which

is used to increase the output torque, introduces both static and dynamic frictions into

the robotic system. If friction is not compensated in the control system, the response

will have a steady state error, which is proportional to the amount of friction in the

system.

Proportional-Integral-Derivation (PID) controllers are used extensively in the po-

sitioning of robotic system, where the integral terms are used to compensate the fric-

tional errors. However, these control method give an inconsistently large overshoot

especially when the frictions found in the system are quite large. These performances

can be improved by incorporating the dynamics of the robots into the controllers.

As far as incorporating of robot dynamics into its controller are concerned, dynam-

ics identification itself can prove to be a very challenging and tedious task. On the

other hand, the performances of the system also depend on how accurate the actual


dynamics of the system are being identified. While in some robotic systems, dynam-

ics identifications are completely impossible. Thus, with the presence of inner loop

Torque Control, these frictions will be compensated while still giving the system a

response which is reasonably fast and consistently accurate. The purpose of the inner

loop torque control is to modulate an output torque which is as close as possible to

the command torque computed by the position controller. Refer to Section 3.3.2 for

more details regarding the Inner Loop Torque Control.

Thus, force/torque control is not only capable of modulating accurate force, but

able to also simplify the process of achieving good position control and improving its

performance at the same time. The elasticity will protect the robotic system from

impact load and maintain its stability.

1.2 Scope of Investigation

A rotary actuator with a series elastic element was designed and built to evaluate some

of the claims of the previous section. The design of this rotary actuator is inspired

by the Elastic Actuators invented by Pratt et.al.[1][2] and Robinson[3]. Studies are

conducted to understand the design of the elastic element, the use of extension spring

to compute the torsional stiffness of the actuator, the effect of spring stiffness on

the performance of the manipulation, to determine a suitable control law for both

position and force/torque controlled system as well as model and simulate the system

dynamically using computer software. Experiments were also carried out to verify

the performance of the actuator as predicted by the simulations.


1.3 Review of Thesis Content

The thesis is organized as follows:

Chapter 2: The Review of Literature This chapter describes some of the back-

ground literature on force/torque control, ways to improve the performance of

the position control and recent developments on elastic actuators.

Chapter 3: Modelling and Control This chapter discusses the dynamic mod-

elling of the actuators and their corresponding control laws.

Chapter 4: Actuator Design This chapter details the design of a single degree

of freedom actuator, discussions on the mechanical hardware, the motor, the

design of its elastic element and the experiment setups.

Chapter 5: Simulations and Experiments This chapter describes some of the

simulation and experimental results, including tuning of control gains and com-

parison of performance.

Chapter 6: Conclusions provides summary and recommendations for future work.

Chapter 2

Related Work

2.1 Introduction

In this section, both control methods and early work on robotic manipulations, where

there are contacts between robotic systems and working environments will be re-

viewed. It details different methods for achieving good and stable control, such as

placing the force control sensor at the endpoint of the robot or by closing torque

control loops around each robotic joint. It discusses the problems of dynamic in-

stability under existing force/torque controlled actuators and some of the ways that

researchers have came up with to solve the problem. Some of the work on controlling

flexible manipulators, their actuation methods and the compliant or elastic mecha-

nisms they used are discussed. This chapter then discusses the traditional position

control method and methods implemented to improve its performance. This chap-

ter finishes off with the type of actuator system which can be applied for robotic

applications.

6

Chapter 2: The Review of Literature 7

2.2 Interactions between robots and environments

In order for a manipulator to interact its work piece or environment under kinematic

constraints, the torque applied to each joints or at least the output position of its

endpoint need to be controlled to a certain extent. There are two main type of control

used to deal with robotic manipulations when they are in contact with their working

environments. The first group consists of control system with passive compliance.

Most of the other type of control systems are likely to fall into the category of active

control.

2.2.1 Passive Compliant

Traditional position-controlled robots can achieve an apparent or pseudo force control

by incorporating passive compliance into their control systems. Passive compliance

can be thought of as a component or material used to absorb the impact force between

the robot and the surface with which it came in contact with. Passive compliance

is commonly found in the robot structures, joints and at the end effectors. Typical

components or materials used that are compliant are soft rubber, plastic, low stiffness

spring and air damper. The main purposes for using passive compliant materials are

to lower the servo stiffness and add some compliance behavior to the end effectors [3].

Passive compliant materials placed between the joints can effectively lower the

position control loop gain. This effect can be further enhanced by lowering the rigidity

of robot structure (links). To lower the structural stiffness, material such as aluminum

is used as the mainframe of the robot. The reason behind this is that aluminum is a

strong and yet ductile material [4]. Thus, it will absorb a fair bit of load before it will

yield and break apart. Other advantages of using aluminum are that it is lightweight,


cheap and its machinability. However, there is almost a risk for ”softening” the

control system too much, as this will make the robot become sloppy and have sluggish

response [5]. Thus, detailed calculations are required to access the right amount of

compliance needed by the robot and the use of control system to compensate the

“softness”. A damping system can also be used to offset the over compliance of the

robot structure ([5] and [6]).

Honda Research and Development Group have successfully implement passive

compliance into their biped robots, namely P2 and P3[7]. Figure 2.1 showed the

picture of P2 and P3. The compliant materials are placed between their actuators

and joints. The compliant material not only protects the robot’s actuators but also de-

couple the reflected inertia through the large Harmonic drive gear reduction. Another

way of achieving passive compliance is by placing a layer of compliant material at

the end effectors. The compliant material at the end effectors will allow for the

inaccuracy in the positioning control. However, passive compliance failed to provide

a force feedback to the control system of the robot ([8] and [9]). Thus, these robots

can only operate under preprogrammed environments. When there is an unexpected

obstacles in their working environments, they might just fail.

2.2.2 Active Control

As far as the capability of the robot is concerned, passive methods have their limits.

Often passive techniques are task specific, such as a certain types of jobs at a specific

working environment with a given position manipulation [2]. In order for the robots

to be more flexible and adaptable to the workspace under kinematics constraints

such as blind walking of biped, there is a need for active force control. Active control


Figure 2.1: Honda Biped.[7]

system has constant active feedback of measurements from the working environment

to modulate force control at the joint or at the end effectors of the robot.

There is a large range of active force control methods, which are commonly used

in robotic fields. Mason [10] and Whitney [9] gave a good summary of general active

force control methods. Various active force control methods include explicit force

control, stiffness control [11], impedance control [12], hybrid position/force control

[13]and virtual model control. These controls have different methods of calculating

the torque each joints needed in order to achieve a desired endpoint force. Although

there might be force sensors and force control loop at each joints, the control of the

joints are still very much feed forward.

Canon [14] studied the effects of the location of sensors against the performance


of the robots. It was found that good stable control can be achieved through co-

location, where the sensor is located at the actuator to be controlled. As far as

the flexibility between the sensor and actuator, which leads to sluggish response is

concerned, the link of manipulator is designed to be as stiff as possible. Co-location

also made closing the torque control loop around a joint possible. By closing control

loop around a joint, the effects of frictions, torque ripple and backlash can reduced.

However, stiff manipulator can lead to heavy robotic system, which is not desirable

in robotic applications. An [6] suggested a combination of joint torque control and

end point force sensing to obtain good stability and generating accurate steady state

force. But these methods exhibit instability when they come in contact with hard

surfaces due their stiff nature.

To overcome the instability, Roberts [8] and Whitney [9] used compliant cover-

ing at the end effectors of a manipulator. Other methods for dealing with contact

instability are non-linear control [15] which use low control gains when robots are

moving towards contact and increase the gains in free moving, joint torque control

[16] and event based system [17] to detect contact and simple control law ([18]and

[19]). However they are not good at dealing with unexpected collision under high

speed applications. Thus apart from closing the torque control loop of each joint, it

is obvious that some sort of elasticity is needed between the robots and their working

surfaces.

2.3 Recent Developments in Elastic Actuator

There are a few types of actuation systems which are commonly used in robotic fields.

Some examples of these commonly used actuation systems are electromagnetic motor,


hydraulic and pneumatic. There are also other types of actuation system such as

shape memory alloy (NiTi), electro-active polymers, polymer gels and piezoelectric.

These actuation systems are not applicable in macro-scaled robotics because they

have long actuation time and low power density.

2.3.1 Electro-magnetic (EM)

Most of the robotic systems have some sort of actuation, which is powered by electro-

magnetic motor and transmission. Electromagnetic motor is an actuation system,

which is the easiest to model and control as the motor torque is directly proportional

to the current.

The purpose of having a transmission is to increase the force density of the ac-

tuator. This allows the EM motor to run at peak efficiency operating conditions

(high speed and low torque). The output power is at low speed and high torque,

which is suitable for the robot’s operation. Although motor torque varies linearly

with the increase in current, transmission such as a gearbox on the other hand is not.

Non- linearity in the form of backlash, increased dynamic mass and increased output

impedance are all functions of the transmission system.

To overcome these problems, Asada[20] have came up with Direct Drive system.

In his attempt, motors are directly installed at the joint of the robot. This method

effectively minimizes backlash. However, a large motor is needed to provide an ade-

quate torque to move the robot. Thus, this will add a weight penalty on the robot

structure. Also, Direct Drive has not addressed the force-controlled problems, such

as impact force.

Cable Transmission is another method used to offset the problematic transmission


system. As cable is a naturally compliant, it will allow a certain degree of twist on the

joint before the effect is felt by the transmission system. By joining a cable from the

output shaft of a transmission system to a robotic joint, this will effectively minimizes

backlash and filters shock load. However due to the size constraint, careful design

of the configuration of the actuation system is needed before it is practical to be

implemented.

Another method of improving the non-linearity in transmission is by using Evoloid

gear. Evoloid gears have much coarser pitch than traditional spur gears. According

to Vischer[21], these gears have higher load capabilities than helical gear but are

still back drivable and have smooth torque transfer characteristics. Similar to Direct

Drive method, Evoloid gears only improved the potential problems encountered by

position-controlled joint. Thus, a mechanism that is capable of absorbing impact

force and modulating an accurate output force is required.

Although all these methods have improved the backdrive-ability of the robotic

joints, they have not addressed the force control problems encountered by robotic

joints. Moreover, some of these designs are somehow bulky and not very modular

and impractical to be implement into some robotic applications.

Series Elastic Actuator (SEA)[1] developed by the Massachusetts Institute of Tech-

nology (MIT) Leg laboratory group is currently one of the most impressive force-

controlled actuator available. SEA has linear springs intentionally placed in series

between the electric motor and actuator output. The springs will then de-couple

the dynamics of the actuator from the robot, such as filtering the shock loads of the

joints. In addition, the force applied to the joint can be calculated by measuring the

compression or elongation of the springs and then feedback it to the controller to


13

of the springs and then feedback it to the controller to modulate a desired output. The

schematic configuration and CAD rendered image of SEA is shown as in fig. 3 and fig. 4.

Fig. 3 Schematic Diagram of Series Elastic Actuator (SEA)

Fig. 4 CAD Rendered Image of Series Elastic Actuator (SEA). Ball Screw is used as a transmission to achieve high force/mass, while the spring allows

for good force control, high force fidelity, minimum impedance, and large dynamic range.

Since SEA is specifically designed for biped applications, its linearly arranged

configuration might not be very suitable for other robotic applications. On the hand, some

modifications can be done on the robotic joints in order to incorporate SEA into its

actuation system.

� Control

System Actuation System Output

Transmission System

+

-

Fload

Sensor

Compliant Material Signal

Fdesired Xload

Electric motor

Potentiometer

Compression spring

Ball Screw

Output shaft

Figure 2.2: Block Diagram of Series Elastic Actuator(SEA).[1]

13

of the springs and then feedback it to the controller to modulate a desired output. The

schematic configuration and CAD rendered image of SEA is shown as in fig. 3 and fig. 4.

Fig. 3 Schematic Diagram of Series Elastic Actuator (SEA)

Fig. 4 CAD Rendered Image of Series Elastic Actuator (SEA). Ball Screw is used as a transmission to achieve high force/mass, while the spring allows

for good force control, high force fidelity, minimum impedance, and large dynamic range.

Since SEA is specifically designed for biped applications, its linearly arranged

configuration might not be very suitable for other robotic applications. On the hand, some

modifications can be done on the robotic joints in order to incorporate SEA into its

actuation system.

� Control

System Actuation System Output

Transmission System

+

-

Fload

Sensor

Compliant Material Signal

Fdesired Xload

Electric motor

Potentiometer

Compression spring

Ball Screw

Output shaft

Figure 2.3: Picture of Series Elastic Actuator(SEA).[1]

modulate a desired output. The schematic configuration and CAD rendered image

of SEA is shown as in Figures 2.2 and 2.3 respectively.

Ball Screw is used as a transmission to achieve high force output /mass, while the

spring allows for good force control, high force fidelity, minimum impedance, and large

dynamic range. Since SEA is specifically designed for biped applications, its linearly

arranged configuration might not be very suitable for other robotic applications. On

the other hand, some modifications can be done on the robotic joints in order to

incorporate SEA into its actuation system.


2.3.2 Hydraulic

Hydraulic actuator converts the pressure of hydraulic fluid into mechanical force. The

output force can be calculated by measuring the pressure of the hydraulics fluid in

the transmission lines. The main advantage of hydraulic system is that it has a high

force output at low flow rate. This is a very desirable factor for robots. But hydraulic

system can be very heavy, as it requires a compressor, which can be quite bulky and

input and output valves for every actuator.

14

However, improvement on the configurations of linear SEA can be done to make it more

compatible to a wide variety of robotic applications.

2.3.2 Hydraulic [2]

Hydraulic actuator converts the pressure of hydraulic fluid into mechanical force. The

output force can be calculated by measuring the pressure of the hydraulics fluid in the

transmission lines. The main advantage of hydraulic system is that it has a high force

output at low flow rate. This is a very desirable factor for robots. But hydraulic system

can be very heavy, as it requires pump, compressor and input and output valves for every

actuator.

Fig. 5 Hydraulic Series Elastic Actuator.

Apart from being a heavy and complex system, hydraulic system also exhibit a potential

messiness in its workspace as leakage of fluid is very common. Loose seals used at its

Input pressure 1

Input pressure 2

Compression Springs

Potentiometer

Output Shaft

Figure 2.4: Hydraulic Series Elastic Actuator(SEA).[1]

Apart from being a heavy and complex system, hydraulic system also exhibits a

potential messiness in its workspace as leakage of fluid is very common. Loose seals

used at its piston to minimize friction are part of the cause for the leakage of fluid.

Contamination in hydraulic fluid due to the loose seals being used can result in non-

linearity of the output. In order for hydraulic system to be applicable for robotic

system, the problem above must be solved first. On the other hand, hydraulic system

can be implemented very successfully into application where there is no size constraint

and large output force is required. However, where lightweight actuator is required, it


is really quite hard to minimizes the overall weight of the hydraulics system. Figure

2.4 shows the Hydraulic Series Elastic Actuator (HSEA)[1] without its actuation

system.

2.3.3 Pneumatic

The basic concept behind the mechanism of the pneumatic system is pretty much

the same as the hydraulic system, except it uses air as the medium to converts its

pressure to force. Thus, the output can be controlled by measuring the pressure of

the compressed air. Like hydraulic system, pneumatic system can also delivers rea-

sonable high pressure at low flow rate. The difference of the pressure density between

hydraulic and pneumatic is due to the fact that air is naturally compliant. Pneu-

matics operates at approximately 8− 12 bars and hydraulics at 100− 300 bars. This

means air is more compressible than hydraulics fluid. This can be an advantageous

characteristic for the robot actuators as pneumatics can introduces ”softness” into

the robotic system when it is in contact with its working surface.

However at low-pressure conditions, the system can be very unstable due to the

fact that the system is potentially under-damped. If pneumatic system is operated

at high-pressure condition, the amount of damping would be acceptable but this will

pose a potential danger, such as explosion when there is a rupture in its pipeline.

As far as the safety is concerned, pneumatic system is always set to operate under

low-pressure condition. Therefore an appropriate damping system is needed to offset

the compliance of air in the actuation system.


Figure 2.5: Mckibben Muscles.[22]

A variation on the standard configuration above is an inflatable elastic tube cov-

ered by a flexible braided mesh typically called McKibben muscles [22]. When pres-

surized, the elastic tube inside expands but is constrained by the mesh. The flexible

mesh shortens or contracts like a muscle due to the expanding tube. It has been

found that McKibben muscles can exhibit passive behavior very similar to biological

muscle since it has both series and parallel elasticity.

Similar to hydraulics system, pneumatic system also requires a compressor and

hoses and valves to control the air pressure. Thus, if weight and modularity are part

of the design constraints of a force control actuator, pneumatics system is definitely

not the way to go.

2.4 Recent development in position control

Majority of robotic applications are still being performed successfully under position

control. This is because position controls are simple and stable by nature. Since some

of these applications do not require the robots to interact with the working environ-

ments under kinematics constraints, the positioning accuracy in these manipulators

are still capable of completing most of the tasks.

Gearbox and transmission system, which are used to increase the torque capacity


of a joint can introduce both dynamic and static friction into the actuator. Friction are

responsible for damping the system and resulting errors in the steady state position.

To minimize the steady state errors, higher proportional(P) gains of the controller

are used. But these gains cannot be raised without a cost as this will result in higher

requirements in actuation system, i.e. a powerful motor [20]. At the same time, it will

also pose a potential danger to its environment in the case of malfunctions. Although

the accuracy of the steady state position can also be improved by adding an integral

term in to the low proportional gain position controller, this sometimes results in a

large overshoot in the response of the system.

It is known that the performance of a robot can be improved with the incorporation

of the robot dynamics in to its controller. However, derivations and identifications of

each robotic joint’s dynamics might be very complex and tedious tasks. Moreover,

these tasks are very noise prone. On the other hand, dynamic identifications are

also not fully possible in most existing robots. Thus, a simpler and more generalized

method is needed to compensate for the friction in the transmission system while

achieving a reasonably good performance.

Chapter 3

Modelling and Control

3.1 Introduction

This chapter will describe the modelling of the actuators under loading condition as

well as appropriate control laws used to achieve good performance and stability. The

modelling of both Rotary Elastic Actuator (REA) and Rigid Actuator (RA) will be

considered here. The control laws which are used by the actuators are Computed

Torque Control and Proportional-Integral-Derivative (PID) for position and torque

control respectively. While, PID and Hybrid Speed/Force control will be used to

control the output force of the actuators.

3.2 Model of Actuator

3.2.1 Rigid Actuator(RA)

A rigid actuator is made up of a motor coupled with a gearbox and the output shaft

connected directly to the load. The purpose of a gearbox is to increase the output

torque and step down the speed. However, frictions in the gearbox will decrease the

18

Chapter 3: Modelling and Control 19

efficiency of the motor drive system and affect the performance of the actuator.

Gearbox

Motor

Motor Encoder

Coupler

Output Encoder

Output Load

Figure 3.1: Rigid Actuator

Figure 3.1 shows a picture of rigid rotary actuator with an output load, which is

modelled as a simple pendulum. While, Figure 3.2 shows its corresponding model.

The motor and gearbox combination is modelled as a low speed, high torque motor

taking into considerations such as the frictions of the gearbox and the inertia of the

motor.

The dynamics of the Rigid Actuator (RA) can be derived from Newton’s Law and

Laplace Transform, as follows:

τm − τL − τfr = Jθm (3.1)


3

As far as the torque control is concerned, the elastic flywheels are not only capable of giving a control system that delivers an accurate output torque, but the elastic elements are also shock absorbers. Thus, impact force transmitted to the motor wil l be greatly reduced and stored in the springs as potential energy. Furthermore, this actuator is capable of multi-revolution. As different applications may require different specified performance criteria, the elastic flywheels are designed to accommodate different spring stiffness, which in turn make up the overall stiffness of the actuator. Since the extension springs used in the flexible flywheels are stock springs, this means they are easily available and have a variety of stiffness. This is a very favorable factor in the commercial or industrial area.

III Model of Actuator

III.1 Rigid Actuator

A rigid actuator is made up of a motor coupled

with a gearbox and the output shaft connected directly to the load. The purpose of a gearbox is to increase the output torque and step down the speed. However, frictions in the gearbox will decrease the efficiency of the motor drive system and affect the performance of the actuator.

Figure 5 showed a rigid rotary actuator with the load applied to the actuator is modeled as a simple pendulum. The motor and gearbox combination is modeled as a low speed, high torque motor [8], taking into considerations such as the frictions of the gearbox

and the inertia of the motor. Thus, mτ is the torque

applied to the motor, Jm is the inertia of the motor,

Lτ is the output torque, frτ is the frictional torque,

which made up of both static or holding, sfτ and

dynamic term, •

∗θb and θ is the angular position of both motor and load.

Figure 5 Model of a Rigid Actuator

By applying Newton’s Law and Laplace Transform,

••=−− mmfrLm J θτττ (6)

mbsffr

•∗+= θττ (7)

••= LL ml θτ 2

(8) •

∗+++= θτθτ sbsJmlsss sfmm )())(()( 22 (9)

III.2 Elastic Actuator

Like Rigid Actuator, an Elastic Actuator requires motor and gearbox with an additional of a flexible flywheel, which is used as torque feedback.

Figure 6 Model of the Rotary Elastic Actuator with Load.

In this case, the angular position of the motor, mθ

and the output load, Lθ is different due the elasticity of the elastic flywheel. Equations (6), (7), (8) and (9) also apply to the elastic model with the additional of

)( LmSL K θθτ −= (10)

IV Control

IV.1 Position Control

Computed Torque control [9] is used to control

the positioning of the actuator. It is a control law which computes torque applied by the actuator as a function of the sensed feedback as:

βαττ += 'm (11)

Compare equation (9) and (11) and let •••

∆−∆−== θθθτ KvKp' (12)

Thus, )(

2

ssb

mlJm

sf θτβα

∗+=+=

(13)

frτ

Lθ Ks

Mθ

mτ

frτ

mτ

Lθ

Lτ

g

J

m

J Lτ

m g

Figure 3.2: Model of Rigid Actuator

τfr = τsf + b ˙θm (3.2)

τL = ml2θ̈L + mglsinθL (3.3)

Since θm=θL, let θ = θm = θL:

τm(s) = s2θ(s)(ml2 + J) + bsθ(s) + mglsinθ(s) (3.4)

where τm is the torque applied to the motor, J is the inertia, τL is the output

torque, τfr is the frictional torque, which made up of both static or holding torque,

τsf and the dynamic friction term, bθ̇ and θ is the angular position of both motor and

load. The gravitational term is made up of mass of load (m), gravitational constant

(g), leverage (l) and θ.

The ”dead zone” as shown in Figure 3.3 is used to simulate the static friction of

the gearbox. Refer to Figure 3.3 for the model of Rigid Actuator. The actuator will

not rotate if the command torque is lower than the range of the static torque. While,


Output Torque

OUTPUT DYNAMICS +

MOTOR DRIVE DYNAMICS

Modelling of REA

Motor Torque

Speed

Position

Output Torque

Quantizer(due to encoder)

1s

Int.

1s

Int

f(u)

Grav. Term

Dead Zone(Holding Torque)

-K-

Damping from

Gearbox

-K-

1 / (Motor Drive Inertia

+ Load Inertia)

Figure 3.3: Modelling of Rigid Actuator using SimuLink

the ”quantizer”block set is to simulate the quantization effect of an optical encoder

due to its digital nature.

3.2.2 Elastic Actuator(EA)

There are numerous ways can be used to achieve elasticity in an actuator. Typical

components or material used are soft rubber, plastic and dampers. However, springs

are chosen as the compliant material to provide elasticity for this actuator. The

detailed design of the Elastic Actuator will be discussed in Chapter 4.

Like Rigid Actuator, an Elastic Actuator also requires motor and gearbox with

an additional of a flexible flywheel, which is used as torque feedback and provides

elasticity into the system. The Elastic Actuator and its corresponding dynamics

model are shown in Figure 3.4 and 3.5 respectively.

For Elastic Actuator(EA), the angular position of the motor, θm and the output

load, θL are different due the elasticity of the elastic flywheel. Equations 3.1, 3.2,

3.3 and 3.4 also apply to the elastic model with the additional of τL = Ks(θm − θL),


Gearbox

Motor

Motor Encoder

Coupler

Elastic Flywheel

Output Encoder

Output Load

Figure 3.4: Rotary Elastic Actuator

3

As far as the torque control is concerned, the elastic flywheels are not only capable of giving a control system that delivers an accurate output torque, but the elastic elements are also shock absorbers. Thus, impact force transmitted to the motor wil l be greatly reduced and stored in the springs as potential energy. Furthermore, this actuator is capable of multi-revolution. As different applications may require different specified performance criteria, the elastic flywheels are designed to accommodate different spring stiffness, which in turn make up the overall stiffness of the actuator. Since the extension springs used in the flexible flywheels are stock springs, this means they are easily available and have a variety of stiffness. This is a very favorable factor in the commercial or industrial area.

III Model of Actuator

III.1 Rigid Actuator

A rigid actuator is made up of a motor coupled

with a gearbox and the output shaft connected directly to the load. The purpose of a gearbox is to increase the output torque and step down the speed. However, frictions in the gearbox will decrease the efficiency of the motor drive system and affect the performance of the actuator.

Figure 5 showed a rigid rotary actuator with the load applied to the actuator is modeled as a simple pendulum. The motor and gearbox combination is modeled as a low speed, high torque motor [8], taking into considerations such as the frictions of the gearbox

and the inertia of the motor. Thus, mτ is the torque

applied to the motor, Jm is the inertia of the motor,

Lτ is the output torque, frτ is the frictional torque,

which made up of both static or holding, sfτ and

dynamic term, •

∗θb and θ is the angular position of both motor and load.

Figure 5 Model of a Rigid Actuator

By applying Newton’s Law and Laplace Transform,

••=−− mmfrLm J θτττ (6)

mbsffr

•∗+= θττ (7)

••= LL ml θτ 2

(8) •

∗+++= θτθτ sbsJmlsss sfmm )())(()( 22 (9)

III.2 Elastic Actuator

Like Rigid Actuator, an Elastic Actuator requires motor and gearbox with an additional of a flexible flywheel, which is used as torque feedback.

Figure 6 Model of the Rotary Elastic Actuator with Load.

In this case, the angular position of the motor, mθ

and the output load, Lθ is different due the elasticity of the elastic flywheel. Equations (6), (7), (8) and (9) also apply to the elastic model with the additional of

)( LmSL K θθτ −= (10)

IV Control

IV.1 Position Control

Computed Torque control [9] is used to control

the positioning of the actuator. It is a control law which computes torque applied by the actuator as a function of the sensed feedback as:

βαττ += 'm (11)

Compare equation (9) and (11) and let •••

∆−∆−== θθθτ KvKp' (12)

Thus, )(

2

ssb

mlJm

sf θτβα

∗+=+=

(13)

frτ

Lθ Ks

Mθ

mτ

frτ

mτ

Lθ

Lτ

g

J

m

J Lτ

m g

Figure 3.5: Model of Rotary Elastic Actuator


ELASTICFLYWHEEL

Output Torque

Output Position

MOTOR DRIVE SYSTEM

OUTPUT DYNAMICS

Modelling of REA

Motor Torque

Static Friction

Quantizer1 Quantizer

-K-

Motor Drive

Inertia 1s

Int6

1s

Int5

1s

Int4

1s

Int2

f(u)

Grav. Term

E F

E

-K-

Dynamic Friction

-K-

1/Load Inertia

Figure 3.6: Modelling of Rotary Elastic Actuator using SimuLink

which models the torque measured by the Elastic Flywheel. Figure 3.6 shows the

architecture of Rotary Elastic Actuator with output load as modelled by SimuLink.

Thus, the equations represent the Rotary Elastic Actuator are as below:

τm(s) = s2[Jθm(s) + ml2θL(s)] + bsθ(s) + mglsinθL(s) (3.5)

τL = Ks(θm(s)− θL(s)) (3.6)

3.3 Control

There are three type of control algorithms which are used to control the actuators.

Depending on the application of the robots, these actuators are capable of performing

position, torque and force control. However torque control is only performed on

Rotary Elastic Actuator(REA) as shown in Chapter 5. The main purpose of these

control algorithms are to compare the performance of both Rigid and Elastic Actuator

in position and force/torque control.


3.3.1 Position Control of Rigid Actuator(RA)

Computed Torque Control[23] is used to control the positioning of the actuator. It is

a control law which computes torque applied by the actuator as a function of sensed

feedback.

τm = ατ′+ β (3.7)

Compare Equation 3.4 and 3.7 and let

τ′= −Kp∆θ −Kv∆θ̇ (3.8)

Thus,

α = J + ml2 (3.9)

J = Jm + n2Jgb (3.10)

β = τsf (s) + bsθ(s) + mglsinθL(s) (3.11)

,where n = gearbox ratio, Jgb = inertia of gearbox,Jm = inertia of motor, Kp, Kv

= controller’s gain, ∆θ = the difference between the desired position and output

position and ∆θ̇ = the difference between the desired velocity and output velocity.

From the equations computed (Equations 3.8 - 3.11), the position control archi-

tecture of a Rigid Actuator is represented by Figure 3.7. Refer to Chapter 5for the

performance of the Rigid Actuator.

3.3.2 Position Control of Rotary Elastic Actuator(REA)

It is proven that the performance of an actuator can be improved by closing the loop

between the motor and its end point. The position control of the REA as shown


Output Torque

OUTPUT DYNAMICS +

MOTOR DRIVE DYNAMICS

Modelling of REA

Motor Torque

Speed

Position

Output Torque

COMPUTED TORQUE

CONTROL

Quantizer

(due to encoder)

-K-Kv

388Kp

1s

Int.

1s

Int

f(u)

Grav. Term

DesirePosition

Dead Zone(Holding Torque)

-K-

Damping from

Gearbox

-K-


+ Load Inertia)1

-K-


+ Load Inertia)

Figure 3.7: Position Control Architecture of Rigid Actuator

in Figure 3.8 will incorporate an inner loop PID torque control into the original

computed torque control.

The inner loop torque control will modulate an output torque based on the differ-

ence between the torque commanded by the computed torque control and the actual

output torque at its end point. This control system is also used to compensate the

softness of the actuator to a certain extent. The equation used for the inner loop PID

torque control is shown as below:

τm =Kps + Kvs

2 + KI

s(τ − τL) (3.12)

where KP = Proportional gain, KV = Derivative gain, KI = Integral gain, τ =

Torque commanded by Computed Torque Control, τL = Output load (Refer Equation

3.6) and τm = Motor torque.


ELASTICFLYWHEEL

Gravitational Term

T

INNER LOOP PID TORQUE

CONTROL

Output Torque

Output Position

Output Velocity

COMPUTED TORQUE

CONTROL

MOTOR DRIVE SYSTEM

OUTPUT DYNAMICS

COMPUTED TORQUE CONTROL WITH INNER LOOP PID TORQUE CONTROL

Without Inner Loop

Static Friction


-K-

Motor Drive

Inertia -K-

LoadInertia

-K-Kv

3Kp

1s

Int6

1s

Int5

1s

Int4

1s

Int2

PID

Inner Loop PID

f(u)

Grav. Term

E F

E

-K-

Dynamic Friction

Desire

-K-

1/Load Inertia

Figure 3.8: Position Control Architecture of Rotary Elastic Actuator

3.3.3 Torque Control

The control of torque in the robotic joints will ultimately lead to the control of force

at the end effector of a robot. PID torque control is used to control the output torque

of the elastic actuator. The PID controller here is similar to the inner loop PID torque

controller in Equation 3.12, except in this case, the output torque will be compared

with a desired torque as shown in Equation 3.13.

τm =Kps + Kvs

2 + KI

s(τD − τL) (3.13)

where τD = desired torque.

The torque control architecture of Rotary Elastic Actuator is shown in Figure 3.9.

The performances of the Rotary Elastic Actuators are presented in Chapter 5. These

performances are based on the results obtained from simulations as well as real life

experiments.


ELASTICFLYWHEEL

PID TORQUECONTROL

Output Torque

Output Position

MOTOR DRIVE SYSTEM

OUTPUT DYNAMICS

Static Friction


-K-

Motor Drive

Inertia

1s

Int6

1s

Int5

1s

Int4

1s

Int2

PID

Inner Loop PID

f(u)

Grav. Term

E F

E

-K-

Dynamic Friction

DesireTorque

-K-

1/Load Inertia

Figure 3.9: Torque Control Architecture of Rotary Elastic Actuator

3.3.4 Force Control: Contact Start

There are two type of force control commonly used in robotic system. The first

type is a force control with its end-point contacting the working surface. While, the

latter is a force control with its end-point initially moving towards a working surface

and ultimately in contact with the surface to generate a desired output force. This

controller is particularly useful in applications such as blind walking of biped where

the biped are designed to walk on unknown terrain and experience unexpected impact.

In general , force control started with contacting to a surface is easier to implement

and stabilize than those moving towards contact surfaces.

Similar to Torque Control, PID is used to control the force at the point of contact

between the actuator and the working surface. The force controller computes a motor

torque, τm (Equation 3.14) based on the difference between the desired force, FD and

the contact force, FL. A simple load cell is used to measure the contact force and


thus providing force feedback into the control loop. Refer to Figure 3.10 for the force

control architecture of Rigid Actuator in contact with surface.

Output Position

FORCE CONTROL

MOTOR DRIVE SYSTEM + OUTPUT DYNAMICS

Contact Force

Tm

Dynamic Compensation

Static Friction

PID

Outer Loop PID

f(u)

Load Cell

1s

Int4

1s

Int2

f(u)

Grav. Term

-K-

Gain

-K-

Dynamic Friction

DesiredForce

-K-

1/Load Inertia

Figure 3.10: Force Control Architecture of Rigid Actuator in Contact with Surface.

τm =Kps + Kvs

2 + KI

s(FD − FL) (3.14)

In addition to the outer loop PID force control (Equation 3.15), the inner loop

torque control (Equation 3.16) similar to Equation 3.12 will also be implemented into

the force controller of REA. Refer to Figure 3.11 for the force control architecture of

REA in contact with surface.

τO =Kps + Kvs

2 + KI

s(FD − FL) (3.15)

τm =Kps + Kvs

2 + KI

s(τO − τL) (3.16)


ELASTICFLYWHEEL


CONTROL

MOTOR DRIVE SYSTEM

OUTPUT DYNAMICS

Tm

Output Position

Output Torque

Contact Force

FORCE CONTROL

To Static Friction


PID

Outer Loop PID

-K-

Motor Drive

Inertia

f(u)

Load Cell

1s

Int6

1s

Int5

1s

Int4

1s

Int2

PID

Inner Loop PID

f(u)

Grav. Term

-K-

Gain

E F

E-K-

Dynamic Friction

DesiredForce1

-K-

1/Load Inertia

Figure 3.11: Force Control Architecture of Rotary Elastic Actuator in Contact withSurface.

, where τO = the torque computed by the Outer Loop Force Control and τL = the

output torque measured by the Elastic Flywheel.

3.3.5 Force Control: Moving to Contact

When the actuator is moving in free space, the response of the actuator under the

PID controller used for force control in Sect. 3.3.4 can be quite slow. Although the

gains can be increased to speed up the positional response, the impact force will be

also be greatly increase by doing so. Furthermore, it might cause instability of the

robot upon an impact. Thus, hybrid speed/force control is used. As the actuator is

moving towards the contact surface, speed control under Computed Torque Control

(refer to Equations 3.17 to 3.21) will be used.

For Contact Force, FL ≤ 0.5N, then Speed Control:


τm = ατ′V + β (3.17)

Compare Equation 3.4 and 3.17 and let

τ′V = −Kv∆θ̇ (3.18)

Thus,

α = J + ml2 (3.19)

J = Jm + n2Jgb (3.20)

β = τsf (s) + bsθ(s) + mglsinθL(s) (3.21)

,where τ′V = the torque computed by Computed Torque Control for Speed Control,

n = gearbox ratio, Jgb = inertia of gearbox,Jm = inertia of motor, Kv = controller’s

gain and ∆θ̇ = the difference between the desired velocity and output velocity.

Once there is a contact between the actuator and the surface i.e. the impact force

exceeded 0.5 N, the controller will switch over to the PID force control (Equation

3.22) which is described in Sect.3.3.4 previously .

For Contact Force, FL > 0.5N, then Force Control:

τm =Kps + Kvs

2 + KI

s(FD − FL) (3.22)

Refer to Fig.3.12 and Fig.3.13 for the Force Control of Rigid Actuator and Rotary

Elastic Actuator(REA) moving to contact respectively. The Outer Loop Force Con-

trol of REA moving to contact surface will be the same as the Hybrid Speed/Force

Control used in the Rigid Actuator. An Inner Loop PID Torque Control will be


incorporated into the Force Control of REA moving to contact surface as shown in

Equations 3.23.

τm =Kps + Kvs

2 + KI

s(τO − τL) (3.23)

, where τO = the torque computed by the Outer Loop Force Control and τL = the

torque measured by the Elastic Flywheel. Refer to Figure 3.13.

HYBRID SPEED/ FORCE CONTROL

Output Position

Contact Force

MOTOR DRIVE SYSTEM + OUTPUT DYNAMICS

Tm

Dynamic Compensation

Output Velocity

Static Friction

else

Vd

tl

Vl

T

SpeedController

f(u)

Load Cell1

1s

Int3

1s

Int1

u1

if(u1>0.5)

elseif(u1<-0.5)

else

Hybridf(u)

Grav. Term1

-K-

Gain

Fl

Fd

if

else if

T

ForceController

-K-

Dynamic Friction

DesiredSpeed

DesiredForce -K-

1/Load Inertia1

Figure 3.12: Force Control Architecture of Rigid Actuator Moving to Contact.

The advantage of using hybrid speed/force control is that the maximum impact

force can be controlled to a certain extent by controlling the speed of the actuator just

before it came into contact with the working environment. The impact force can be

reduced by decreasing the desired speed. But this will contribute to the sluggishness

of the actuators’ response. Thus the impact force and the desired speed have to

be optimized in order to achieve an appropriate force response when the actuator is


ELASTICFLYWHEEL


CONTROL

HYBRID SPEED/ FORCE

CONTROL

MOTOR DRIVE SYSTEM

OUTPUT DYNAMICS

Tm

To

Output Position

Output Velocity

Output Torque

Contact Force

Static Friction

else

Vd

Vl

tl

T

SpeedController


-K-

Motor Drive

Inertia

f(u)

Load Cell

1s

Int6

1s

Int5

1s

Int4

1s

Int2

PID

Inner Loop PID

u1

if(u1>0.5)

elseif(u1<-0.5)

else

Hybrid

f(u)

Grav. Term

-K-

Gain

Fl

Fd

if

else if

T

ForceController

E F

E-K-

Dynamic Friction

DesiredSpeed

DesiredForce

-K-

1/Load Inertia

Figure 3.13: Force Control Architecture of Rotary Elastic Actuator Moving to Con-tact.

initially not in contact with the working surface.

Chapter 4

Actuator Design

4.1 Introduction

This chapter describes the design and construction of the Rotary Elastic Actua-

tor (REA). As discussed previously in Chapter 2 there are a few ways to achieve

force/torque control while adding elasticity into the system. The flywheel design is

chosen here because of its modularity and its elegance way of computing torque from

the elongation and contraction of the springs. The details of the torque computation

will be discussed in Section 4.3. In addition, this design is also capable of adding

elasticity into the actuator and accurate torque generation, which in turn can be

used to improve the positioning control. As far as the modularity of the design is

concerned, it is designed to implement in most of the existing actuators such as direct

drive robots. Figure 4.1 shows a photograph of the Rotary Elastic Actuator (REA)

realized and used in the experimental setup. However the first prototype of REA will

be very flexibly designed to suit a wide range of loading conditions for the purpose of

experiment . Thus, the size of REA might appear to be slightly bulky at the moment.

However, suggestions to further reduce the size of the actuator will be discussed in

33

Chapter 4: Actuator Design 34

the later part of this thesis.

Bearing Support Units

Output Load

Gearbox

Elastic Flywheel

Coupling

Output Encoder

Motor

Motor Encoder

Motor Driver

Figure 4.1: A photograph of Rotary Elastic Actuator

Rotary Elastic Actuator consists of a servomotor coupled with a gearbox, a cou-

pler, the Elastic Flywheel(EF ), bearing support units and encoders. The maximum

detectable range of the actuator’s output torque depends on the stiffness of the exten-

sion springs it used. The relationship between the output torque range and the spring

stiffness will be discussed in the later part of this chapter. The following sections of

this chapter will describe in detail the power-train system, the design of the elastic

flywheel, the choice of sensors used, the control hardware that was used as well as

the control algorithms implemented on the actuator.


4.2 The Power-train System

The selection of the power-train system, which is the combination of motor with

gearbox, depends on the maximum output torque and speed required. Since the

Rotary Elastic Actuator (REA) is designed mainly for experimental purposes, the

system is chosen to produce around 50 Nm of continuous torque at a speed of around

80 rpm. In addition, gearbox is chosen according to its efficiency and back-drivability.

Details of the chosen combination of power-train system are shown in Tables 4.1 and

4.2.

SpecificationPower 400 WTorque 1.3 Nm (Continuous), 5.0 Nm (Stall)Weight 750 GmCurrent 2.5 A (Continuous), 10.5 A (Maximum)Inertia 0.36 x 10−4 kgm−2

No load Speed 5000 rpm

Table 4.1: Specification of Panasonic Servo Motor MSDA043A1A

SpecificationReduction Ratio 40 : 1Torque 60 Nm (Continuous), 200 Nm (Maximum)Efficiency 92Weight 1.5 KgSpeed @ 50 Nm 76.4 rpmInertia 0.28 x 10−4 kgm−2

Table 4.2: Specification of ZF PG50/100-040 Gearbox

The servomotor comes with a 2500 quadrature pulse per revolution (ppr) encoder.

This encoder is used to measure the position of the motor shaft and served as part

of the torque sensor system. Since a 40:1 ratio step down gearbox and quadrature

decoding is used ot enable higher resolution, the output position of the powertrain


system will have a maximum resolution of (40 x 2500 x 4) pulses per revolution

(ppr), which is equivalent to 0.001 degree. The gearbox selected is claimed by the

manufacturer to have close to zero backlash and have an efficiency of 92 percent.

4.3 Elastic Flywheel Design

As far as robotic applications are concerned, contacts between its end effectors with

working surfaces are always unavoidable. Thus, some sort of elasticity between the

robotic structure and its contact surface are needed. In addition, torque sensory sys-

tem is also required in order for the actuator to detect certain motions, which are

used as feedback to the control loop. So, the Elastic flywheel is designed to accommo-

date these two requirements. The Elastic Flywheel is made up of extension springs,

flywheels, bearings and bushes for smooth rotation while fastener and connectors to

hold the whole structure in place.

In a Rotary Elastic Actuator, an electric motor-gearbox combination is used to

drive the motor flywheel, which transmits a torque to drive the output flywheel

through the extension springs. The output flywheel is then connected to the out-

put load. The arrangement of the springs between the motor flywheel and the output

flywheel can be viewed more clearly in Figure 4.2.

In Figure 4.2, an eight springs, rotary elastic actuator is shown and the motor

flywheel is hidden for the ease of understanding. Initially, the springs are pre-extended

to their mid-extension length to allow torque measurements in both clockwise and

anti-clockwise directions. When there is an input torque generated by the actuator,

four alternately arranged springs (i.e. Spring 1) will be extended over their mid

extension points, while the other four alternately arranged springs(i.e. Spring 2) will


Connect to Motor Shaft

Extension Spring

Spring Length Adjuster

Spring Slider

Angular Limiter

Connect to Output Load

Figure 4.2: Front View and Isometric View of Elastic Flywheel

Attached to Output Flywheel

Attached to Motor Flywheel

Rad

ius,

R Relative angle

Final Length of Spring 1

Final Length of Spring 2

Initial Length of Spring 1

Initial Length of Spring 2

a

t

Figure 4.3: Schematic Diagram of a Quarter of the Elastic Flywheel before and Afterthe Transmission of Torque


be extended under their mid-extension point.

To calculate the length of the spring, encoders are used to measure the angular

position of the motor flywheel and the output flywheel respectively. Instead of using

strain gauges, which are very noise prone, encoders are used to maintain the accuracy

of the measurements. Figure 4.3 shows a quarter of the Elastic Flywheel schematically.

F1 = KS[2R

cosasin(

π

ns

− a− ∆θ

2)]− Lfl1 (4.1)

F2 = KS[2R

cosasin(

π

ns

− a +∆θ

2)]− Lfl2 (4.2)

τ1 = F1cos(π

ns

− a− ∆θ

2)

R

cosa(4.3)

τ2 = F2cos(π

ns

− a +∆θ

2)

R

cosa(4.4)

τ =ns

2(τ2 − τ1) (4.5)

Symbol DefinitionR Radiusns No. of springLfln Free length of spring, n=1,2.a tan−( t

R)

∆θ Relative angleKS Stiffness of SpringFn Force in springτn Torque generated by each springτ Net Torque

Table 4.3: Definition of Symbols


By measuring the angular position between the output and the motor, the length

of the springs can be calculated using geometrical equations and the overall torque

that is being transmitted can then be computed as in Equations 4.1 - 4.5, with Table

4.3 explaining the symbols used.

The accuracy of the output torque relies heavily on the accurate response of the

spring under loading conditions. As far as the linear extension range of the springs are

concerned, angle limiters are installed in the core of the elastic flywheel to ensure the

maximum and minimum operating lengths of the springs are not exceeded under any

loading condition. Figure 4.4 shows the configuration of the angular limiter between

the flywheels in detail.

A deep groove ball bearing and a thrust bearing are used to provide smooth

relative rotation between the flywheels and maintain a consistent gap between the

two flywheels. To further reduce the frictional errors in the system, dry running

bushes are placed between the loop end of each spring and the screws that hold the

spring to its holder. Refer to Figure 4.5 for the configuration of the spring-slider

assembly.

For the purpose of experimental work, the first prototype of the rotary elastic

actuator will be very modularly designed to suit a wide range of loading conditions.

For example, if an application requires a high torque operation, then a stiffer spring

will be used. Thus, large flywheels are designed to accommodate a wide range of

extension springs. However there is always a compromise between the resolution of

the torque generated and its maximum detectable range. The relationship between

the spring stiffness and the characteristics of the actuator will be discussed in the

next section. Refer to AppendixA for the technical drawings of the actuator.


)]2

sin[cos

2( 11 fls Ln

piRKF −∆−−= θα

α (Eqn. 4.1)

)]2

sin[cos

2( 22 fls Ln

piRKF −∆+−= θα

α (Eqn. 4.2)

αθατ

cos)

2cos(11

R

n

piF

∆−−= (Eqn. 4.3)

αθατ

cos)

2cos(22

R

n

piF

∆+−= (Eqn. 4.4)

)(2 12 τττ −= n

net (Eqn. 4.5)

The accuracy of the output torque relies heavily on the accurate response of the spring

under loading conditions. As far as the linear extension range of the springs are

concerned, angle limiters are installed in the core of the elastic flywheel to ensure the

maximum and minimum operating lengths of the springs are not exceeded under any

loading condition. Figure 4.5 shows the configuration of the angular limiter between

the flywheels in detail.

Fig. 4.5 The Configurations of Angular Limiters Between The Flywheels.

A deep groove ball bearing and a thrust bearing are used between the flywheels to

provide smooth rotation relative each other and maintain a consistent gap between the

two flywheels. To further reduce the frictional errors in the system, dry running

Figure 4.4: The Configuration of Angular Limiters Between the Flywheels.

31

A deep groove ball bearing and a thrust bearing are used between the flywheels to

provide smooth rotation relative each other and maintain a consistent gap between the

two flywheels. To further reduce the frictional errors in the system, dry running bushes

are placed between the loop end of each spring and the screws that hold the spring to its

holder. Refer to Fig. 4.6 for the configuration of the spring-slider assembly.

Fig. 4.6 The Exploded View of The Spring-slider Configuration.

For the purpose of experimental work, the first prototype of the rotary elastic actuator

will be very modularly designed to suit a wide range of loading conditions. For example,

if an application requires a high torque operation, then a stiffer spring will be used. Thus,

large flywheels are designed to accommodate a wide range of extension springs.

However there is always a compromise between the resolution of the torque generated

and its maximum detectable range. The relationship between the spring stiffness and the

characteristics of the actuator will discuss in the next section.

4.4 Characteristic of Elastic Flywheel

Figure 4.5: The Exploded View of The Spring-slider Configuration.


4.4 Characteristic of Elastic Flywheel

The characteristics of the elastic flywheel depend on the extension spring it used.

Table 4.5 shows the characteristic of the elastic flywheel versus the extension springs

as calculated using Equations 4.1 - 4.5. While Table 4.4 is the characteristic of the

extension springs supplied by Associated Spring[24]. Part numbers in Tables 4.4 and

4.5 are for the extensions manufactured by Associated Spring.

Extension springPart No. Diameter Free Length Max. Extension Stiffness Max. Force

(mm) (mm) (mm) (N/mm) (N)T42340 14 50.0 23.60 5.88 164T42430 20 48.0 10.10 21.90 259T42660 14 44.2 7.65 44.60 400T42690 20 53.8 20.30 12.30 293

Table 4.4: Characteristic of Extension Spring

Elastic FlywheelPart No. Rel. Angle Stiffness Max. Torque Resolution

(deg) (Nm/deg) (Nm) (Nm/pulse)T42340 ±7.56 5.97 ±45.14 0.21T42430 ±3.78 17.24 ±65.20 0.62T42660 ±2.7 30.21 ±81.64 1.09T42690 ±6.12 13.39 ±81.88 0.48

Table 4.5: Characteristic of Elastic Flywheel.

Table 4.4 and 4.5 show that the stiffness of the elastic flywheel is directly propor-

tional to the stiffness of the extension springs used. As far as the range of detectable

torque is concerned, extension springs which are short in lengths but capable of long

extensions are desire. But as a matter of fact, short springs tend to be very stiff and

their lengths of extensions are also shorter. In other words, as the stiffness of the

elastic flywheel increases, its resolution in torque generation will decrease at the same


time. The stiffness of the elastic flywheel is inversely proportional to its resolution.

The calculation of the resolution of the elastic flywheel is based on 10000 pulses per

revolution (ppr) encoders. From Table 4.5, it shows that the stiffness of the elastic fly-

wheel will affect the resolution of the actuator in torque generation. If the actuator is

needed to generate torque with finer resolution, higher resolution encoders or encoder

signal interpolators are then required. Alternatively, softer extension springs can be

used to construct a softer elastic flywheel. However, high resolution can sometimes

be redundant in certain robotic applications and the performance of an actuator also

depends on the stiffness of the elastic flywheel. Excessive of softness in actuator can

cause the performance to be somehow sluggish and hard to stabilize the system.

4.5 Sensor System

The Elastic Flywheel which provides elasticity for the actuator also made up part

of the torque sensory system. As shown in the previous section, the amount of the

torque generated by the actuator can be computed by the angle of twist of the elastic

flywheel. Thus, the accuracy of the computed torque depends on how well the angular

positions of both the motor end and the output end are being sensed.

4.5.1 Method of Sensing

As far as calculating the output toque of the actuator is concerned, there are two

methods of sensing the angle of twist. The first method would be to measure the

angular positions of the motor end and the output end respectively and then, calculate

the angle of twist by subtracting the two readings.


Alternately, a position sensor can be installed in between the two flywheels to

measure the relative angular position of the flywheels. Since this actuator is also

designed for position control, there will be another sensor needed to sense the actual

output position of the actuator.

Thus, the first method was chosen as the mounting of sensors onto the actuator

is much simpler than the the latter. This is also due to the fact that the servomotor

already comes with an encoder. Refer to Figure 4.6 for the schematic layout of the

Rotary Elastic Actuator. So all that is needed here is to install another sensor at the

output end. On the other hand, the mechanical design to accommondate a relative

sensor in between the flywheels will also be a very complex one. Furthermore, the

wiring of these sensors can also limit the actuator from making a full revolution.

Other considerations such as the ease of assembly , cost and machinability of parts

also favor the first method.

4.5.2 Choice of Sensors

There are three types of sensors that can be used in this application. Namely, opti-

cal encoder, strain gauge and potentiometer. Optical encoders are by far the most

suitable choice for this application. This is because optical encoder signals are digital

and less noisy. Also, due to the fact that strain gauges and potentiometers are inher-

ently analog sensors which means their signals are generally noise prone. Thus extra

circuits are needed to filter these signals and convert them into digital. In spite of

their noise prone nature, these sensors also give small readings down to a few microns

for a relatively large deflection which make them potentially inaccurate in certain ap-

plications. The messy wiring of strain gauges also can limit the degree of revolution


Gearbox

Motor

Motor Encoder

Coupler

Elastic Flywheel

Output Encoder

Output Load

Figure 4.6: The Schematic Layout of Rotary Elastic Actuator (REA).

of the actuator.

Thus, optical encoders are chosen on the basis that they are inherently easier to

use, more compatible to this setup and potentially more accurate than the strain

gauges and potentiometer.

4.6 Testing of Elastic Flywheel

In order to test the accuracy of the torque computed using the Elastic Flywheel, a

simple test is conducted. Refer to Figure 4.7 for the layout of the test use to verify the

accuracy of Elastic Flywheel in torque feedback. The motor shaft is held stationary

by engaging its mechanical clamp. The torque computed by the Elastic Flywheel

using Equation 4.1-4.5 will be compared against the actual torque applied to the


Gearbox

Motor with mechanicalclamp engaged

Motor Encoder

Coupler

Elastic Flywheels (EF)Output Encoder

Applied Mass, m

Leverage, l

Figure 4.7: The Layout of the Test for Elastic Flywheel.

output end of the actuator according Equation 4.6.

τg = mglsinθL (4.6)

,where the actual torque, τg applied to the actuator is simply a known mass, m applied

to at a certain leverage, l with respect to the output axis of the actuator.

From Figure 4.8 the torque measured by the Elastic Flywheel varies linearly with

the applied torque. There are slight non-linearity found in results, which could due to

the frictional errors in the elastic flywheel and the quantization effects of the encoders.

However, these non-linearities are very small and thus, it is still acceptable in most

of the robotic applications.


Measured Torque vs. Applied Torque

-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30

Applied Torque, Tap (Nm)

Mea

sure

d T

orq

ue,

Ts

(Nm

)

Experimental Results

Theorectical

Figure 4.8: Measured Torque against Actual Torque.


Window Base PC with Real-time Extension (RTX)

Servo Togo Card

Motor Driver

E Motor - Gearbox

E

M

Elastic Flywheel

Window Base PC with Real-time Extension (RTX)

Servo Togo Card

70 Motor Driver

E Motor - Gearbox

E

M

100

90

80 40

23

31

Figure 4.9: The Block Diagram of Experiment Setup.

4.7 Experiment Setup

This section will describe the electronics and control hardware used to set up the

test rig for the experiment. Although the experiment setups for both position and

force/torque control are the same, the control algorithms implemented will be different

as discussed in Chapter 3. Figure 4.9 shows the schematic layout of the experiment

setup.

Servotogo V.2 card[25] is the data acquisition card used to control the actuator.

This controller card is a low cost, general purpose, control input and output board

which can control up to eight motors simultaneously from an ISA bus based computer

such as IBM compatible PC. It has up to eight channels of encoder inputs with a 24

bit counter. The analog output has control signals spanning from -10 V to + 10 V


Figure 4.10: Servotogo Data Acquisition Card

with a resolution of 13 bit. This card is also capable of interrupting the PC with a

timer interval, which is programmable to 10 minutes in 25 microseconds interval.

Windows 2000 is used as the operating system for the computer with Venture Com

Real-time Extension (RTX) 5.0[26] installed. The purpose of installing a RTX server

is to boast the real-time capabilities of Windows. The control loop is set to run at

1kHz. The matching motor driver supplied by Panasonic contains circuits to power

up the encoders and hardware to provides power to the motor. The Windows based

PC with RTX is used for higher level processing. It communicates with the motor

driver, sending control signals and receiving encoder inputs to compute the control

loop. The control codes are written in Visual C++ language. Refer to AppendixB for

the control codes of position, torque and force control. Comments on the top of the

source codes indicate the purpose of the program. Added comments are embedded

throughout the body of the code, explaining what each lines of the code do.

Chapter 5

Simulation and Experiment Results

5.1 Introduction

This chapter discuss the performance of the actuator. The results from the simulations

as described in Chapter 3 are compared to the data taken from the experimental setup

used in Chapter 4. The ability of the actuators in both position and force/torque

control are examined. A calibration method is used to calibrate the overall stiffness

of REA. While, a simplified version of dynamic identification method as discussed by

Jamisola et. al. [27] is used to find the full dynamics of the actuator.

5.2 Calibration

As far as the overall stiffness of REA is concerned, there is some sort of elasticity found

in the actuator apart from the intentionally placed elastic flywheel. The coupling

which is used to provide tolerance in misalignments between the shafts introduced

softness into the actuator at the same time. Thus, calibrations are performed to fully

determine the overall stiffness of the actuator.

This calibration method is very similar to the method used in Section 4.6, which

49

Chapter 5: Simulation and Experiment Results 50

is used to verify the stiffness of the elastic flywheel. The overall stiffness of REA

can be calculated with the stiffness of the elastic flywheel computed by Equation 4.1

- 4.5 plus the stiffness of the coupling quoted by the manufacturer. However, the

quoted value of the stiffness of coupling, (17Nm/deg) is claimed by the supplier to be

conservative. Thus, an experiment is performed to verify the stiffness of the coupling

and then calibrate the response of the actuator against the actual output torque.

The procedures taken in the experiments are shown as below:

1. REA is assembled with the output shaft of the motor-drive system being held

stationary by engaging the mechanical clamp of the motor. engaged.

2. Known weights, m are placed one by one at a known leverage, l to apply a

known torque to the actuator.

3. The applied torque can be calculated by the Equation 4.6.

4. The overall angle of deflection between the motor end and the output end can

be measured using optical encoders.

5. Thus, the overall stiffness of REA, KREA can be calculated from the plot of

applied torques, τap against the angle of deflections, ∆θ.

The relationship between the applied torque and the angle of deflections can be

seen in Figure 5.1.

The stiffness of the coupling can be calculated according to the Ohm’s Law.

1

KREA

=1

KC

+1

KEF

(5.1)


, where KREA is the overall stiffness of Rotary Elastic Actuator which can be

calculated by the slope of lines in Figure 5.1, KC is the stiffness of the coupling and

KEF is the stiffness of the Elastic Flywheel as calculated in Chapter 4. By rearranging

Equation 5.1, the stiffness of the coupling can be calculated as in Equation 5.2.

KC =1

1KREA

− 1KEF

(5.2)

Stiffness (Nm/deg.)Spring KEF KREA KC

T42340 5.97 4.399 16.722T42430 17.24 8.488 16.730T42660 30.21 10.762 16.705T42690 13.39 7.435 16.710

Table 5.1: Stiffness

Rotary Elastic ActuatorSpring Stiffness, Rel. Angle Max. Torque Resolution

KREA(Nm/deg) (deg) (Nm) (Nm/pulse)T42340 4.399 ±10.26 ±45.14 0.16T42430 8.488 ±7.68 ±65.20 0.31T42660 10.762 ±7.59 ±81.64 0.39T42690 7.435 ±11.00 ±81.88 0.27

Table 5.2: Characteristic of Rotary Elastic Actuator.

Although the stiffness of the coupling calculated is slightly lower than the quoted

value, but its elasticity shown good linearity, which is reflected in Figure 5.1. So, the

use of coupling should not affect the accuracy of the actuator in torque generation.

The maximum torque that REA can measure is limited by the linear extension range

of the springs. At the same time, the torque transmitted through the coupling is

equal to the torque transmitted through the Elastic Flywheel (EF).


Applied Torque Vs. Angle of Deflections

-100

-80

-60

-40

-20

0

20

40

60

80

100

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Angle of Deflections (deg)

Ap

plie

d T

orq

ue

(Nm

)

T42340

T42430

T42660

T42690

Figure 5.1: The Relationship between the Applied Torque and the angle of deflectionsfor ∆θEF ≤ (∆θEF )max..


On the other hand, once the maximum deflection of the Elastic Flywheel (i.e.

∆θEF = (∆θEF )max.) is reached, the coupling by itself can also be used as part of the

torque sensor as the Elastic Flywheel is now considered as a rigid component. The

torque is transmitted through the Angle Limiters in the core of the Elastic Flywheel.

Refer to Figure 4.4 for the configuration of the Angle Limiters between the flywheels.

In this case, the resolution of torque will be coarser than the previous method but the

resolution of torque might not be that important at high torque generation. The range

of torque measurable will be then limited by the maximum torque of the coupling

(100Nm). However, this method is left as an option as the linearity of the coupling

might not be reliable enough for torque sensing feedback in certain applications.

Thus, this approach gives a good guideline to design an actuator which is capa-

ble of fine torque generation at low range of torque, while generating coarser torque

at high range of torque. This point is better illustrated by going through Equa-

tions 5.3- 5.5 and the data in Tables 5.3 and 5.4. The responses of the actuator

for ∆θEF ≤ (∆θEF )max. and ∆θEF > (∆θEF )max. are shown in Figure 5.2. Figure 5.2

shows that the slope of the graph are increased after the maximum elongation of the

springs are reached.

For ∆θEF ≤ (∆θEF )max.,

∆τREA1 = KREA1 ×∆θREA1 (5.3)

For ∆θEF > (∆θEF )max., i.e.KREA2 = KC .

∆θREA2 = (∆θREA1)max. + (∆θC)∆θEF >(∆θEF )max. (5.4)


∆τREA2 = (∆τREA1)max. + KC × (∆θC)∆θEF >(∆θEF )max. (5.5)

,where ∆θREA = the range of the torque tranmitted by REA, KREA = the stiffness

of REA. ∆θREA = the angle of twist of REA, δθC = the angle of the twist of the

coupler, while subscript 1 and 2 denotes the operation of REA when it is under and

equal to the maximum elongation of the springs respectively.

Applied Torque Vs. Angle of Deflections

-100

-80

-60

-40

-20

0

20

40

60

80

100

-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

Angle of Deflections (deg)

Ap

plie

d T

orq

ue

(Nm

)

T42340

T42430

T42660

T42690

Figure 5.2: The Relationship between the Applied Torque and the angle of deflectionsfor ∆θEF ≤ (∆θEF )max. and ∆θEF > (∆θEF )max..


∆θEF ≤ (∆θEF )max.

Spring KREA1 , ∆θREA1 ∆τREA1 Resolution(Nm/deg) (deg) (Nm) (Nm/pulse)

T42340 4.399 ±10.26 ±45.14 0.16T42430 8.488 ±7.68 ±65.20 0.31T42660 10.762 ±7.59 ±81.64 0.39T42690 7.435 ±11.00 ±81.88 0.27

Table 5.3: Characteristic of Rotary Elastic Actuator for ∆θEF ≤ (∆θEF )max.

∆θEF > (∆θEF )max.

Spring KREA2 = KC , ∆θREA2 ∆τREA2(∆τC) Resolution(Nm/deg) (deg) (Nm) (Nm/pulse)

T42340 16.718 ±13.54 ±100.0 0.60T42430 16.718 ±9.76 ±100.0 0.60T42660 16.718 ±8.68 ±100.0 0.60T42690 16.718 ±12.10 ±100.0 0.60

Table 5.4: Characteristic of Rotary Elastic Actuator for ∆θEF > (∆θEF )max.

5.3 Dynamic Identification

Since a gearbox is used in the actuator, there bound to be some sort of friction intro-

duced into the system. Thus, dynamic compensations are needed in the controller.

It is known that the performance of an actuator can be improved with the incorpo-

ration of the friction compensation into the controller. The purpose of the friction

compensation is to make up the energy that is lost in the system through friction

such that the system will perform like an ideal case system.

5.3.1 Static Friction

Static Friction is also called the holding torque. It is the minimum torque that the

actuator need before there will be a slight rotation. The steps below are used to

determine the static torque.


1. All load are disconnected from the actuator.

2. Small increments of torque are continuously applied to the actuator until the

motor start to rotate.

3. Thus, static torque is the torque when the motor starts to rotate freely.

5.3.2 Dynamic Friction and Inertia

Dynamic Friction which is also known as the inherent damping of a system can

stabilize the system but it can also make a system overdamped. While inertia can be

defined as the property of a matter which cause to resist changes of velocity. Hence,

the damping and inertia of a system is needed to simulate and tune the gains of

a controller in order to optimize the performance of a system. Refer to Jamisola

et. al.[27] for the steps taken to find the dynamic friction and inertia of the Rigid

Actuator. Thus, the frictions and inertia of the rigid actuator are found as in Table

5.5.

Parameters valueStatic Frictions 4 Nm

Dynamic Frictions 7 Nms/radInertia 0.050 kgm2

Table 5.5: Frictions and Inertia of Rigid Actuator.

To check the inertia of RA, SolidWork is used to calculate the inertia of the

shaft and the coupling. While, the inertia of the motor gearbox combination can be

calculated according to the Equation 5.6.

Jmg = n2JGb + Jm (5.6)


Thus,

JRA = Jcs + n2JGb + Jm = 0.0084 + 0.36x10−4 + 402 ∗ 0.28x10−4 = 0.053kgm2

,where JRA is the inertia of the Rigid Actuator, Jcs is the inertia of the coupling and

output shaft, JGb is the inertia of the motor-gearbox, n = the step gearbox ratio and

Jm is the motor’s inertia. The calculated value of the overall inertia of RA is very

close to the value determined by the experiment. The average of the two values are

used to compute the inertia of RA.

5.4 Position Control

This section will discussed the ability of both Rigid Actuator (RA) and Rotary Elastic

Actuator (REA) in position manipulation. As discussed in Chapter 3 previously,

RA will be using Computed Torque Control(CTC) while REA will used CTC with

inner loop PID torque control. These results will also be compared against an ideal

case model, which can be closely represented using a rigid actuator with dynamic

compensation. The actuator will be tested against its response to step and trajectory

input.

5.4.1 Position Control: Step Response

The main interests here are to examine how fast and how accurate the actuator can

track a desired position. Since the inertia and friction parameters of the actuator are

already determined in the previous section, SimuLink can then be used to accurately

simulate the response of the actuator. At the same time, SimuLink is also use to

determine the appropriate gains for the controller. The actuators are tuned to be


0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

70

Time, t (s)

Pos

ition

,tl (

deg)

Step Response : Position vs. Time

Desired PositionRigid 1 : Kp=110, Kv=2sqrt(110), Tsf=4, b=7Elastic : Kp=110, Kv=sqrt(0), P=1, I=22, D=0Rigid 2 : Kp=110, Kv=2sqrt(0)

Rigid 2

Elastic

Rigid 1

Desired Position

Figure 5.3: Simulation Results of Step Position Control.

in critically damped conditions, where settling time is around 0.5 seconds and less

than 1 percent steady state error. Figure 5.3 shows the performance of the actuators

as predicted by SimuLink. Refer to Table 5.6 for the control gains and dynamic

compensation of each actuator, where Rigid 1 is the Rigid Actuator under Computed

Torque Control with Dynamic Compensation, Rigid 2 is the Rigid Actuator under

only Computed Torque Control and Elastic is the Rotary Elastic Actuator Under

Computed Torque Control and Inner Loop Torque Control.


Computed Inner Loop PID DynamicActuator Torque Control Torque Control Compensation

KP KV P I D τsf b

Rigid 1 110 2√

110 0 0 0 4 7

Rigid 2 110 2√

0 0 0 0 0 0

Elastic 110 2√

0 1 22 0 0 0

Table 5.6: The Gains and Dynamic Compensation for Step Position Control.

Step Response : Position Vs. Time

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000

Time, t (ms)

Po

siti

on

of

Lo

ad (

deg

.)

Rigid 1 : Kp 110 Kv 2sqrt(110) Tsf 4 b 7

Elastic : Kp 110 Kv 2sqrt(0) P 1 I 22 D 0

Rigid 2 : Kp 110 Kv 2sqrt(0)

Desired Position

Rigid 2

ElasticRigid 1

Desired Position

Figure 5.4: Experimental Results of Step Position Control.


Figure 5.4 shows the real life performance of the actuators. The performance pre-

dicted by SimuLink (Figure 5.3) are very similar to the experimental results. As far

as the dynamic compensation is concerned, Rigid 1 is the fastest in step positioning

response. This is due to the fact that Rigid 1 is very much an ideal system under

the incorporation of the dynamic compensation. Although the settling time for the

elastic actuator is slightly slower than the dynamically compensated rigid actuator

(Rigid 1), the process and effort of achieving this performance of REA is much simpler

than the rigid counterpart. Furthermore, by introducing inner loop torque control

into a regular position controlled actuator, the accuracy of positional response can be

improved significantly as compared to the rigid actuator without dynamic compen-

sation (Rigid 2). With the presence of inner loop torque control, the motor torque is

modulated as close as possible to output torque regardless of the frictions found in the

motor drive system. Thus, REA not only improve the steady state errors of position

manipulations but also simplify the process of achieving a good position control.

5.4.2 Position Control: Trajectory Response

As far as position control of the actuator is concerned, it is also important that it

can track a desire trajectory reasonably well. In the previous section it is proven that

the friction and inertia of the actuator are fairly well identified. Thus, SimuLink will

be used again to simulate and tune the actuator. The actuator will be tested against

a sinusoidal input. The simulated performances and their corresponding gains are

shown in Figure 5.5 and Table 5.7

From Figures 5.5 and 5.6, the performance of the actuators are very similar. This

is because the desired position in sinusoidal trajectory started from 0 degree and


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-80

-60

-40

-20

0

20

40

60

80

Time (s)

Pos

itin

(deg

.)

Position Control: Trajectory Response

ElasticRigidDesired Trajectory

Elastic

Desire

Rigid

Figure 5.5: Simualtion Results of Trajectory Position Control.

Computed Inner Loop PID DynamicActuator Torque Control Torque Control Compensation

KP KV P I D τsf b

Rigid 1 2000 2√

300 0 0 0 4 7

Rigid 2 2000 2√

600 0 0 0 0 0

Elastic 2000 2√

600 1 22 0 0 0

Table 5.7: The Gains and Dynamic Compensation for Trajectory Position Controlfor step input.


Position Control: Trajectory Response

-80

-60

-40

-20

0

20

40

60

80

0 500 1000 1500 2000

Time, t (ms)

Po

siti

on

of

Lo

ad (

deg

ree)

Desired Trajectory

Elastic: Kp 2000 Kv 2sqrt(600) P 1 I 22 D 0.01Rigid: Kp 2000 Kv 2sqrt(600)

Desired Trajectory Rigid

Elastic

Figure 5.6: Experimental Results of Trajectory Position Control.


changes gradually. As compared to step positioning, there is a drastic change of

desired position. Thus, the effect of the inner loop PID torque control is not as

significant in trajectory response.

5.5 Torque Control

Torque control is more significantly needed when the robot is in contact with a surface

than when it is moving in free space. The actuator will be tested against its response

to step and trajectory input. The main interests here are to examine how fast and

how accurate the actuator can track a desire torque. The position controller gains for

both step and trajectory response as tuned using SimuLink is shown in Table 5.8.

PID Torque ControlResponse P I D

Step 1 22 0.01Trajectory 20 20 0

Table 5.8: The Gains for PID Torque Controller.

The response of REA to both step and trajectory torque input are shown in Figure

5.7 and 5.8 respectively. The results shown that higher gains are needed to maintain

the tracking of a sinusoidal torque as compare to a step torque. In step torque

control, the controller took about 0.25 seconds to track the desire torque accurately.

These results also explained why the elastic actuator is slightly slower in step position

response as compared to the ideal case actuator. But the trade-off is worthwhile as

it improve the accuracy and precision of the actuator in positioning control.

Figure 5.8 shows that the performances of REA is very well predicted by the

simulation results. At the same time, REA shown good trajectory (sinusoidal) torque


Torque Control : Step ResponseP 20 I 20 D 0.01

-1

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time, t (s)

Ou

tpu

t T

orq

ue,

TL

(N

M)

Desired TorqueSimulation Experiment

Desired Torque

SimulationExperiment

Figure 5.7: Torque Control: Step Response of REA.


Torque Control: Sinusoidal ResponseP 20 I 20 D 0.01

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time, t (s)

Ou

tpu

t T

orq

ue,

TL

(N

M)

Desired Torque

Simulation

Experiment

Desired Torque

Simulation

Experiment

Figure 5.8: Torque Control: Trajectory Response of REA.


control.

5.6 Force Control

There are two types of force control used here. Namely, force control for contact start

and force control for moving to contact.

5.6.1 Contact Start

Start with Contact: Force vs. Time

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

Time,t (s)

Fo

rce,

F (

N)

Elastic: Outer: P 1 I 10, Inner: P 1 I 22

Rigid 1 : P 1 I 10 D 0.03 Tsf 4 b 7

Rigid 2 : P 1 I 10

Desired Force

Rigid 2

Elastic

Rigid 1

Desired Force

Figure 5.9: Simulation Results of Force Control Start With Contact.

The gains of the controllers in Table 5.9 are selected arbitrarily for the purpose of

performance comparison between the actuators. This is to ensure that all actuators


Start with Contact: Force vs. Time

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3

Time,t (s)

Fo

rce,

F (

N)


Rigid 1 : P 1 I 10 D 0.03 Tsf 4 b 7

Rigid 2 : P 1 I 10

Desired Force

Rigid 2

Elastic

Rigid 1

Desired Force

Figure 5.10: Experimental Results of Force Control Start With Contact.

are performed under the same amount of effort of actuation, e.g. the maximum torque

are the same for all actuators. Thus, all the actuators will be controlled by the same

outer loop force control regardless of their performances.

The simulation experimental results of force control that start with contact are

shown in Figures 5.9 and 5.10 respectively. Due to the softness of the Elastic Flywheel,

the response of the REA shown a little bit of overshoot and “discontinuities” as

compared to its rigid counterpart. The experimental results seems to have some

steady state errors as compared to the simulation results. This is due the analog effect

of the load cell used in the experiment which introduced noise in to the feedback loop.

The response of Rigid 2 is about 0.4 seconds slower than the other two actuators.


Outer Loop Inner Loop DynamicActuator Force Control Torq. Control Compensation

P I D P I D Tsf bRigid 1 1 10 0 0 0 0 4 7Rigid 2 1 10 0.08 0 0 0 0 0Elastic 1 10 0 1 22 0 0 0

Table 5.9: The Gains and Dynamic Compensation for Force Control.

This is mainly because the chosen Integral term used in the experiment is not fast

enough to compensate the frictions in the actuator. However, these frictions are well

compensated through the implementation of the inner loop torque control into REA.

Although the response of REA is slightly slower than Rigid 1 according to SimuLink.

But the real-life experiments showed that REA is as fast as Rigid 1 in force control.

In contrast to the simulation, perfect dynamic compensations are almost impossible

in the experiments. In simulations, only dynamic and static frictions are modelled

and compensated. On the other hand, there are also non-linearities such as coulomb

frictions and backlashes exist in the system. Thus, this is why Rigid 1 is slower in ex-

periment than what SimuLink predicted, where as REA can easily compensate these

frictions using inner loop torque control.

5.6.2 Moving to Contact

Force control by itself is found to be inadequate in condition where robots are initially

moving in free space and then come into contact with the environment. Thus, hybrid

speed/control is use to control the robots in both environments.

The gains of force control moving to contact are first simulated using SimuLink

for safety purpose. Then, an uniform set of the controller’s gains is selected for all the

actuators. Thus, it can be assumed that all the actuators are controlled by the same


control system. By doing so, the performance of the actuators can be compared and

evaluated. Refer to Table 5.10 for the gains and dynamic compensation for Hybrid

Speed/Force Control.

Hybrid Inner Loop DynamicActuator Speed Force Torq. Control Compensation

KP KV P I D P I D Tsf bRigid 1 0 200 1 10 0 0 0 0 4 7Rigid 2 0 200 1 10 0.08 0 0 0 0 0Elastic 0 200 1 10 0 1 22 0 0 0

Table 5.10: The Gains and Dynamic Compensation for Hybrid Speed/Force Control.

Figure 5.11 shows the experimental results of the actuator under hybrid speed/force

control, where it needs to move a certain unknown distance, for example 30 degrees

before its end-effector touches the working surface. Figure 5.12 shows that the set-

tling time for Rigid 1 and Elastic are about the same, where as the settling time of

Rigid 2 is about 0.35 seconds slower than the previous two actuators.

Although the collision occurs severely between all the actuators and their working

surface. The reflected torque transmitted to the system are greatly reduced for REA

as the elastic flywheel somewhat low pass the reflected torque. From Figure 5.13,

it can be shown that the reflected torque of REA peak at 5Nm after more than 0.3

seconds, while the reflected torque for the rigid actuators can reach up to 50 Nm

instantaneously, namely in less than 1 miliseconds.

Furthermore, the rigid actuators exhibit great vibration and instability while per-

forming these tasks. To resolve this problem, the size of the gearbox used for the

rigid actuators need to be fairly big in order to withstand the high reflected torque.

However, big heavy-duty gearbox can over burden the system while still failed to

maintain the stability of the system. Thus, elasticity in the actuator is an ideal way


Moving to Contact (30 degree)Hybrid Speed/Force Control: Force vs. Time

-20

0

20

40

60

80

100

120

140

160

180

0 0.5 1 1.5 2 2.5 3 3.5 4

Time,t (s)

Fo

rce,

F (

N)

Rigid 1 : P 1 I 10 D 0.03 Tsf 4 b 7


Rigid 2 : P 1 I 10

Desired Force

Rigid 2

ElasticRigid 1

Desired Force

Speed Control for all actuators:Kp = 0, Kv = 200

Figure 5.11: Experimental Results of Force Control Moving To Contact.


Moving to Contact (30 degree)Hybrid Speed/Force Control: Force vs. Time

0

2

4

6

8

10

12

14

16

18

20

0 0.5 1 1.5 2 2.5 3 3.5 4

Time,t (s)

Fo

rce,

F (

N)

Rigid 1 : P 1 I 10 D 0.03 Tsf 4 b 7


Rigid 2 : P 1 I 10

Desired Force

Rigid 2

ElasticRigid 1

Desired Force


Figure 5.12: Experimental Results of Force Control Moving To Contact (Magnified).

to maintain the stability and protect the system from damages as a consequence of

collision.


Moving to Contact (30 degree)Hybrid Speed/Force Control:

Reflected Torque on Gear vs. Time

-60

-40

-20

0

20

40

60

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time,t (s)

To

rqu

e,T

rf (

Nm

)

Rigid 2 : P 1 I 10

Rigid 1 : P 1 I 10 D 0.03 Tsf 4 b 7


Rigid 2

Elastic

Rigid 1


Figure 5.13: Reflected Torque of Actuators.

Chapter 6

Conclusions

6.1 Summary of Work Done

For a typical robotic application, where frictions and non-linearities of motor drive

system are inherent, the performance can be improved by introducing an inner loop

torque controller into its original position controlled actuator. The main purpose of

the inner loop control is to account for the frictional loss and noises found in between

the motor source and the output load which affect the accuracy of the output position.

The inner loop control served the same purpose as incorporating the dynamics of the

actuator into its controller. However, the process of identifying the dynamics can be

very time-consuming and simply not possible in some existing system.

By using the Elastic Flywheel as part of the torque sensor, REA is also capable

of generating accurate torque. This feature is particularly essential for manipula-

tor when interacting with working surfaces under kinematic constraints. With the

presence of elasticity, the actuator becomes more shock tolerant and enable better in-

teraction between the robotic structure and its working surface. The elasticity in the

actuator which minimize the vibrations of the robotic system can improve stability

73

Chapter 6: Conclusions 74

of torque/force control. Some other added advantages of the elasticity such as lower

reflected inertia, better energy storage capacity and less inadvertent damage to the

environment are also very favorable in robotic application.

As far as the movements of animals are concerned, their contact with environment

are felt through a series of elastic tendons to maintain their stability in locomotion.

These tendons not only allow the animal to have immediate cognition in moving itself

in unknown environment but also its energy can be stored and released elastically.

Animals commonly utilize the elasticity of tendons to store energy from one part of a

locomotive cycle to release it in another. Since the muscles are doing less work overall

than it otherwise would be, this potentially improves efficiency. Thus, actuators with

series elasticity will allow the same effect to happen in robots, extending the life of

battery.

The Rotary Elastic Actuator have proven to boast the performance of the tradi-

tional position control methods, especially in cases where non-linearities are excessive

in the motor drive and transmission systems. At the same, the actuator is also capa-

ble of force/torque control, multi-revolution and its elastic nature have already shown

to contribute improvements and benefits in applications such as bipedal walking[1],

human-robots interactions [9] and other torque /force inherent tasks[5].

6.2 Future Work

Several avenues are open for future works. Although significant efforts have been put

in making the elastic flywheel to be a compact and yet modular one, its current size

can still be minimize. This has opened doors to future effort in reducing the size

of this elastic torque sensor. Some suggested ways of improvements are rearranging

Chapter 6: Conclusions 75

the springs diagonally or over-lapping the springs to achieve smaller diameter of the

elastic flywheel.

As far as the precision of the measurements of the deflection of the flywheel are

concerned, sensors e.g. encoders should be mounted as close as possible to the fly-

wheel. Since non-linearities such as backlash and friction are found in the gearbox

and couplings , this will contribute to the systematic errors. To minimize these er-

rors, one encoder should be installed in between the elastic flywheel to measure the

torsional deflection of the elastic flywheel and another encoder on the output of the

actuator to measure the actual output position of the actuator.

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[14] Cannon R. H. and Rosenthal D. E. Experiments in control of flexible struc-

tures with noncolocated sensors and actuators. AIAA Journal of Guidance and

Control, 3(3):546–553, Sept.-Oct. 1984.

[15] Xu Y. and Ma D. Force and transient control using nonlinear pd control. IEEE

Intl Conf on Robotics and Automation, pages 924–930, 1984.

[16] Wu C. H. and Paul R. Manipulator compliance based on joint torque control.

Proc IEEE Conf on Decision and Control, Alberquerque, NM., pages 88–94, 1990.

[17] Tarn T. J. Marth G. T. and Bejczy A. K. An event based approach to impact

control: Theory and experiments. EEE Intl Conf on Robotics and Automation,

pages 918–923, 1994.

[18] Volpi R. and Khosla P. A theoretical and experimental investigation of ex-

plicit force control stategies for manipulators. IEEE Trans. Automatic Con-

trol, 38(11), November 1993.

[19] Yousef-Toumi K. and Gutz D. A. Impact and force control. IEEE Intl Conf on

Robotics and Automation, pages 410–416, 1989.

[20] Asada H. and Kanade T. Design of direct-drive mechanical arms. ASME Journal

of Vibration, Acoustics, Stress, and Reliability in Design, 105(3):312–316, 1992.

[21] Dieter Vischer and Khatib Oussama. Design and development of high perfor-

mance torque-controlled joints. IEEE Transactions on Robotics and Automa-

tions, 4(11):537–544, 1995.

[22] B. Tondu and P. Lopez. Modeling and control of mckibben artificial muscle robot

actuators. IEEE Control Systems Magazine, April 2000.

[23] John J Craig. Introduction to Robotics : Mechanics and Control. Addison-Wesley

Publishing Company, 2nd edition, 1989.

[24] Barnes Group. Catalogue of Stock Springs and Spring Washers, 2001.

[25] Servo To Go, Inc., 1716 221 place NE, Redmond, WA 98053. ISA Bus Servo I/O

Card Model 2 Hardware Manual., 2.0 edition, May 1999.

[26] Venture Com, Inc., Fice Cambridge Center, Cambridge MA 02142. RTX 5.0

User Manual, 1.0 edition, 2000.

[27] Khatib O. Jamisola R., Ang M. Jr. and Lim S. Y. Dynamics identification and

control of an industrial robot. Proceedings of the Ninth International Conference

on Advanced Robotics (ICAR’99), pages 323–328, October 1999.

Appendix A

Technical Drawings

79

A.1 Part List of Rotary Elastic Actuator (REA)

1

2

3

45

6

9

1011

7

8D E FC

12

34

BA

32

15

C D

46

78

A B

A4

SHEE

T 1

OF

1SC

ALE

:1:2

DW

G N

O.

TITL

E:NA

TIO

NA

L U

NIV

ERSI

TY O

F SI

NG

APO

RE

DO

NO

T SC

ALE

DRA

WIN

GW

EIG

HT:

MA

TERI

AL:

DA

TEN

AM

E

FIN

ISH

:

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE IN

MIL

LIM

ETER

SSU

RFA

CE

FIN

ISH

:TO

LERA

NC

ES:

L

INEA

R:

�

� +/- 0

.1

AN

GU

LAR:

� +/- 0

.1M

FG

APP

V'D

CH

K'D

DRA

WN

PRO

PRIE

TARY

AN

D C

ON

FID

ENTI

AL

THE

INFO

RMA

TIO

N C

ON

TAIN

ED I

N T

HIS

DRA

WIN

G IS

TH

E SO

LE P

ORP

ERTY

OF

AD

ELA

IDE

UN

IVER

SITY

. AN

Y RE

PRO

DU

CTI

ON

IN P

ART

OR

AS

A W

HO

LE W

ITH

OU

TTH

E W

RITT

EN P

ERM

ISSI

ON

OF

AD

ELA

IDE

UN

IVER

SITY

IS P

ROH

IBIT

ED

EMC

HA

I22

/10/

'02

VA

RIES

VA

RIES

EM -

PL -

01

Part

List

1-

Ge

ne

ral

613.

9 G

M

Ite

m N

o:

De

sc

rip

tio

ns

:1

MO

TO

R E

NC

OD

ER

25

00

PP

R2

PA

NA

SO

NIC

40

0W

SE

RV

OM

OT

OR

34

0 :

1 G

EA

RB

OX

4M

OT

OR

BR

AC

KE

T5

CO

UP

LIN

G6

FL

EX

IBL

E F

LY

WH

EE

L7

BE

AR

ING

SU

PP

OR

T U

NIT

8D

UM

MY

WE

IGH

T

9E

NC

OD

ER

BR

AC

KE

T1

0B

EA

RIN

G U

NIT

11

OU

TP

UT

EN

CO

DE

R 2

50

0 P

PR

Figure A.1: Part List of Rotary Elastic Actuator.

A.2 Part List of Elastic Flywheel

13

14

11

15

1118

20

16

3

45

2

106

87

17

19

1

9

12

Ass

em

ble

d V

iew

Exp

lod

ed

Vie

w

D E FC

12

34

BA

32

15

C D

46

78

A B

A4

SHEE

T 1

OF

1SC

ALE

:1:2

DW

G N

O.

TITL

E:NA

TIO

NA

L U

NIV

ERSI

TY O

F SI

NG

APO

RE

DO

NO

T SC

ALE

DRA

WIN

GW

EIG

HT:

MA

TERI

AL:

DA

TEN

AM

E

FIN

ISH

:

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE IN

MIL

LIM

ETER

SSU

RFA

CE

FIN

ISH

:TO

LERA

NC

ES:

L

INEA

R:

�

� +/- 0

.1

AN

GU

LAR:

� +/- 0

.1M

FG

APP

V'D

CH

K'D

DRA

WN

PRO

PRIE

TARY

AN

D C

ON

FID

ENTI

AL

THE

INFO

RMA

TIO

N C

ON

TAIN

ED I

N T

HIS

DRA

WIN

G IS

TH

E SO

LE P

ORP

ERTY

OF

AD

ELA

IDE

UN

IVER

SITY

. AN

Y RE

PRO

DU

CTI

ON

IN P

ART

OR

AS

A W

HO

LE W

ITH

OU

TTH

E W

RITT

EN P

ERM

ISSI

ON

OF

AD

ELA

IDE

UN

IVER

SITY

IS P

ROH

IBIT

ED

EMC

HA

I22

/10/

'02

VA

RIES

VA

RIES

EM -

PL -

02

Part

List

2 -

Fle

xib

le F

lyw

he

el

ITE

M N

O.

QTY

.P

AR

T N

O.

RE

FE

NC

E N

O.:

MA

TER

IAL

WE

IGH

T (G

M)

11

MID

DLE

SH

AF

TE

M-F

F-0

8S

tain

less

Ste

el38

3.67

212

M3

CA

P S

CR

EW

x 1

0 m

mS

002-

003-

010

Har

dene

d S

teel

33

1TH

RIS

T B

EA

RIN

G 1

5 TO

PG

S.8

1102

Har

dene

d S

teel

104

1TH

RU

ST

BE

AR

ING

15

BA

SE

WS

.811

02H

arde

ned

Ste

el10

51

THR

US

T B

EA

RIN

G 1

5 C

EN

TER

KS

.811

02LP

BH

arde

ned

Ste

el6

61

BA

LL B

EA

RIN

G

6180

0TH

igh

Str

engh

Ste

el5

71

M6

CA

P S

CR

EW

x 1

0 m

mS

022-

006-

010

Hig

h S

tren

gh S

teel

48

1M

6 W

AS

HE

RW

10-0

06-0

000

Hig

h S

tren

gh S

teel

19

1M

OTO

R H

UB

E

M-F

F-0

4S

tain

less

Ste

el13

5.86

101

CE

NTE

R

BE

AR

ING

HO

US

ING

E

M-F

F-0

2S

tain

less

Ste

el79

.31

118

SP

RIN

G S

LID

ER

E

M-F

F-1

4A

lum

inum

Allo

y12

.99

128

SP

RIN

G W

AS

HE

R

EM

-FF

-15

Sta

inle

ss S

teel

3.24

138

M5

PH

ILLI

P S

CR

EW

x 8

0 m

mP

10-0

05-0

80H

igh

Str

engh

Ste

el15

1416

M4

CS

K x

16

mm

S02

9-00

4-01

6H

igh

Str

engh

Ste

el4

1516

CE

RA

MIC

BU

SH

(D

ia.

5.5

mm

)P

AP

040

3 P

10S

tain

less

Ste

el1

1616

M3

SE

T S

CR

EW

x 4

mm

S30

-003

-004

Hig

h S

tren

gh S

teel

317

16E

XTE

NS

ION

SP

RIN

GT4

2690

Hig

h S

tren

gh S

teel

5018

1O

UTP

UT

FLY

WH

EE

L E

M-F

F-0

7A

lum

inum

Allo

y36

1.21

198

M4

CA

P S

CR

EW

x 1

6 m

mS

002-

004-

016

Hig

h S

tren

gh S

teel

420

1M

OTO

R F

LYW

HE

EL

EM

-FF

-05

Alu

min

umA

lloy

361.

21

Figure A.2: Part List of Elastic Flywheel.

A.3 Part Files

A.3.1 Center Bearing Housing

40

28

16

30

QQ

FRO

NT

VIE

W

4 H

OLE

S M

3 X

0.5

-6H

EQU

I-SPA

CED

ON

35

MM

4 H

OLE

S M

4 X

0.6

- 6H

EQU

I-SPA

CED

ON

30

MM

45°

ISO

MET

RIC

VIE

WSc

ale

1 :

1

13.5

0 65.

50

16

19

40

283

Q-Q

SE

CTI

ON

AL

VIE

W

B C D

12

A

32

14

BA

56

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE

IN M

ILLI

MET

ERS

SUR

FAC

E FI

NIS

H: G

RA

DE

6TO

LER

AN

CES

:

LIN

EAR

:

+

/- 0

.1

AN

GU

LAR

:

+

/- 0

.1

FIN

ISH

:

NA

ME

DA

TE

MA

TER

IAL:

WEI

GH

T:

NA

TIO

NA

L U

NIV

ERSI

TY O

F SI

NG

APO

RETI

TLE:

DW

G N

O.

SCA

LE:2

:1SH

EET

1 O

F 1

A4C

Ce

nte

r Be

arin

g H

ous

ing

EM -

FF -

02

DR

AW

N

CH

K'D

DR

AW

N

MFG

AP

PV

'D

CH

K'D

PRO

PRIE

TARY

AN

D C

ON

FID

ENTI

AL

THE

INFO

RMA

TIO

N C

ON

TAIN

ED IN

TH

IS

DR

AW

ING

IS T

HE

SOLE

PRO

PERT

Y O

FA

DEL

AD

IE U

NIV

ERSI

TY. A

NY

REPR

OD

UC

TIO

N

IN P

ART

OR

AS

A W

HO

LE W

ITH

OU

T TH

E W

RIT

TEN

PER

MIS

SIO

N O

F A

DEL

AID

EU

NIV

ERSI

TY IS

PRO

HIB

ITED

.

STA

INLE

SS S

TEEL

MIL

LEMC

HA

I19

/10/

'02

DO

NO

T SC

ALE

DRA

WIN

G77

.54

GM

Figure A.3: Center Bearing Housing.

A.3.2 Motor Hub

40

20

C C

4 H

OLE

S M

4 X

0.7

- 6H

EQU

I-SPA

CED

ON

30

FRO

NT

VIE

W

30

4

40

1215

19R1

3 5

R1

C-C

SEC

TIO

NA

L V

IEW

ISO

MET

RIC

VIE

WSC

ALE

: 1:

1

135.

85 G

M

B C D

12

A

32

14

BA

56

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE

IN M

ILLI

MET

ERS

SUR

FAC

E FI

NIS

H: G

RA

DE

6TO

LER

AN

CES

:

LIN

EAR

:

+

/- 0

.1

AN

GU

LAR

:

+

/- 0

.1

FIN

ISH

:

NA

ME

DA

TE

MA

TER

IAL:

WEI

GH

T:

NA

TIO

NA

L U

NIV

ERSI

TY O

F SI

NG

APO

RETI

TLE:

DW

G N

O.

SCA

LE:2

:1SH

EET

1 O

F 1

A4C

Mo

tor H

ub

EM

-FF-

04

DR

AW

N

CH

K'D

DR

AW

N

MFG

AP

PV

'D

CH

K'D

PRO

PRIE

TARY

AN

D C

ON

FID

ENTI

AL

THE

INFO

RMA

TIO

N C

ON

TAIN

ED IN

TH

IS

DR

AW

ING

IS T

HE

SOLE

PRO

PERT

Y O

FA

DEL

AD

IE U

NIV

ERSI

TY. A

NY

REPR

OD

UC

TIO

N

IN P

ART

OR

AS

A W

HO

LE W

ITH

OU

T TH

E W

RIT

TEN

PER

MIS

SIO

N O

F A

DEL

AID

EU

NIV

ERSI

TY IS

PRO

HIB

ITED

.

STA

INLE

SS S

TEEL

TURN

ING

EMC

HA

I27

/09/

'01

DO

NO

T SC

ALE

DRA

WIN

G

Figure A.4: Motor Hub.

A.3.3 Motor Flywheel

24

4

2022

SID

E V

IEW

200

R90

76

4025

20

EQU

I-SPA

CED

ON

30

4 H

OLE

S 4

74

EQU

I-SPA

CED

O

N R

97

8 H

OLE

S 2

1020

22

4 H

OLE

S 7

X 2

MM

DEE

P EQ

UI-S

PAC

ED

ABO

UT

CEN

TERL

INE

4 W

EBS

X 4M

M T

HK

CEN

TERE

D

8 H

OLE

S 20

4 H

OLE

S 50

90 A

PART

A

BOU

T C

ENTE

RLIN

E

FRO

NT

VIE

W

R97

30

45°

22.5

0°

ISO

MET

RIC

VIE

WSC

ALE

: 1:

4

B C D

12

A

32

14

BA

56

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE

IN M

ILLI

MET

ERS

SUR

FAC

E FI

NIS

H: G

RA

DE

6TO

LER

AN

CES

:

LIN

EAR

:

+

/- 0

.1

AN

GU

LAR

:

+

/- 0

.1

FIN

ISH

:

NA

ME

DA

TE

MA

TER

IAL:

WEI

GH

T:

NA

TIO

NA

L U

NIV

ERSI

TY O

F SI

NG

APO

RE

TITL

E:

DW

G N

O.

SCA

LE:1

:2SH

EET

1 O

F 1

A4C

Mo

tor F

lyw

hee

l

EM -

FF -

05

DR

AW

N

CH

K'D

DR

AW

N

MFG

AP

PV

'D

CH

K'D

PRO

PRIE

TARY

AN

D C

ON

FID

ENTI

AL

THE

INFO

RMA

TIO

N C

ON

TAIN

ED IN

TH

IS

DR

AW

ING

IS T

HE

SOLE

PRO

PERT

Y O

FA

DEL

AD

IE U

NIV

ERSI

TY. A

NY

REPR

OD

UC

TIO

N

IN P

ART

OR

AS

A W

HO

LE W

ITH

OU

T TH

E W

RIT

TEN

PER

MIS

SIO

N O

F A

DEL

AID

EU

NIV

ERSI

TY IS

PRO

HIB

ITED

.

ALU

MIN

UM

ALL

OY

MIL

LEMC

HA

I27

/09/

'01

DO

NO

T SC

ALE

DRA

WIN

G34

9.95

GM

PRO

J.:

Figure A.5: Motor Flywheel.

A.3.4 Output Flywheel

2

4

4

2022

SID

E V

IEW

EQU

I-SPA

CED

ON

304

HO

LES

4R

3.50

4

20

2540

76

200

R90

1020

22

FRO

NT

VIE

W

4 W

EBS

X 4M

M T

HK

CEN

TERE

D

4 H

OLE

S 7

X 2M

M D

EEP

EQU

I-SPA

CED

A

BOU

T C

ENTE

RLIN

E

8 H

OLE

S 20

4 H

OLE

S 50

90 A

PART

ABO

UT

CEN

TERL

INE

R97

22.50°

45°

ISO

MET

RIC

VIE

WSC

ALE

: 1:

4

B C D

12

A

32

14

BA

56

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE

IN M

ILLI

MET

ERS

SUR

FAC

E FI

NIS

H: G

RA

DE

6TO

LER

AN

CES

:

LIN

EAR

:

+

/- 0

.1

AN

GU

LAR

:

+

/- 0

.1

FIN

ISH

:

NA

ME

DA

TE

MA

TER

IAL:

WEI

GH

T:

NA

TIO

NA

L U

NIV

ERSI

TY O

F SI

NG

APO

RE

TITL

E:

DW

G N

O.

SCA

LE:1

:2SH

EET

1 O

F 1

A4C

OU

TPU

T FL

YWH

EEL

EM -

FF -

07

DR

AW

N

CH

K'D

DR

AW

N

MFG

AP

PV

'D

CH

K'D

PRO

PRIE

TARY

AN

D C

ON

FID

ENTI

AL

THE

INFO

RMA

TIO

N C

ON

TAIN

ED IN

TH

IS

DR

AW

ING

IS T

HE

SOLE

PRO

PERT

Y O

FA

DEL

AD

IE U

NIV

ERSI

TY. A

NY

REPR

OD

UC

TIO

N

IN P

ART

OR

AS

A W

HO

LE W

ITH

OU

T TH

E W

RIT

TEN

PER

MIS

SIO

N O

F A

DEL

AID

EU

NIV

ERSI

TY IS

PRO

HIB

ITED

.

ALU

MIN

UM

ALL

OY

MIL

LEMC

HA

I27

/09/

'01

DO

NO

T SC

ALE

DRA

WIN

G34

7.18

GM

PRO

J.:

Figure A.6: Output Flywheel.

A.3.5 Middle Shaft

Q Q

FRO

NT

VIE

W

8 H

ole

s M

3 X

0.5

ON

35

MM

TH

REA

DED

TH

RU

4 H

OLE

S M

4 X

0.7

ON

30

MM

THRE

AD

ED T

HRU

TOP

VIE

W

FRO

NT

VIE

W

ISO

MET

RIC

VIE

WSc

ale

: 1:

2

20°

20°

21°

21° 30 35

10

55

6

10

7.50

Q-Q

SEC

TIO

NA

L V

IEWM

6 H

OLE

MIN

. 18

MM

DEE

P

10

MM

HO

LEM

IN. 1

8 M

M D

EEP

2 H

OLE

S M

4 X

0.70

90 A

PART

THRE

AD

ED T

HRU

1013

15

4024

7815

8

6

R3R3

20

B C D

12

A

32

14

BA

56

UN

LESS

OTH

ERW

ISE

SPEC

IFIE

D:

DIM

ENSI

ON

S A

RE

IN M

ILLI

MET

ERS

SUR

FAC

E FI

NIS

H: G

RA

DE

6TO

LER

AN

CES

:

LIN

EAR

:

+

/- 0

.1

AN

GU

LAR

:

+

/- 0

.1

FIN

ISH

:

NA

ME

DA

TE

MA

TER

IAL:

WEI

GH

T:

Na

tion

al U

niv

ers

ity o

f Sin

ga

po

re

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Appendix B

Controller Code Part I -

Calibration and Position Control

B.1 Calibration

94

B.1.1 Calibration - Header File

// MOTORCNTLRTX.H #define PI 3.14159265359 #define Jl 0.0149 //Inertia #define Js 0.0676 #define Jb1 0.2646 #define F0 43.3 //Initial force for spring #define Kp 60.0 #define Kv (2*sqrt(0.0)) #define fr 0.092 double t= 7.0; //ff double R =94.0; #define KS 760 #define alp atan(t/R) #defineK 10.4 #define Kc 240 #define L0 53.8 #define Lr 55*PI/180 //************** ServoToGo ************************************** #define STG_A 0x240 //ServoToGo Card A base address #define STGOff 0x400 //offset for high address space #define DAC0 0x250 #define pSharedMemory "SharedMemory" typedef struct Data { int handshake; BOOL startrtss; BOOL killRT; } DATASTRUCT; DATASTRUCT *pdata;

Figure B.1: Calibration - Header File.

B.1.2 Calibration - Main File

//CALIBRATION : SPRING'S STIFFNESS TEST. //By: Eddie Chai //Main File #include "stdafx.h" #include <iostream.h> #include <windows.h> #include <stdio.h> #include <conio.h> #include <stdlib.h> #include <fstream.h> #include <math.h> #include <rtapi.h> #include "motorcntlrtx.h" double f1[200000]; double f2[200000]; double dt[200000]; double c1[200000]; double c2[200000]; double Tc[200000]; double V[200000]; double M [200000]; double L [200000]; double Md [200000]; double Mdd [200000]; double Ld [200000]; double Ldd [200000]; double TS[200000]; int d = 20; // delay int p = 1 ; // interval time int i = 1; int v= 1; int runtime =200000/p; //100 of interval int n=0; double voltage; double interval = 0.001*p*d; //interval time BOOL flag=TRUE; BOOL start=TRUE; void Analog_Out (int channel, double voltage)

Figure B.2: Calibration - Main File Page 1.

{ //check voltage double t_voltage=0.0; int dig; if (voltage >10.0) t_voltage = 10.0; else if (voltage < -10.0) t_voltage = -10.0; else t_voltage = voltage; //t_voltage = -t_voltage; dig = (int)(8191 * (t_voltage+10)/20.0); //write to DAC Channel RtWritePortUshort( (PUSHORT) (DAC0), (USHORT)dig); } //Initialise encoders(pg27). void RltZeroCntr(int channel) { // int offset; PUCHAR addresspuc, addresspuc1; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C RtWritePortUchar(addresspuc, (UCHAR)0x20); //Master Control Register. MRST master reset RtWritePortUchar(addresspuc, (UCHAR)0x68); //Input Control Register. RtWritePortUchar(addresspuc, (UCHAR)0x80); //Output Control Register. RtWritePortUchar(addresspuc, (UCHAR)0xc3); //Quadrature Register 4x quadrature mode RtWritePortUchar(addresspuc, (UCHAR)0x04); //Reset encoder counters to zero. addresspuc1=(PUCHAR)(STG_A+ 0x400 + 0x0e); //TMRCMD RtWritePortUchar(addresspuc1, (UCHAR)0x3a); //chose timer 0 RtWritePortUchar(addresspuc1, (UCHAR)0x7a); //chose timer 1 RtWritePortUchar(addresspuc1, (UCHAR)0xba); //chose timer 2 printf("ENCODER %d Initialization COMPLETE\n",channel); return; } //Read encoder counter i. Return counter reading value long RltReadCntr(int channel) { PUCHAR addresspuc, addresspuc1; UCHAR cntl; UCHAR cntm; UCHAR cnth; long cntr;


addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C RtWritePortUchar(addresspuc,(UCHAR)0x02); //transfer counter to latch addresspuc1 = (PUCHAR)(STG_A+ channel*2 - 2); //select CNTi.D cntl = RtReadPortUchar(addresspuc1); //read counter latch low 8 bit cntm = RtReadPortUchar(addresspuc1); //read counter latch medium 8 bit cnth = RtReadPortUchar(addresspuc1); //read counter latch high 8 bit cntr=(long) (((cntl << 8) + (cntm << 16) + (cnth << 24)) / 256); return(cntr); } void RTFCNDCL TimerJob1(PVOID unused) { if(start) { n=0; start=FALSE; } // Initial conditions M[0]=0; L[0]=0; n+=1; // Positions in radian M[n]=RltReadCntr(1)*2*PI/10000; L[n]=RltReadCntr(3)*2*PI/10000; //Speeds in rad/s Md[n]=(M[n]-M[n-d])/interval; Ld[n]=(L[n]-L[n-d])/interval; //Acc Mdd[n]=(Md[n]-Md[n-d])/interval; Ldd[n]=(Ld[n]-Ld[n-d])/interval; // LOAD TORQUE by GEOMETRY dt[n] = M[n]/40-L[n]; f1[n] = K*((R/cos(alp))*sin(PI/8-alp-dt[n]/2)*2+5.5-L0)+F0; // N f2[n] = K*((R/cos(alp))*sin(PI/8-alp+dt[n]/2)*2+5.5-L0)+F0; // N c1[n] = (R/cos(alp))*cos((PI/8)-alp-dt[n]/2)/1000; // m


c2[n] = (R/cos(alp))*cos((PI/8)-alp+dt[n]/2)/1000; // m Tc[n] = 4*(f2[n]*c2[n]-f1[n]*c1[n]);// Nm // Load Torque assume linear relationship: TS[n] = dt[n]*KS; Analog_Out(0,0); if (n>= runtime) flag=FALSE; } int main() { LARGE_INTEGER x; LARGE_INTEGER Period; HANDLE hTimer; // HANDLE hToSharedMemory; RltZeroCntr(1); RltZeroCntr(3); printf("\n\nPlz Wait...\n"); Period.QuadPart=10000*p; if (!(hTimer = RtCreateTimer(NULL,0,TimerJob1,NULL,RT_PRIORITY_MAX,CLOCK_FASTEST))) // Always use fastest available clock { printf("SHUTDOWN: ERROR: Could not create the timer.\n"); ExitProcess(1); } if (!RtSetTimerRelative( hTimer, &Period, &Period)) { printf("SHUTDOWN: ERROR: Could not set and start the timer.\n"); ExitProcess(1); } printf("Kspring = %2.2fNm/rad\n",K); printf("Rspring = %3.1fmm\n",R); printf("sampling time = %3.1dms\n",p); printf("t(ms)\tM\t\tL\t\tdt\t\tMd(rpm)\tLd\t\tTs\n"); while(flag) {


printf("%5d\t%3.6f\t%3.6f\t%3.6f\t",n*p,M[n]*180/(40*PI),L[n]*180/PI,dt[n]); printf("%3.3f\t%3.3f\t\t",Md[n]*60/(2*PI),Ld[n]*60/(2*PI)); printf("%3.4f\n",dt[n]*252); Sleep(500); } RtCancelTimer(hTimer, &x); RtDeleteTimer(hTimer); printf("\n\n%ld END OF THE PROGRAM\n\n",n); return 0; }


B.2 Position Control

B.2.1 Position Control - Header File // POSITION CONTROL FOR STEP AND SINUSOIDAL INPUT // By: Eddie Chai // Header File // Control Architecture // Tm = [PID]*(Tl-Td) , where Tl = Ks(M-L) // Dynamics of Actuator // Tm = Tl + frictions // Tl = m*g*l*sin(L) + m*l^2*Ldd // Inertia term of Load, m*l^2 (kgm^2) #define Jl 0.0149 // lever only #define Js 0.0676 // small weight + lever // Gravitational term of Load, m*g*l (kgm^2s^-2 or N ) #define Gs 2.854 // small weight + lever // Coupling Parameters #define Kc 16.718 // Stiffness (Nm/deg) #define KS 426.0 // Overall Stiffness of Elastic Flywheel (Nm/rad) #define PI 3.14159265359 // Control Gains #define Kp 110 #define Kv 2*sqrt(110) #define P 1.0 #define I 22.0 #define D 0.0 // Desired Torque #define desire PI/3 // step //#define desire 20*sin((2*PI)*n/500) // Sinusoidal // Friction compensation #define fr 0.0 // Static/holding torque (% of Tm,max) //************** ServoToGo ************************************** #define STG_A 0x240 // ServoToGo Card A base address #define STGOff 0x400 // offset for high address space #define DAC0 0x250 // Analog Out Address #define pSharedMemory "SharedMemory" typedef struct Data { int handshake; BOOL startrtss; BOOL killRT; } DATASTRUCT; DATASTRUCT *pdata;

Figure B.7: Position Control - Header File.

B.2.2 Position Control - Main File

// POSITION CONTROL FOR STEP AND SINUSOIDAL INPUT // By: Eddie Chai // Main console #include "stdafx.h" #include <iostream.h> #include <windows.h> #include <stdio.h> #include <conio.h> #include <stdlib.h> #include <fstream.h> #include <math.h> #include <rtapi.h> #include "motorcntlrtx.h" // Elastic Flywheel double f1[50000]; // Force in Spring 1 (N) double f2[50000]; // Force in Spring 2 (N) double dt[50000]; // Deflection of Flywheel (rad) double c1[50000]; // Tangential Distance of Spring 1 relative to center of ff (mm) double c2[50000]; // Tangential Distance of Spring 2 relative to center of ff (mm) double Tc[50000]; // Output Torque // Dynamics of Actuator double M [50000]; // Position of Motor (rad) double L [50000]; // Position of Load (rad) double Md [50000]; // Speed of Motor (rad/s) double Mdd [50000]; // Acceleration of Motor (rad/s^2) double Ld [50000]; // Speed of Load (rad/s) double Ldd [50000]; // Acceleration of Load (rad/s^2)

Figure B.8: Position Control - Main File Page 1.

// Torque double TM[50000]; // Motor Torque double TS[50000]; // Output Torque - assume linear i.e. T = K*theta double Tr[50000]; // Desire Torque double er[50000]; double Ier[50000]; // PID parameters double Der[50000]; double V[50000]; // Voltage double tr[50000]; // Desire Position int d = 1; // delay int p = 1 ; // interval time int runtime =3000/p; int n=0; double voltage; double interval = 0.001*p*d; // interval time BOOL flag=TRUE; BOOL start=TRUE; void Analog_Out (int channel, double voltage) { double t_voltage=0.0; // check voltage int dig; if (voltage >10.0) t_voltage = 10.0; // make sure motor signal is between -10v to +10v else if (voltage < -10.0) t_voltage = -10.0; else t_voltage = voltage;

dig = (int)(8191 * (t_voltage+10)/20.0); RtWritePortUshort( (PUSHORT) (DAC0), (USHORT)dig); // write to DAC Channel } void RltZeroCntr(int channel) //Initialise encoders { PUCHAR addresspuc, addresspuc1; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C RtWritePortUchar(addresspuc, (UCHAR)0x20); //Master Control Register. MRST master reset RtWritePortUchar(addresspuc, (UCHAR)0x68); //Input Control Register. RtWritePortUchar(addresspuc, (UCHAR)0x80); //Output Control Register. RtWritePortUchar(addresspuc, (UCHAR)0xc3); //Quadrature Register 4x quadrature mode RtWritePortUchar(addresspuc, (UCHAR)0x04); //Reset encoder counters to zero. addresspuc1=(PUCHAR)(STG_A+ 0x400 + 0x0e); //TMRCMD RtWritePortUchar(addresspuc1, (UCHAR)0x3a); //chose timer 0 RtWritePortUchar(addresspuc1, (UCHAR)0x7a); //chose timer 1 RtWritePortUchar(addresspuc1, (UCHAR)0xba); //chose timer 2 printf("ENCODER %d Initialization COMPLETE\n",channel); return;


} long RltReadCntr(int channel) //Read encoder counter i. Return counter reading value { PUCHAR addresspuc, addresspuc1; UCHAR cntl; UCHAR cntm; UCHAR cnth; long cntr; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C RtWritePortUchar(addresspuc,(UCHAR)0x02); //transfer counter to latch addresspuc1 = (PUCHAR)(STG_A+ channel*2 - 2); //select CNTi.D cntl = RtReadPortUchar(addresspuc1); //read counter latch low 8 bit cntm = RtReadPortUchar(addresspuc1); //read counter latch medium 8 bit cnth = RtReadPortUchar(addresspuc1); //read counter latch high 8 bit cntr=(long) (((cntl << 8) + (cntm << 16) + (cnth << 24)) / 256); return(cntr); } void RTFCNDCL TimerJob1(PVOID unused) { if(start) { n=0; start=FALSE; } M[0] =0; // Initial conditions L[0] =0; Ier[0] =0; er[0] =0; Der[0] =0; n+=1; M[n]=RltReadCntr(1)*2*PI/10000; // Positions in radian L[n]=RltReadCntr(3)*2*PI/10000; Md[n]=(M[n]-M[n-d])/interval; //Speeds in rad/s Ld[n]=(L[n]-L[n-d])/interval; Mdd[n]=(Md[n]-Md[n-d])/interval; //Acc

Ldd[n]=(Ld[n]-Ld[n-d])/interval; TS[n] = dt[n]*KS; // Load Torque assume linear relationship if (n>1000) // Desired Torque { tr[n]= desire; } Tr[n]=(Kp*(tr[n]-L[n])-Kv*Ld[n])*Js*40; er[n] = Tr[n]-TS[n]; // Torque Control Loop Ier[n] = er[n]*0.001+Ier[n-1]; Der[n] = (er[n]-er[n-1])/0.001; if (n<runtime)


{ TM[n]=(P*er[n]+I*Ier[n]+D*Der[n])/40; if (TM[n]<1.3) { if (TM[n]>0) { V[n]=TM[n]*4/1.3+fr*4; Analog_Out(0,V[n]); } else { V[n]=TM[n]*4/1.3-fr*4; Analog_Out(0,V[n]); } } else {Analog_Out(0,0);} } if (n>= runtime) flag=FALSE; } int main() { LARGE_INTEGER x; LARGE_INTEGER Period; HANDLE hTimer; HANDLE hToSharedMemory; RltZeroCntr(1); RltZeroCntr(3); printf("\n\nPlz Wait...\n"); Period.QuadPart=10000; if (!(hTimer = RtCreateTimer(NULL,0,TimerJob1,NULL,RT_PRIORITY_MAX,CLOCK_FASTEST)))

// Always use fastest available clock { printf("SHUTDOWN: ERROR: Could not create the timer.\n"); ExitProcess(1); } if (!RtSetTimerRelative( hTimer, &Period, &Period)) { printf("SHUTDOWN: ERROR: Could not set and start the timer.\n"); ExitProcess(1); } printf("J = %2.4f kgm^2\n",Js); printf ("Kp %3.1f\tKv %3.1f\n",Kp,Kv); printf("Kff = %4.2f Nm/rad\n",KS); printf("sampling time = %3.4f s\n",interval);


printf("P=%1.3f\tI=%1.3f\tD=%1.3f\tfr=%1.3f\n",P,I,D,fr); printf("t(ms)\ttr\t\tM\tL\tdt\t\tMd(rpm)\tLdd\t\tTM(Nm)\t\tTS(Nm)\n"); while(flag) { printf("%3.3f\t%3.4f\t\t%3.4f\t%3.4f\t%3.4f\t\t",n*p*0.001,tr[n]*180/PI,M[n]*180/(40*PI),L[n]*180/PI,dt[n]); printf("%3.4f\t%3.4f\t\t",Md[n]*60/(2*PI),Ldd[n]); // Motor speed (rpm) , Output Acc (rad/s^2) printf("%3.4f\t\t%3.4f\n",V[n]*52/4,TS[n]); // Toutput , Tdesired Sleep(1); } RtCancelTimer(hTimer, &x); RtDeleteTimer(hTimer); return 0; }


Appendix C

Controller Code Part II - Torque

Control

C.1 Torque Control

108

C.1.1 Torque Control - Header File

// TORQUE CONTROL FOR STEP AND SINUSOIDAL INPUT // By: Eddie Chai // Header File // Control Architecture // Tm = [PID]*(Tl-Td) , where Tl = Ks(M-L) // Dynamics of Actuator // Tm = Tl + frictions // Tl = m*g*l*sin(L) + m*l^2*Ldd // Inertia term of Load, m*l^2 (kgm^2) #define Jl 0.0149 // lever only #define Kc 16.718 // Coupling Stiffness (Nm/deg) #define KS 426.0 // Elastic Flywheel Stiffness (Nm/deg) #define PI 3.14159265359 #define P 1.0 // Control Gains #define I 60.0 #define D 0.1 #define desire 5.0 // Desire Input: step //#define desire 20*sin((2*PI)*n/500) // Desire input: Sinusoidal #define fr 0//0.09 // Static/holding torque (% of Tm,max) //************** ServoToGo ************************************** #define STG_A 0x240 // ServoToGo Card A base address #define STGOff 0x400 // offset for high address space #define DAC0 0x250 // Analog Out Address #define pSharedMemory "SharedMemory" typedef struct Data { int handshake; BOOL startrtss; BOOL killRT; } DATASTRUCT; DATASTRUCT *pdata;

Figure C.1: Torque Control - Header File.

C.1.2 Torque Control - Main File

// TORQUE CONTROL FOR STEP AND SINUSOIDAL INPUT // By: Eddie Chai // Main console #include "stdafx.h" #include <iostream.h> #include <windows.h> #include <stdio.h> #include <conio.h> #include <stdlib.h> #include <fstream.h> #include <math.h> #include <rtapi.h> #include "motorcntlrtx.h" // Dynamics of Actuator double M [50000]; // Position of Motor (rad) double L [50000]; // Position of Load (rad) double Md [50000]; // Speed of Motor (rad/s) double Mdd [50000]; // Acceleration of Motor (rad/s^2) double Ld [50000]; // Speed of Load (rad/s) double Ldd [50000]; // Acceleration of Load (rad/s^2) double TM[50000]; // Motor Torque double TS[50000]; // Output Torque - assume linear i.e. T = K*theta double Tr[50000]; // Desire Torque // PID parameters double er[50000]; double Ier[50000];

Figure C.2: Torque Control - Main File Page 1.

double er[50000]; double Ier[50000]; double Der[50000]; // Voltage double V[50000]; int d = 1; // delay int p = 1 ; // interval time int runtime =3000/p; int n=0; double voltage; double interval = 0.001*p*d; //interval time BOOL flag=TRUE; BOOL start=TRUE; void RTFCNDCL TimerJob1(PVOID unused) { if(start) { n=0; start=FALSE; } // Initial conditions M[0] =0; L[0] =0; Ier[0] =0; er[0] =0; Der[0] =0; n+=1; // Positions in radian M[n]=RltReadCntr(1)*2*PI/10000; L[n]=RltReadCntr(3)*2*PI/10000; //Speeds in rad/s Md[n]=(M[n]-M[n-d])/interval; Ld[n]=(L[n]-L[n-d])/interval;


//Acc Mdd[n]=(Md[n]-Md[n-d])/interval; Ldd[n]=(Ld[n]-Ld[n-d])/interval; // LOAD TORQUE by GEOMETRY dt[n] = M[n]/40-L[n]; f1[n] = K*((R/cos(alp))*sin(PI/8-alp-dt[n]/2)*2+5.5-L0)+F0; // N f2[n] = K*((R/cos(alp))*sin(PI/8-alp+dt[n]/2)*2+5.5-L0)+F0; // N c1[n] = (R/cos(alp))*cos((PI/8)-alp-dt[n]/2)/1000; // m c2[n] = (R/cos(alp))*cos((PI/8)-alp+dt[n]/2)/1000; // m Tc[n] = 4*(f2[n]*c2[n]-f1[n]*c1[n]); // Nm // Load Torque assume linear relationship: TS[n] = dt[n]*KS; // Desired Torque if (n>1000) { Tr[n]= desire; } // Torque Control Loop er[n] = Tr[n]-TS[n]; Ier[n] = er[n]*0.001+Ier[n-1]; Der[n] = (er[n]-er[n-1])/0.001; if (n<runtime) { TM[n]=(P*er[n]+I*Ier[n]+D*Der[n])/40; if(n<19000){


if (TM[n]<1.3) { if (TM[n]>0) { V[n]=TM[n]*4/1.3+fr*4; Analog_Out(0,V[n]); } else { V[n]=TM[n]*4/1.3-fr*4; Analog_Out(0,V[n]); } }} else {Analog_Out(0,0);} } if (n>= runtime) flag=FALSE; } void Analog_Out (int channel, double voltage) { // check voltage double t_voltage=0.0; int dig; // make sure motor signal is between -10v to +10v if (voltage >10.0) t_voltage = 10.0; else if (voltage < -10.0) t_voltage = -10.0; else t_voltage = voltage; dig = (int)(8191 * (t_voltage+10)/20.0); //write to DAC Channel RtWritePortUshort( (PUSHORT) (DAC0), (USHORT)dig); } //Initialise encoders void RltZeroCntr(int channel) {


PUCHAR addresspuc, addresspuc1; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C RtWritePortUchar(addresspuc, (UCHAR)0x20); //Master Control Register. MRST master reset RtWritePortUchar(addresspuc, (UCHAR)0x68); //Input Control Register. RtWritePortUchar(addresspuc, (UCHAR)0x80); //Output Control Register. RtWritePortUchar(addresspuc, (UCHAR)0xc3); //Quadrature Register 4x quadrature mode RtWritePortUchar(addresspuc, (UCHAR)0x04); //Reset encoder counters to zero. addresspuc1=(PUCHAR)(STG_A+ 0x400 + 0x0e); //TMRCMD RtWritePortUchar(addresspuc1, (UCHAR)0x3a); //chose timer 0 RtWritePortUchar(addresspuc1, (UCHAR)0x7a); //chose timer 1 RtWritePortUchar(addresspuc1, (UCHAR)0xba); //chose timer 2 printf("ENCODER %d Initialization COMPLETE\n",channel); return; } //Read encoder counter i. Return counter reading value long RltReadCntr(int channel) { PUCHAR addresspuc, addresspuc1; UCHAR cntl; UCHAR cntm; UCHAR cnth; long cntr; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C //printf("\t%uc",&addresspuc); RtWritePortUchar(addresspuc,(UCHAR)0x02); //transfer counter to latch addresspuc1 = (PUCHAR)(STG_A+ channel*2 - 2); //select CNTi.D cntl = RtReadPortUchar(addresspuc1); //read counter latch low 8 bit cntm = RtReadPortUchar(addresspuc1); //read counter latch medium 8 bit cnth = RtReadPortUchar(addresspuc1); //read counter latch high 8 bit cntr=(long) (((cntl << 8) + (cntm << 16) + (cnth << 24)) / 256); return(cntr); }


int main() { LARGE_INTEGER x; LARGE_INTEGER Period; HANDLE hTimer; // HANDLE hToSharedMemory; RltZeroCntr(1); RltZeroCntr(3); printf("\n\nPlz Wait...\n"); Period.QuadPart=10000*p; if (!(hTimer = RtCreateTimer(NULL,0,TimerJob1,NULL,RT_PRIORITY_MAX,CLOCK_FASTEST))) // Always use fastest available clock { printf("SHUTDOWN: ERROR: Could not create the timer.\n"); ExitProcess(1); } if (!RtSetTimerRelative( hTimer, &Period, &Period)) { printf("SHUTDOWN: ERROR: Could not set and start the timer.\n"); ExitProcess(1); } printf("J = %2.4f kgm^2\n",Js); //printf ("G = %2.4f N\n",Gb2); printf("Kff = %4.2f Nm/rad\n",KS); // printf("sampling time = %3.4f s\n",interval); printf("P=%1.3f\tI=%2.3f\tD=%1.4f\n",P,I,D); printf("t(ms)\tM\tL\tdt\t\tMd(rpm)\tLdd\t\tTM(Nm)\t\tTd(Nm)\tTS(Nm)\n"); while(flag) { printf("%3.3f\t%3.4f\t%3.4f\t%3.4f\t\t",n*p*0.001,M[n],L[n],dt[n]); printf("%3.4f\t%3.4f\t\t",Md[n]*60/(2*PI),Ldd[n]); // Motor speed (rpm), Output Acc (rad/s^2) printf("%3.4f\t\t%3.4f\t%3.4f\n",V[n]*52/4,Tr[n],TS[n]);// Toutput , Tdesired Sleep(1); } RtCancelTimer(hTimer, &x); RtDeleteTimer(hTimer);


Appendix D

Controller Code Part III - Force

Control

D.1 Force Control

116

D.1.1 Force Control - Header File

// FORCE CONTROL FOR CONTACT START AND MOVING TO CONTACT // By: Eddie Chai // Header File // Control Architecture // Tm = [PID]*(Tl-Td) , where Tl = Ks(M-L) // Dynamics of Actuator // Tm = Tl + frictions // Tl = m*g*l*sin(L) + m*l^2*Ldd #define KS 426.0 #define PI 3.14159265359 #define Op .1 //Outer Control Gain #define Oi 0 #define Od 0 #define P 1.0 //inner Control Gain #define I 30.0 #define D 0.0 #define desire 10.0 //step //#define desire 20*sin((2*PI)*n/500) // Sinusoidal #define fr 0//0.09 // Static/holding torque (% of Tm,max) //************** ServoToGo ************************************** #define STG_A 0x240 // ServoToGo Card A base address #define STGOff 0x400 // offset for high address space #define DAC0 0x250 // Analog Out Address #define D_DIR 0x647 #define START_CONV ((PUSHORT) (STG_A+0x410)) #define PORT_ADC ((PUSHORT) (STG_A+0x410)) #define BRDTST ((PUSHORT) (STG_A+0x403)) #define pSharedMemory "SharedMemory" #define CNTRL0 ((PUSHORT) (STG_A+0x401)) typedef struct Data { int handshake; BOOL startrtss; BOOL killRT; } DATASTRUCT; DATASTRUCT *pdata;

Figure D.1: Force Control: Header File.

D.1.2 Force Control - Main File

// FORCE CONTROL FOR CONTACT START AND MOVING TO CONTACT // By: Eddie Chai // Main console #include "stdafx.h" #include <iostream.h> #include <windows.h> #include <stdio.h> #include <conio.h> #include <stdlib.h> #include <fstream.h> #include <math.h> #include <rtapi.h> #include "motorcntlrtx.h" HANDLE hshmData; HANDLE hSharedMem; // Elastic Flywheel double f1[50000]; // Force in Spring 1 (N) double f2[50000]; // Force in Spring 2 (N) double dt[50000]; // Deflection of Flywheel (rad) double c1[50000]; // Tangential Distance of Spring 1 relative to center of ff(mm) double c2[50000]; // Tangential Distance of Spring 2 relative to center of ff(mm) double Tc[50000]; // Output Torque // Dynamics of Actuator double Pot1 [50000]; double Pot [50000]; double M [50000]; // Position of Motor (rad) double L [50000]; // Position of Load (rad) double Md [50000]; // Speed of Motor (rad/s) double Mdd [50000]; // Acceleration of Motor (rad/s^2) double Ld [50000]; // Speed of Load (rad/s) double Ldd [50000]; // Acceleration of Load (rad/s^2) // Torque double TM[50000]; // Motor Torque

Figure D.2: Force Control: Main File Page 1.

double TS[50000]; // Output Torque - assume linear i.e. T = K*theta double Tr[50000]; // Desire Torque double To[50000]; // Torq computed by Outer double Tf[50000]; // force from pot // PID parameters double er[50000]; double Ier[50000]; double Der[50000]; double Oer[50000]; double OIer[50000]; double ODer[50000]; // Voltage double V[50000]; int d = 1; // delay int p = 1 ; // interval time int runtime =50000/p; int n=0; double voltage; double interval = 0.001*p*d; //interval time BOOL flag=TRUE; BOOL start=TRUE; void Analog_Out (int channel, double voltage) { // check voltage double t_voltage=0.0; int dig; // make sure motor signal is between -10v to +10v if (voltage >10.0) t_voltage = 10.0; else if (voltage < -10.0) t_voltage = -10.0; else t_voltage = voltage; dig = (int)(8191 * (t_voltage+10)/20.0);


//write to DAC Channel RtWritePortUshort( (PUSHORT) (DAC0), (USHORT)dig); } //Initialise encoders void RltZeroCntr(int channel) { PUCHAR addresspuc, addresspuc1; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C RtWritePortUchar(addresspuc, (UCHAR)0x20); //Master Control Register. MRST master reset RtWritePortUchar(addresspuc, (UCHAR)0x68); //Input Control Register. RtWritePortUchar(addresspuc, (UCHAR)0x80); //Output Control Register. RtWritePortUchar(addresspuc, (UCHAR)0xc3); //Quadrature Register 4x quadrature mode RtWritePortUchar(addresspuc, (UCHAR)0x04); //Reset encoder counters to zero. addresspuc1=(PUCHAR)(STG_A+ 0x400 + 0x0e); //TMRCMD RtWritePortUchar(addresspuc1, (UCHAR)0x3a); //chose timer 0 RtWritePortUchar(addresspuc1, (UCHAR)0x7a); //chose timer 1 RtWritePortUchar(addresspuc1, (UCHAR)0xba); //chose timer 2 printf("ENCODER %d Initialization COMPLETE\n",channel); return; } //Read encoder counter i. Return counter reading value double RltReadCntr(int channel) { PUCHAR addresspuc, addresspuc1; UCHAR cntl; UCHAR cntm; UCHAR cnth; long cntr; addresspuc = (PUCHAR)(STG_A + channel*2); //select CNTi.C //printf("%1d\n",channel); RtWritePortUchar(addresspuc,(UCHAR)0x02); //transfer counter to latch


addresspuc1 = (PUCHAR)(STG_A+ channel*2 - 2); //select CNTi.D cntl = RtReadPortUchar(addresspuc1); //read counter latch low 8 bit cntm = RtReadPortUchar(addresspuc1); //read counter latch medium 8 bit cnth = RtReadPortUchar(addresspuc1); //read counter latch high 8 bit cntr=(long) (((cntl << 8) + (cntm << 16) + (cnth << 24)) / 256); return(cntr); } void RTFCNDCL TimerJob1(PVOID unused) { if(start) { n=0; start=FALSE; } // Initial conditions Pot[0] =0; M[0] =0; L[0] =0; Ier[0] =0; er[0] =0; Der[0] =0; n+=1; // Positions in radian M[n]=RltReadCntr(1)*2*PI/10000; L[n]=RltReadCntr(3)*2*PI/10000; Pot[n]=(convert_from_digital(Analog_In(1)))*(-47.024) -57.664; Pot1[n]=(convert_from_digital(Analog_In(0))); //Speeds in rad/s Md[n]=(M[n]-M[n-d])/interval; Ld[n]=(L[n]-L[n-d])/interval; //Acc Mdd[n]=(Md[n]-Md[n-d])/interval; Ldd[n]=(Ld[n]-Ld[n-d])/interval; // LOAD TORQUE by GEOMETRY dt[n] = M[n]/40-L[n];


f1[n] = K*((R/cos(alp))*sin(PI/8-alp-dt[n]/2)*2+5.5-L0)+F0; // N f2[n] = K*((R/cos(alp))*sin(PI/8-alp+dt[n]/2)*2+5.5-L0)+F0; // N c1[n] = (R/cos(alp))*cos((PI/8)-alp-dt[n]/2)/1000; // m c2[n] = (R/cos(alp))*cos((PI/8)-alp+dt[n]/2)/1000; // m Tc[n] = 4*(f2[n]*c2[n]-f1[n]*c1[n]); // Nm Tf[n] = Pot[n]; // Load Torque assume linear relationship: TS[n] = dt[n]*KS; // Desired Torque if (n>0) { Tr[n]= desire; } // Outer Force Control Loop Oer[n] = Tr[n]-Tf[n]; OIer[n]= er[n]*0.001+Ier[n-1]; ODer[n] = (er[n]-er[n-1])/0.001; To[n] = (Op*Oer[n]+Oi*OIer[n]+Od*ODer[n]); // inner Torque Control Loop er[n] = To[n]-TS[n]; Ier[n] = er[n]*0.001+Ier[n-1]; Der[n] = (er[n]-er[n-1])/0.001; if (n<runtime) { TM[n]=(Op*Oer[n]+Oi*OIer[n]+Od*ODer[n])/40; //rigid //TM[n]=(P*er[n]+I*Ier[n]+D*Der[n])/40; //elas if(n<19000){


if (TM[n]<.65) { if (TM[n]>0) { V[n]=TM[n]*4/1.3+fr*4; // Analog_Out(0,V[n]); } else { V[n]=TM[n]*4/1.3-fr*4; // Analog_Out(0,V[n]); } }} else {Analog_Out(0,0);} } if (n>= runtime) flag=FALSE; } void CalADC(void) { UCHAR ctrl0; RtWritePortUchar((PUCHAR)(D_DIR),(UCHAR)0x8b); //Initialize register D_DIR to enable writing on CNTRL0 RtPrintf("Configure D_DIR register successful...\n"); Sleep(10); //Wait for the command to settel ctrl0=RtReadPortUchar((PUCHAR)CNTRL0) & 0x07; //Get CNTRL0 value and save the IRQ RtWritePortUchar((PUCHAR)CNTRL0,ctrl0); //cal is low RtWritePortUchar((PUCHAR)CNTRL0,(UCHAR)(ctrl0|0x08)); //cal is high Sleep(10); } //This implementation is according to STG version2.0 //Refer to manual pp. 31 for more detail int Analog_In(int channel) { //for port I/O code


int count=0; USHORT sX, temp; UCHAR ctrl0; int sign; int ret; //Step 1 & 2: Set multiplexer (CNTRL0) and wait for 4 us ctrl0 =RtReadPortUchar((PUCHAR)(CNTRL0)) & 0x07; //Save irq (last 3 bits) ctrl0 |= (channel<<4) | 0x88; //Select channel to perform conversion (channel = 0,1,2) RtWritePortUchar((PUCHAR)(CNTRL0),ctrl0); //Send command to CNTRL0 //STEP 3: Start conversion by send dummy value to START_CONV RtWritePortUshort(START_CONV, 0x00); //write to register to initiate conversion //STEP 4: Wait until conversion finish while((RtReadPortUshort(BRDTST) & 0x08) && count<10000); { count++; //wait for /EOC } //STEP 5: Reading sX = RtReadPortUshort(PORT_ADC); sX = sX & 0x1fff; sign = sX & 4096; if (sign) { temp = (~sX & 0x1fff) +1; ret = -temp; } else ret = sX; return (ret); } /* working in degreees 0 == -10V == -120 degrees 4096*2(8192) == 10V == 120 deg */ double convert_from_digital(int dig)


{ return (10*(dig+4096)/8192.0 - 5.0); } int main() { LARGE_INTEGER x; LARGE_INTEGER Period; HANDLE hTimer; // HANDLE hToSharedMemory; CalADC(); RltZeroCntr(1); RltZeroCntr(3); /***end of Pot initialisation***/ printf("\n\nPlz Wait...\n"); Period.QuadPart=10000*p; hshmData = RtCreateSharedMemory(PAGE_READWRITE, 0, sizeof(pdata), "SharedMemory", (LPVOID*) &pdata); if (!(hTimer = RtCreateTimer(NULL,0,TimerJob1,NULL,RT_PRIORITY_MAX,CLOCK_FASTEST))) // Always use fastest available clock { printf("SHUTDOWN: ERROR: Could not create the timer.\n"); ExitProcess(1); } if (!RtSetTimerRelative( hTimer, &Period, &Period)) { printf("SHUTDOWN: ERROR: Could not set and start the timer.\n"); ExitProcess(1); } //RtWritePortUchar((PUCHAR)(0x647),(UCHAR)0x8b); //so that CNTRL0 is usable...refer to the manual!!! ResumeThread(hTimer); // printf("J = %2.4f kgm^2\n",Js); //printf ("G = %2.4f N\n",Gb2);


// printf("Kff = %4.2f Nm/rad\n",KS); // printf("sampling time = %3.4f s\n",interval); //printf("P=%1.3f\tI=%2.3f\tD=%1.4f\n",P,I,D); printf("t(ms)\tM\tL\tPOt\t\tdt\t\tMd(rpm)\tLdd\t\tTM(Nm)\t\t\tTd(Nm)\tTS(Nm)\n"); while(flag) { printf("%3.3f\t%3.4f\t%3.4f\t%5.5f\t%3.4f\t\t\n",n*p*0.001,M[n],L[n],Pot[n],dt[n]); printf("%3.4f\t%3.4f\t\t",Md[n]*60/(2*PI),Ldd[n]); // Motor speed (rpm), Output Acc (rad/s^2) printf("%3.4f\t\t%3.4f\t%3.4f\n",V[n]*52/4,Tr[n],TS[n]);// Toutput , Tdesired // printf("%3.3f\t\t%5.3f\t%5.4f\n",n*p*0.001,Pot[n],Pot1[n]); Sleep(10); } RtCancelTimer(hTimer, &x); RtDeleteTimer(hTimer); return 0; }


Appendix E

Suppliers

This section contains a list of all the suppliers that were used in development of the

actuator.

Accord Network Services Pte. Ltd.

23, Kelantan Lane, 05-01A

Singapore 208642

Tel.: 9766 2038

Fax: 6294 9283

E-mail: [email protected]

servomotors, gearbox

Yong Seng Screws Pte. Ltd.

Blk 802 01-57

French Road,

Singapore 200802.

Tel.: 6294 1866

Fax: 6294 1178

website: www.ysscrews.com

connectors, screws

127

Heidenhain Pacific Pte. Ltd.

50, Lorong 21, Geylang,

Heidenhain Building,

Singapore 388465.

Tel.: 6749 3238

Fax: 6749 3922

encoders, encoder bearing unit

Servo Dynamics Pte. Ltd.

10, Kaki Bukit Road,

10-30 Kaki Bukit Industrial Park,

Singapore 416715.

Tel.: 6844 0288

Fax: 6844 0070


website: www.servo.com.sg

servomotors, gearbox, coupling

PBA (s) Pte. Ltd.

157, Sin Ming Road,

Amtech Building(Annex Blk), 02-01,

Singapore 575624.

Tel.: 6552 7992

Fax: 6552 6992


ceramic bush, ball bearings

Bosch Rexroth Pte. Ltd.

19 Kian Teck Way,

Singapore 628740.

Tel.: 6265 6033

Fax: 6265 0813


Aluminum profile tube for stand

Elite Springs Industries

50 Bukit Batok st. 23

06-23/24 Midview Building

Singapore 659578.

Tel.: 6556 2252

Fax: 6566 2115

springs

Associated Spring Asia Pte. Ltd

28 Tuas Ave 2

Singapore 639459.

Tel.: 6863 5636

Fax: 6863 6325


springs

rotary elastic actuator - core

Documents