notes on the control of teleoperation systems · 2010. 11. 1. · notes on the control of...

Notes on the Control of

Teleoperation Systems

Dennis van Raaij

CST 2010.050

Version 06/07/2010

General report

Eindhoven University of Technology

Department of Mechanical Engineering

Control Systems Technology Group

Eindhoven, July, 2010

Preface

This document contains a collection of notes written within the first two years

of my PhD project titled ‘haptic feedback in medical robotic systems’ (an IOP-

MMI project). Despite the fact that I was not able to finish the research, I’ve

nonetheless decided to bundle the notes as they may be interesting for those

working in the field.

Remember that all that is written are notes. As such, they are neither

complete, nor peer reviewed, may contain non-objective statements and may

even be incorrect at some points. Therefore, using them is at one’s own risk.

Publication of this document does not claim any new facts or contributions to

the field. It is merely an ordered overview and interpretation – at least that is

what it was meant to be – of what was already found by various researchers

working on the control of teleoperation systems.

Dennis van Raaij

Eindhoven, july 2010

ii

Contents

Contents iii

1 Introduction 2

1.1 Teleoperation Systems . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Some Remarks on the Notation . . . . . . . . . . . . . . . . . . 6

2 Human, Environment and Performance 8

2.1 Performance Objective . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 The Human Interacting with the System . . . . . . . . . . . . . 11

2.3 The System Interacting with the Environment . . . . . . . . . . 16

2.4 A Preliminary Example . . . . . . . . . . . . . . . . . . . . . . 17

3 Control Problem 22

3.1 Control for Teleoperation . . . . . . . . . . . . . . . . . . . . . 22

3.2 Some Solutions to the Model-Matching Problem . . . . . . . . 25

3.3 Concepts found in Literature . . . . . . . . . . . . . . . . . . . 32

3.4 Shunt Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Design Example 44

4.1 A Passive System or a Passive Controller? . . . . . . . . . . . . 44

4.2 Controller Synthesis in Literature . . . . . . . . . . . . . . . . . 45

A Motion and Force Control 48

B Two-Port Networks 54

B.1 Two-Ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

B.2 Properties of Two-Port Networks . . . . . . . . . . . . . . . . . 57

B.3 Passivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

B.4 Absolute Stability . . . . . . . . . . . . . . . . . . . . . . . . . 60

C Wave-variable Controller 62

iii

iv CONTENTS

C.1 An Example: Simple Beam Model . . . . . . . . . . . . . . . . 62

D Common and Differential Modes 66

E More Performance Measures 70

E.1 Z-Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

E.2 Performance Index of Maneuverability . . . . . . . . . . . . . . 71

E.3 Operationality and Reproducibility . . . . . . . . . . . . . . . . 72

E.4 Çavuşoğlu’s Fidelity Measure . . . . . . . . . . . . . . . . . . . 73

F More Practical Issues & Safety 76

F.1 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

F.2 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

G Human Factors 84

G.1 Somatic Sensory System . . . . . . . . . . . . . . . . . . . . . . 84

G.2 Somatic Motor System . . . . . . . . . . . . . . . . . . . . . . . 86

G.3 Models Representing Behavior . . . . . . . . . . . . . . . . . . 87

H More Documents 90

H.1 Historical Documents . . . . . . . . . . . . . . . . . . . . . . . . 90

H.2 Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Bibliography 94

Index 102

Chapter 1

Introduction

1.1 Teleoperation Systems

Teleoperation systems (or telemanipulation systems) are meant to perform

tasks in remote environments. Today their application is more widespread

and various researchers attempt to design dedicated teleoperation systems in

order to make the execution of various tasks more flexible, more comfortable

and eventually more cost effective. Some of the applications are discussed be-

low in order to obtain an impression of the utilizability of the technology. For a

more extensive overview, please consult (e.g.) Sheridan [1989], Sheridan [1992,

Chapter 2] and Sheridan [1995].

Nuclear – Maintenance and Material Handling

Most teleoperation systems were initially build to handle nuclear material in so-

called ‘hot-cells’1. Figure 1.2 shows one of the first systems build by Raymond

Goertz at Argonne National Laboratory. A more recent application in nuclear

engineering can be found at JET (Joint European Torus); a nuclear fusion

plant build in Oxford, UK. To perform maintenance tasks inside the reactor, a

dedicated teleoperation system based ion Elsag Bailey’s MASCOT (Manipola-

tore Servo COntrollato Transistorizzato) was developed along with the design

and construction of the plant. The system features haptic feedback. Using this

versatile system, of which a photo is shown in figure 1.3, various tasks ranging

from the replacement of shielding to the rewiring devices are executed up till

today. See Colombi and Raimondi [1995] and references therein for some tech-

nical information. Visit the website of JET2 for some more recent information

1http://www.centres.com/2http://www.jet.efda.org/remote-handling/

2

http://www.centres.com/http://www.jet.efda.org/remote-handling/

1.1. TELEOPERATION SYSTEMS 3

Figure 1.1: Ralph Mosher’s ‘Handyman’ build at General Electric Co. in the late1950s. Its usability is demonstrated by twirling a hoola hoop. TheHandyman did not feature force feedback. Photo adapted from cyber-neticzoo.com

Figure 1.2: Raymond Goertz’ ‘E1’ build at Argonne National Laboratory, Chicagoin 1954. This and other similar systems were developed during thelate 1940s and 1950s for handling nuclear material. Photo adaptedfrom Sheridan [1989, Figure 4].

http://cyberneticzoo.comhttp://cyberneticzoo.com

4 CHAPTER 1. INTRODUCTION

Figure 1.3: Remote handling at JET, Oxford, UK. The left photo shows the userinterface, the right shows the end-effectors of the MASCOT slave robot.Left photo © Mounty Rakusen, right photo © Elsag Bailey.

and movies. New remote handling systems are currently under development3

Medical – Minimally Invasive Surgery

The application of teleoperation systems in the field of surgery emerged in the

1990s. After years of research by NASA and SRI International the daVinci®

surgical system was introduced by the spin-off company Intuitive Surgical, Inc.,

Sunnyvale, CA4. The daVinci® robot is used worldwide to perform surgical in-

terventions with minimal trauma. Because the system does not feature force

feedback, various researchers investigated the possibility of enabling the feed-

back. See for example Madhani [1998], Çavuşoğlu et al. [2002] and De Gersem

[2005]. Recently, the German Aerospace Center DLR has build a new surgical

robot called the MIRO (MInimally invasive surgical RObot) which is intended

to be used as a slave robot in a teleoperation setup shown in figure 1.4. The

robot, which is described in Hagn et al. [2010], is based on the DLR lightweight

arm and features compliant joints and a multi-DOF force sensor at the tip to

enable haptic feedback to the surgeon.

Other Applications

Other (industrial) applications are deep sea construction and maintenance5,

mining6, remote handling in space (European Robotic Arm, ERA) and bomb

dismantling.

Note that by-wire systems build by the aerospace and automotive industry

may also considered to be teleoperation systems. Mechanical parts are removed

3http://www.oxfordtechnologies.co.uk/4http://www.intuitivesurgical.com/5http://www.oceaneering.com/rovs/6http://www.gmminingelectrics.com.au/.../remote control equipment

http://www.oxfordtechnologies.co.uk/http://www.intuitivesurgical.com/http://www.oceaneering.com/rovs/http://www.gmminingelectrics.com.au/index.php/services/category/remote_control_equipment

1.2. TERMS AND DEFINITIONS 5

Figure 1.4: Three MIRO robots each equipped with a preliminary design of theMICA instrument adapter. Photo © DLR.

and replaced by electronic controllers which need to reestablish the connection.

In steer-by-wire, for example, the steering rod is replaced by a controller which

reestablishes the connection between the steering wheel and wheels.

1.2 Terms and Definitions

The field of teleoperation contains a vast amount of terms to distinguish prop-

erties and functionalities of systems. Some of them are informally defined

below.

Telesystems

The word tele originates from the Greek language and means ‘far’ in English.

Complete telepresence is achieved if a human is able to interact with a distant

environment while having the perception (illusion) of being there at the same

time. Examples of systems which partly achieve this are telephones used to

transfer audio information or television systems used in teleconferencing for

transferring visual information over some distance. A tool (e.g. a gripper or

stick) can be used to transfer touch information over a certain distance. Such

a system may be called ‘telehaptic’ system.

Teleoperation

The process of indirectly interacting or altering a distant environment using

a by means of a system is denoted as teleoperation or telemanipulation. If

the teleoperation system consists of distinct mechanical devices, the system is

sometimes called a telerobotic system. The (robotic) device which is expected

to be manipulated by the operator is often denoted as the manipulandum or

6 CHAPTER 1. INTRODUCTION

master , the device which is expected to manipulate the environment denoted

the manipulator or slave. A teleoperation system which provides information

to the operator via the sense of touch is called a haptic teleoperation system.

This information may directly be related to (e.g.) interaction forces measured

at the slave but may also originate from virtual fixtures (see additional notes

of section 3.2)

Haptic

The word haptic is derived from the Greek word ‘Haphe’. The term means

‘pertaining to the sense of touch’7. It is most often used to designate the field

studying the sense of touch. The term can also be used in the same way as terms

like ‘visual’ or ‘audio’. Hence, haptic technology means ‘technology pertaining

to the sense of touch’ and refers to the means and knowledge to design and build

systems that can make use of the sense of touch of the human. The process of

communicating information back to the user using force signals, i.e. feedback

in the sense of human-human or human-machine communication/interaction, is

denoted as haptic feedback . Within the context of control engineering, haptic

feedback is a specific application of force feedback in which the (controlled)

forces acting on the operator are used as a medium to transfer information.

1.3 Some Remarks on the Notation

• The variables position, velocity and acceleration are distinguished by theexplicit symbols x, v and a.

• The use of the terms admittance, impedance, etc. is quite sloppy. Whileboth relate generalized potential variables (here: force) to generalized

flow variables (here: velocity), they sometimes indicate a relation be-

tween force and position during the explanation of concepts. This will,

in principle, not influence any result as long as one is aware of its sloppy

use and obey the correct definitions when working with theorems.

• Whether a variable (signal) or function should be considered in the Laplacedomain or time domain will in general be clear from the context. If the

context allows ambiguity, the domain will be stated explicitly.

7dutch: betrekking hebben op de tastzin.

Chapter 2

Human, Environment and

Performance

In this chapter the performance objective and the role and assumptions of the

operator and environment are discussed. Special attention is given to some the

wide-spread assumptions and their origin. Discussing the concepts before the

discussion and derivation of any controller is believed to be beneficial for the

overall understanding of the problem to be solved.

2.1 Performance Objective

The minimum system performance Psys,0 (system’s 0-line or baseline perfor-mance) is achieved if the predefined (intended) task(s) can be executed using

the system within finite time and without irreversible destruction which will

necessarily lead to the ending of the execution (e.g. destruction of a sample

being handled). It is believed that, for every task, there exists a certain thresh-

old P∗sys. Above this threshold, the increase of the system performance will notlead to a further increase of the task performance. The task performance will

(at least for the greater part) be limited due to the finite capabilities of the

user, not the system. See also figure 2.1.

An illustrating example may be a knife used to cut food. Next to the metal

versions often found at home, cheap disposable plastic versions do exist for

use at parties. Most often it appears that the plastic knife tends to buckle

rather quickly and therefore limits the handling performance. By increasing

the stiffness of the knife, the handling performance is improved. At the same

time, however, increasing the stiffness beyond that of a metal knife will not lead

to further improvement of the handling performance. In this example, (Psys)may be associated with the knife’s stiffness while Ptask may be associated with

8

2.1. PERFORMANCE OBJECTIVE 9

PsysP t

ask

P∗sys

max (Ptask)

Psys,0(better)

(better)

Figure 2.1: System performance Psys vs. task execution performance Ptask.Adapted from Christiansson [2007, Figure 1.6].

the average time to cut a meat ball or the maximum allowable force that can

be exerted by the hungry human.

The former explanation of system versus task performance is intuitive but

in general hard to quantify, in particular if no (comparable) system is available.

Hence, experiments will have to be make clear which measure(s) will represent

the task performance and which system measure(s) will have a significant in-

fluence on that task performance measure. Moreover, it can be assumed that

for one particular task multiple system performance measures will influence a

single task performance measure. Hence, figure 2.1 will, in practice, appear

to be overly simplified. As an example, to perform a typical manipulation

task comfortably, one will not only require sufficient information bandwidth

(position/force), but will also require the mass of the tool presented to the op-

erator to be within some bounds to achieve some comfort. Early fatigue can be

prevented by requiring some damping or friction to prevent sustained cocon-

traction of the antagonist muscles during point-to-point movements. Mental

load can be reduced by making the system’s behavior appear consistent to the

operator.

Master Controller Slave

Figure 2.2: In the ideal case, the operator has the illusion of holding a tool withwhich he or she can explore or manipulate the environment.

Because of these requirements and difficulties with finding system and task

performance variables that correlate well, teleoperation systems are often de-

signed to act like physical tools as illustrated in figure 2.2. Hence, the concep-

tional purpose the controller to be designed for a teleoperation system can be

stated as follows:

10 CHAPTER 2. HUMAN, ENVIRONMENT AND PERFORMANCE

The controller should couple two mutual isolated plants (interac-

tion devices) in such way that the system as a whole is presented

as a consistent tool to the user with which predefined tasks can be

performed.

The objective to make the system act like a tool was already proposed up

to some extend in Yokokohji and Yoshikawa [1994, Section 6b] by the term

‘intervening impedance’. People are typically well capable handling passive

tools like cutlery and construction tools like screwdrivers up to a satisfying

performance. Humans are also capable of handling tools that contain power

sources like drilling machines or a jackhammers. Hence, it is plausible to assume

that if the teleoperation systems will mimic the behavior of a tool, one would at

least achieve the task performance which is comparable with the performance

that can be achieved by real-life tools; without even knowing the explcit relation

between system and task performance.

Additional Notes

• Damping and Coulomb friction may help the operator to extract kinetic energyfrom the system during deceleration and help to suppress small external or op-

erator induced disturbances (tremor). Practical observation shows that a lack

of damping and/or Coulomb friction will typically lead to sustained cocontrac-

tion of the antagonist muscles during motion (which may be measured using

e.g. electromyography EMG). Sustained cocontraction requires large amounts

of metabolic energy; a measure which is likely to be related to the perception

of comfort.

• Consistency means that the system’s inherent dynamics does not change (per-ceptible) over time. It may only be altered after explicit (conscious) acknowl-

edgment of the operator. This requirement is motivated by the believe that the

operator develops a ‘mental model’ or internal model/representation (IM/R)

of the system based on his or her (multi-modal) perception of and experiences

with the system’s responses over time. Using this internal model, the operator

would be able to separate the (haptic) feedback information due to the inter-

action with the environment from the haptic feedback from the inherent device

dynamics. An inconsistent system requires a complex internal model leading

to a larger mental load.

The internal model is also believed to be used as a ‘feedforward’ during the

execution of tasks. Most people have experienced a failure of this system when

they overestimated the force necessary to lift a milk pack. The milk left in the

milk pack and thus its mass was overestimated which led to an incorrect mental

model of the object. See also de Vlugt [2004, Section 8.2.3] and the references

therein (in particular Gerdes and Happee [1994]) for some more information.

• Tools containing power sources are designed such that, if handled correctly (!),the energy discharge will be large towards the environment and small towards

the the human. For a drilling machine the human will have the intend to

minimize the energy discharge into his of her body by holding the tool steady.

The energy flowing into the environment is modulated by the user by the

amount of pushing. For a jackhammer the vibrations are more severe and due to

2.2. THE HUMAN INTERACTING WITH THE SYSTEM 11

the fact that a large amounts of (reactive) energy are exchanged rather quickly

between the tool and user, they are typically considered to be uncomfortable

and difficult to handle.

It may be reasoned that the human is capable of handling active tools as long

as the (co-)energy variables (force and velocity) at the point of interaction stay

within reasonable bounds and the energy sinked into the human can comfort-

ably being dissipated or temporarily stored (reactive energy) by the intrinsic

limb dynamics.

Humans are also capable of handling (controlling) unstable systems up to some

extend as long as the human is capable to persistently extract sufficient energy

from the unstable system; i.e. extract more energy than is being generated

by the system over some time. Again, this mainly depends on whether the

(co-)energy variables stay within reasonable bounds and the time-scale is suf-

ficiently low.

From practical observations however, it should be note that humans are typ-

ically incapable of stabilizing systems asymptotically towards a steady-state

with the exception of systems exhibiting the behavior of a negative stiffness.

In most cases the extraction of energy is irregular and the states of the unstable

system are only bounded.

2.2 The Human Interacting with the System

The moment the user touches a system, a bilateral coupling is established

enabling the exchange of energy as shown in figure 2.3. For teleoperation

systems the human/machine interaction an essential characteristic and a model

describing the user’s dynamic behavior (seen from at point of interaction) will

be necessary. While the intrinsic dynamicsHuman!intrinsic dynamics like the

mass of the limb, stiffness and damping of relaxed muscles, and, up to some

extend, low-level reflexes can be measured and identified, the incomprehensible

complexity of the human’s cognitive behavior remains, for the larger part, a

black box.

The planning and adaption of humans during the execution of tasks varies

for each person and depends on things like (1) on the fly input of other modal-

ities (e.g. vision in tracking tasks, audio information received by other humans

via speech) and (2) on acquired skills and experience. The first point even sug-

gests that if the user crosses the system boundary, also other processes and/or

humans that can possibly influence or interact with the user should be taken

into account. Such processes are, however, in most cases ignored as they would

tend to make a resulting model intractable. Moreover, they are also most often

unpredictable and/or unknown beforehand.

While it is reckless to assume that the cognitive behavior of humans will

ever be caught in a model, it may be interesting to search for behavioral char-

acteristics during the nominal execution of well-defined tasks. It is plausible

to assume that while every human is unique, their behavior is per definition

bounded during the execution of certain tasks. See Flash and Hogan [1985] for

an example regarding point-to-point movements and McRuer [1980] for track-


ing/pursuit tasks. Furthermore, see Sheridan and Ferrell [1974] and Sheridan

[2002] for a survey of existing models and ideas regarding human behavior

during the execution of certain tasks.

Cutaneous Sense(skin indentation)

Proprioceptive/Visual Sense(limb configuration)

Operator Dynamics

Teleoperation System(interaction device)

Fi

vi Bilateral Coupling atthe Point of Interaction

Figure 2.3: Simplified, physical model of the contact between the human and amaster device. The physically correct bilateral coupling at the point ofinteraction (dashed line) is shown. The operator applies a force to theinteraction device which responds with a certain motion to the operator.

Assumption of passive behavior

Despite the availability of models that can predict the behavior of humans

up to a certain extend, it appears that most are either too restrictive (only

applicable for a specific task) or too hard to implement in popular optimization

frameworks (like H∞-optimization). Therefore, alternatives have been sought.The by far the most popular two assumption regarding the operator and its

behavior are as follow.

1. The relation between the force and velocity at the point of interaction

can be described by arbitrary passive dynamics.

2. The forces necessary to set the system into motion do not depend on any

state within the system boundary; they can be considered exogenous.

See Colgate [1988, Section 3.5] and Yokokohji and Yoshikawa [1994, Section 5b]

for an some additional discussions and example applications.

The main advantage that come along with these assumptions is that no

model structure is necessary. The assumptions make it also easier to split up

the problem and it enables the use of a variety of tools available to attack the

design problem. Because of these advantages, the assumptions were quickly

adopted throughout the community after their introduction in the late 1980s.

Remember again that, as far the author is aware, literature even up till today

does not proof the behavior of an operator to be passive; it is considered a

plausible hypothesis mainly based on practical observations and experimental

results which will be discussed next.


I – Human intention: Cognitive behavior

While capable of acting like an persistent energy source (i.e. as if the available

(extractable) energy is infinite; see Wyatt et al. [1981, Definition 11]), it appears

from practical observations that humans will typically intend not to do so;

most often to avoid non-safe situations towards the environment but also for

themselves. As a result, he or she will always attempt to stabilize a system and

prevent energy to build-up in the tool. All energy that was supplied during

a task should eventually either have been transferred to the environment or

dissipated internally by the tool. Energy that remains in the tool at the end

of a task is typically extracted and dissipated again by the operator.

To make the build-up of energy more difficult and/or facilitate the inten-

tion, one should make sure that the resonance frequencies are sufficiently large

to assure the integrity of the system. It is a widespread assumption that hu-

mans cannot be active above approx. 10 [Hz]; even if they intend to. The

vibration like movements necessary to sweep-up a device requires repeatedly ac-

tivation/deactivation of antagonist muscles. Due to the finite response time of

muscles1 Fast activation/deactivation (contraction/relaxation) of these mus-

cles will result in continuous contraction and eventually to fatigue (Try this

yourself by vibrating your arm or hand as fast as you can).

II – Human reflexes: Non-cognitive behavior

Despite the assumption that a human will intend (consciously) to stabilize a

system, the existence of unconscious reflexes may still induce problems as they

are a result from a process that by-passes the human’s cognition. Preliminary

conclusions on whether these (spinal) reflexes tend to induce passive or active

behavior were given in Hogan [1989]. The conclusions are based on some of

the results presented in Mussa-Ivaldi et al. [1985]; an article describing an

extensive investigation on the apparent behavior of the human hand due to

reflexes. The article discusses several experiments in which various subjects

where asked to hold a handle at different locations in a horizontal plane. At

each of these positions the handle was subsequently and repeatedly displaced

5 or 8 [mm] in multiple, predefined directions. After the displacement, the

steady-state interaction force was measured for some time between the end of

the transient and the start of any voluntary (cognitive driven) movements. The

relation between the measured displacement vector and measured force vector

was fitted in the linear relation[F

(x)i

F(y)i

]=

[kxx kxykyx kyy

] [x

(x)i

x(y)i

]. (2.1)

Surprisingly, it appeared that the matrix K was symmetric which suggested

that, at least within some small region around a nominal position, the reflexes

1The response dynamics of muscles is typically represented by a first-order (lag) filterplus some neural delay. This representation excludes the filtering effect due to the intrinsicdynamics of the muscle.


induced a a spring-like behavior (see also the additional notes). The princi-

ple values and directions of the (almost) symmetric matrix K where used to

represent the orientation and relative magnitude of the matrices for various

configurations of the arm as shown in figure 2.4.

10 cm

y

x

200 N/m

Figure 2.4: Example of the stiffness ellipses for four distinct arm configurationswithin a common, horizontal plane. The ellipses are a graphical inter-pretation of the eigenvalues and eigenvectors of the symmetric part ofthe matrixK. Figure adapted from Mussa-Ivaldi et al. [1985, Figure 13].

Despite of this interesting result, it should be noted that these results only

show that the steady-state response (case ω → 0) of the reflex appears to bepassive. No conclusion can be drawn regarding the passivity of the reflexes at

other excitation frequencies.

III – Human tissue: Limb dynamics

The human aspect that remains after the discussion of the human’s conscious

and unconscious feedback behavior is of course the intrinsic tissue dynamics.

The uncontrolled limbs are obviously passive as they cannot generate any en-

ergy without the activation of any muscles.

The identification of dynamics of uncontrolled limbs of living subjects using

excitation-response techniques can be quite challenging. For example, excita-

tion of the limbs will most certainly trigger reflexes which results in responses

that contains the effects of both. Furthermore, also posture, limb configuration,

assignment (e.g resist or comply to excitation), mental state (e.g. alert/tired

or mood), excitation signal and design of the interaction device may all affect

a particular result. As an alternative, one may use available anatomic data

to construct a multi-body model (including the nonlinear muscles dynamics).

By linearizing the model for various nominal configurations, one may obtain a

linear, parameter varying model.

Arguments against the assumption of passivity

Of course, there are arguments against the assumption on the passivity of the

human behavior almost ever since its introduction. The main reproach is that


the assumption leads to a conservative model inducing conservative conclu-

sions; i.e. the set of realizations represented by the set of all (linear) passive

system models would introduce non-existing realizations that would serve as

‘bottle necks’. While the model is almost certainly conservative, it is not fully

understood how the conservatism in the model actually leads to conservative

conclusions. From a physical point of view it may be expected that reactive

(or lossless) models, containing only masses and springs but no damping, will

serve as worst-case realizations. This was already pointed out in Colgate [1988,

Section 3.4]. Hence, obtaining less conservative conclusions will probably be

achieved by either proving that there is some guaranteed dissipation associ-

ated with the human or environment or by imposing a model structure such

that the frequency response (complex uncertainties) or parameter values (real

uncertainties) of pure reactive models can be bounded.

Assuming that the human maintains a posture that is reasonable during

the execution of a certain task, the apparent mass and stiffness seen by the

teleoperation system at the point of interaction will be bounded. Under the

assumption that humans can be represented by (possibly time-varying) linear

models, these bounds will mainly be applicable in the low-frequent area (appar-

ent stiffness) and high-frequent area (apparent mass). A representative model

order and structure, in particular for frequencies up to approx. 10 . . . 20 [Hz],

maintains to be a topic of ongoing research in the field of biological mechanics

and cybernetics. See McRuer [1980, Figure 8] to obtain an impression of a

possible model structure resulting from white/gray box modeling and de Vlugt

[2004] for some results on the frequency response identification of the intrinsic

limb dynamics and (spinal) reflexes of the human arm.

Additional Notes

• It should be stressed that the human as a whole is active. One out of themany examples that shows this is when someone stirs continuously in a viscous

liquid. The energy necessary to compensate drag and sustain motion must be

generated by the operator. Comparing the available energy in one’s body to

the energy necessary to maintain motion for some reasonable time justifies the

assumption that the available energy can be considered infinite (see also Wyatt

et al. [1981, Section 7.3] for more information on this reasoning). Therefore,

the operator can be considered active. However, as the energy is assumed to

be introduced in the system by means of an exogenous signal, it will not affect

stability.

Note that exogenous signals do not exist in physical reality (they may exist in

virtual reality, e.g. computer generated signals) as in nature, everything de-

pends on everything (?). Exogenous signal exists due to model approximations

and assumptions of weak relations between signals. As an example: (weak and

nonlinear) interaction between DOFs in a multi-DOF motion system modeled

as exogenous disturbances in a decoupled, multi-SISO approximation.

A hypothesis (!) is that human cognition and the high-level (motoric) sys-

tems do not (at a macroscopic level) work like continuous feedback systems

(with time delay) but merely as relatively slow batch systems in which actions


are repeatably planned (based on perceived information and knowledge) and

executed (by programming and enabling lower motoric systems). One may

expect that such complex systems will make the identification of relations be-

tween signals within the system boundary and e.g. cognitive component of the

muscle force almost impossible. Hence, ‘cognitive signals’ are assumed to be

exogenous.

• Magnitudes of (co-)energy variables will certainly be bounded and large forcescan only be sustained for a finite amount of time due to fatigue. These ob-

servations may also support the hypothesis that the rate at which energy is

supplied to the teleoperator system is bounded. It is, however, the unknown

model structure and the lack of tools to account for bounds on signals norms

(e.g. the `∞-norm) that keeps the passivity paradigm popular: there seems no

reasonable alternative available (yet).

• The net amount of energy extracted from a force field F (x) by a particle movingover a closed contour ∂Σ can be obtained by evaluating the integral

W∂Σ =

∮∂Σ

FT dr (2.2)

with

F =

[F

(x)i

F(y)i

]=

[kxx kxykyx kyy

]︸︷︷︸

K

[x

(x)i

x(y)i

](2.3)

and, equivalently,

K = Ks +Ka (2.4)

with

Ks =K +KT

2=

[kxx

12

(kxy + kyx)12

(kyx + kxy) kyy

](2.5)

the symmetric part and

Ka =K −KT

2=

[0 1

2(kxy − kyx)

12

(kyx − kxy) 0

](2.6)

the anti-symmetric part of K. From the Kelvin-Stokes theorem it appears that

the the force field represented by (2.3) is conservative or cyclo-passive if∮∂Σ

FT dr =

∫Σ

(∇× F )T dΣ = 0 ⇔ ∇× F = 0 (2.7)

i.e. the curl is zero and thus

∇× F = kyx − kxy = 0 ⇔ kyx = kxy. (2.8)

It appears that the force field, characterized by K, is conservative if K is

symmetric.

2.3 The System Interacting with the Environment

Compared to the assumptions on the human operator, similar assumptions are

used for the environment. This is mainly motivated by the fact that typical en-

vironments have an unknown complexity but appear passive. The assumption

2.4. A PRELIMINARY EXAMPLE 17

x1

x2

F (x)

x1

x2

∂Σ

(a) (b)

Σ

Figure 2.5: The net amount of energy extracted from a force field F (x) by a particlemoving over a closed contour ∂Σ can be computed by the integration ofthe curl over the surface Σ (a). An example of conservative force fieldis a simple spring (b).

of passivity may again result in conservative models and therefore conservative

conclusions. Therefore, one may take the same steps as discussed in the case

of the human operator to restrict uncertainty. Keep in mind, however, that

a typical operator should not be bothered with assertion of whether an envi-

ronment falls within the uncertainty set against which the system is robust.

Apart from whether this is possible at all, it would at least induce an undesired

mental load.

Additional Notes

• Apart from the possible active behavior of the operator, one may consider theoperator as a special case which is closely related to a soft and possibly bounded

environment.

• Within the application of telesurgery, a beating heart is often proposed to bean example of an active environment. It should be noted, however, that this

depends on whether or not the generated muscle forces can be seen as exogenous

forces. Only if the forces correlate to any state in the coupled teleoperation

system, the beating heart may be active.

2.4 A Preliminary Example

What are the immediate consequences of the the assumptions? This seems a

very relevant question and some of the answer has be already been formulated

in Colgate [1989, Section 3] and Newman [1992, Section 3] for systems featuring

both force and position sensors. In Griffiths et al. [2008] and Griffiths et al.

[2010] a more rigorous derivation can be found for systems featuring position

sensors only.

While the results will not be discussed here in full detail, their main point

can be explained as follows. Assume that the system is supposed to mimic

the behavior of a (passive) physical tool. If there exists a controller that can

achieve this behavior then the driving-point immitance will be equal to that of

the physical tool and therefore tend to be passive. Due to practical limitations,

however, the controller will only achieve this behavior in the low-frequent area.


In the high-frequent area, however, the influence of the controller can be ne-

glected and the driving-point immitance will equal the uncontrolled but again

passive behavior of the interaction device. But, while the system appears to be

passive in the low and high frequent area (perfect control and uncontrolled),

it may not appear to be passive in between. If this is true, it is also intuitive

to expect that this problem cannot be solved by redesigning the controller as

the limitations are due to the finite capabilities of actuators and sensors to

transduct signals from one physical domain to the other. The problem will

therefore have to be solved by adjusting the mechanical design.

An illustrative example was already given in Colgate and Hogan [1989,

Section 6]. Consider an interaction device consisting of a single, rigid mass m

that needs to be reduced to mr < m to achieve satisfying task performance. It

appears that there exists such a controller as

vi =1

ms(Fi + Fa) and Fa = C

fFi (2.9)

with Cf = −1 + mmr results in

vi =1

mrsFi. (2.10)

Despite the controller Cf being proper, actuator limitations will prohibit the

controller from proper working at high frequencies. Assume that the actual

controller behavior will be such that it rolls off to zero from ωc on. The actual

driving-point impedance will then equal

vi =1

ms

[1 +

(−1 + m

mr

)1

τcs+ 1

]

︸︷︷︸Yi

Fi with τi =1

ωi. (2.11)

For the system to be passive, the driving-point admittance should be positive

real. However, as

ReYi =mr −mmrm

τc1 + τ2c ω

2(2.12)

it would appear that the system will never (!) be passive if mr < m. Note

that although the angle of Yi indeed tends to −90 [deg] in the low and highfrequency areas as expected, the real part of Yi tends to

limω→0

ReYi =mr −mmrm

τc and limω→∞

ReYi = 0. (2.13)

The obvious question is now: how to deal with such a situation? Intuitively

there should be some guaranteed dissipation to counterbalance the energy gen-

erated by the system. As proposed in Dohring and Newman [2002, Section 4],

proper application of shunt dynamics will result in a passive system. This at

the cost of system performance. How such a decrease in system performance

will eventually affect the task performance depends on the sensitivity between

the the measures.


As an example, consider an interaction device which can be modeled by

a single 1 [kg] mass. Suppose one would like to reduce the apparent mass

such that the user perceives only 0.4 [kg]. Figure 2.7 shows the resulting

driving-point admittance as presented in (2.11) if τc equal to 1/15 [s]. The

system appears to be non positive real. It’s phase (not shown), however, tends

to −90 [deg] in both low and high frequent area as expected. Damping ofthe interaction device (1 [Ns/m]) and introducing a compliant force sensor

(stiffness 103 [N/m], damping 50 [Ns/m]) will, however, result in a passive

system as depicted in figure 2.8.

Additional Notes

• Note that the uncoupled device appears to be stable as its poles are equal to

λ (Yi) =

{0,− 1

τc

}. (2.14)

Note that only τc influences the locations of the pole. This is because only

the low-pass filter feasures an local feedback loop. As long as the system is in

uncoupled (i.e. in free-air), then the original controller Cf won’t be part of a

feedback loop and hence influence stability. A similar observation was already

made in Colgate [1988, Section 7.2].

• One may show that reducing the uncertainty set to pure stiffnesses and massesonly will not result in a less conservative conclusion as depicted in figure 2.6.

Consider the following loop gains

Lk = −Yi(s)kes

and Lm = −Yi(s) mes (2.15)

with ke and me environmental stiffness and mass respectively. It now appears

that if mr < m (mass of the interaction device is reduced)

Im(−Lk) =keω

(τc

1 + τ2c ω2m−mrmmr

)> 0, ∀ke > 0, ∀ω > 0 (2.16)

and

Im(−Lm) = −meω(

τc1 + τ2c ω2

m−mrmmr

)< 0, ∀me > 0, ∀ω > 0. (2.17)

It appears that the Nyquist curve will be located in the upper-half plane for

pure stiffnesses and in the lower-half plane for pure masses. This implies that

the system will be unstable if the interaction device is coupled to any (time

invariant) stiffnesses, but will be stable if the interaction device is coupled to

any (time invariant) mass greater than zero.

• The smallest value (wrt. minus infinity) of the real part of an immitance, i.e.

ν(Y ) = infω

ReY (ω), ν(Z) = infω

ReZ(ω) (2.18)

is sometimes called the ν-index as defined in Wen [1988, Definition 2]. It may

be interpreted as (citing) ‘a measure of distance to positive realness’. In the

case of (2.11), it appears that the ν-index is equal to (2.13) (case ω → 0).


me

ke

FsFi

mr mr

Yi(s)

−

kes

Yi(s) mes

vi vi vi

vi vi

Fs

Fi

Fi Fi

(a) (b)

−

Lm Lk

Figure 2.6: The controlled interaction device Yi(s) coupled to either a pure mass me(a) or a pure spring ke (b). The force sensor is assumed to rigid. Notethat, according to Newton’s second and third law, (mes)vi = −Fs + Fiimplies Fs = −(mes)vi + Fi.

• A practical problem during the interpretation of the results is the initial lackof intuition for the numbers. First of all, it may be a good idea to buy a set

of springs and masses or even build a mechanical device with which you can

actually feel a particular mass, inertia or stiffness. Second, one may also express

stiffness and damping into [kg/cm] and [kg s/cm] instead of [N/m] and [Ns/m].

The kilogram and centimeter are more closer to our daily experience and the

scale of our hand movements respectively. Note that by approximation (one

should not be interested in the exact numbers; its just to trigger the intuition):

1 [N/m] ≈ 10−3 [kgf/cm] ⇔ 103 [N/m] ≈ 1 [kgf/cm] (2.19)


100

101

102

103

−80

−70

−60

−50

−40

−30

−20

−10

0

Frequency f [Hz]

Mag

intu

de

Uncontrolled DeviceReference BehaviorControlled Device

10−2

100

102

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Frequency f [Hz]

Re

Yi

Figure 2.7: Numerical example for the case m = 1 [kg], mr = 0.4 [kg] and τc =15 [Hz]. Shown are the magnitudes of the FRFs (Left) and the real partof Yi (Right).

100

101

102

103

−70

−60

−50

−40

−30

−20

−10

0

Frequency f [Hz]

Mag

intu

de

Uncontrolled DeviceReference BehaviorControlled Device

10−2

100

102

−0.2

−0.1

0

0.1

0.2

infω Re Yi = 8.55e−004

Frequency f [Hz]

Re

Yi

Figure 2.8: Numerical example with after the introduction of some guaranteed,physical damping. Shown are the magnitudes of the FRFs (Left) andthe real part of Yi (Right).

Chapter 3

Control Problem

This chapter will deal with concepts only. Practical issues like non-causality

and limitations imposed on controllers due to plant dynamics (zero’s, uncer-

tainties, etc.) will not be discussed at this point.

3.1 Control for Teleoperation

It should be clear that, for a teleoperation system to function properly, the

mutual isolated devices should be coupled. While some teleoperation systems

are coupled by complex mechanical mechanisms, most systems are coupled by

some virtual dynamics (a controller). For a single degree-of-freedom system, the

general control architecture consists of a MIMO controller which takes various

measurements from both devices and provides each with a control signal to

achieve a bidirectional information flow (see also figure 3.1). The measurements

typically consist of forces and positions which are sometimes augmented with

explicit velocity measurements () or acceleration (accelerometer). The control

signal is typically an actuation force, but may sometimes be a position reference

if the device has an inherent position control loop which cannot be bypassed

(which may be the case for off-the-shelf industrial robots).

The design of the controller can be done based on different objectives. While

not mutually exclusive, one may roughly distinguish two major approaches to

achieve the bidirectional information flow: by either matching the system’s

behavior to a (physical) tool or implement a mediator that estimates and filters

information explicitly. In this report, only the first approach is considered. The

latter is discussed concisely in the additional notes.

22

3.1. CONTROL FOR TELEOPERATION 23

F(1)i

v(1)i

F(2)i

v(2)i

Interaction

Device1

Interaction

Device2

Con

troller

Controlsignals

Variousmeasurements

Figure 3.1: Blockdiagram illustrating the general control architecture of teleopera-tion systems

Force sensor Fs

Actuator 〈Fa, xa〉End-effector 〈Fi, xi〉

Figure 3.2: General situation where the end-effector, force sensor and actuator/po-sition sensor are all non-collocated.

Interaction Devices

Before the derivation of any controller it is necessary to present the model

of the interaction device (‘plant model’). Under the assumption that a single

degree-of-freedom can be considered linear (after feedback linearization and

decoupling), it is supposed that the result from the identification of the kth

interaction device can be represented by the 3× 3 transfer matrix

x

(k)i

x(k)a

F(k)s

=

g11 g12 g13g21 g22 g23g31 g32 g33

︸︷︷︸G

F

(k)i

F(k)a

F(k)d

. (3.1)

The symbols xi, xa, Fi and Fa correspond to the (integrated) (co-)energy

variables at the point of interaction and actuator as depicted in figure 3.2.

Furthermore, Fs represents the force as measured by the force sensor while

Fd represents the forces (disturbances) acting on the system which are not

measured (detected) by the force sensor. In this chapter, only a nominal model

will be considered.

Please note that the disturbance input Fd is not properly defined at this

point as it is not clear where the disturbance forces will act. Multiple dis-

turbances may occur anywhere along the (possibly non-rigid) transmission dy-

namics between the actuator and force sensor. They need not to be collocated

with either one.

24 CHAPTER 3. CONTROL PROBLEM

Additional Notes

• Controllers that are designed from the perspective of explicit mediation typ-ically consist of an estimator and a virtual world as depicted in figure 3.3.

The estimator is used to identify certain properties of the environment. The

identified properties are (haptically) available to the operator through a virtual

world. As the estimator ‘decides’ which properties are identified and the virtual

world (render system) ‘decides’ how these properties are presented, this class

of controllers is called mediation controllers. Mediation controllers are, mainly

due to the estimators, inherently non-linear and their design can therefore be

quite challenging. Examples of mediation control can be found in De Gersem

[2005] in which an extended Kalman filter is applied to identify the environ-

ment’s stiffness and Mitra and Niemeyer [2008] in which the application of

mediation control for cases with time-delays is discussed.

F(1)i

v(1)i

F(2)i

v(2)i

TaskCommands

EnvironmentProperties

Estimator

Interaction

Device1

Virtual

World

Interaction

Device2

Figure 3.3: Block diagram illustrating the concept of the class of mediation con-trollers.

• The identification of the interaction device may need some additional attention.One may need external systems for the excitation of and measuring at the point

of interaction (Fi and xi respectively).

• The assumption that Fd is exogenous can pose difficulties on the mechanicaldesign of the interaction device, in particular if the teleoperation system is

supposed to act in highly unstructured and time-varying environments. The

assumption may rather easily be violated if the mechanics between the actuator

and force sensor make contact with some external physical system or a human

(e.g. if he/she touches it).

3.2. SOME SOLUTIONS TO THE MODEL-MATCHING PROBLEM 25

3.2 Some Solutions to the Model-Matching Problem

The ideal controller minimizes the behavioral difference between the prede-

fined reference dynamics and the controlled teleoperation system. Under the

assumption that the reference dynamics is robustly stable to the uncertainty

sets representing the operator and/or environment, an ideal controller can be

obtained by solving for the controller in terms of the reference behavior and the

given device model. As it may be clear that such a symbolic derivation may be

intractable, one may consider a simplified case first in order to develop some

intuition the concepts. In the following two (simplified) cases will be discussed:

a single device (N = 1) and teleoperation system (N = 2).

Matching the behavior of a single interacting device (N = 1)

Before starting of, two assumptions will be made about the plant. The first

assumption is that the disturbance force Fd acts on the same location (physi-

cally) as the actuation force Fa. The second assumption is that the force sensor

is located at the point of interaction. This assumption certainly restricts the

class of device that can be used for now. Section 3.4 will, however, provide

some additional comments on this.

The two assumptions of collocation implies that (3.1) changes to

xixaFs

=

g11 g12 g12g21 g22 g22g31 0 0

FiFaFd

. (3.2)

The equivalence of the 2nd and 3rd column are due to the first assumption;

the zeros in the 3rd row are due to the second assumption.

Consider the general two degrees-of-freedom controller mapping the mea-

sured force Fs and actuator position xa to the actuation force Fa as

Fa =[Cf Cp

] [Fsxa

]. (3.3)

The resulting motion at the point of interaction due to the interaction force

Fi and disturbance Fd can be obtained by substitution of (3.3) into (3.2) and

solve for xi. It appears that,

xi = YiFi + YdFd (3.4)

with

Yi =g11 + C

fg12g31 − Cp(g11g22 − g12g21)1− Cpg22

(3.5)

and

Yd =g12

1− Cpg22(3.6)

It can be seen that Cp should be large and negative in order to attenuate the

effect of disturbances and assure a negative feedback loop. However, it can


also be seen that Cp is part of the driving-point admittance Yi. To see whether

this will impose a problem the system’s driving-point admittance is set equal

to the desired admittance as

Yi = RY . (3.7)

By solving for Cf and substitution of the result in (3.3), one obtains

Fa = CsFs + C

p(xar − xa) (3.8)

with

Cs =

(RYg12− g11g12

)1

g31(3.9)

the shaping controller and

xar =

[g22

(R

g12− g11g12

)+ g21

]Fsg31

. (3.10)

the desired motion of the actuator. First of all, observe that a large Cp poses no

problem. Even more interesting, it seems desired as the second term indicates

that Cp is used for motion tracking. All terms in (3.9) and (3.10) can be given

an intuitive explanation by substituting the transfer function by their signal

ratio’s (not shown here).

The term Cs in (3.8) can be seen as the controller term which shapes

the behavior of the system at the point of interaction1. The actuation force

Fa necessary to achieve the desired displacement x̂i at the point of interaction

given the sensed interaction force (first term) while compensating for the open-

loop effect of Fi (a correction on Fa; second term).

The reference xar for the motion feedback controller is computed in (3.10)

by considering the effect of the shaping computed by (3.9) on the actuator

position xa corrected for the open-loop response of interaction force Fi on the

actuator position xa system.

Matching the behavior of a teleoperation system (N = 2)

In the previous section, the model-matching equations were solved for a (linear)

single interaction device under some various assumption. This section will

go one step further and sketch the results for the case of two interconnected

interaction devices; a teleoperation. To keep the equations tractable, only

the case of full-collocation plus ideal force sensor will be considered. Full-

collocation means that all forces and all velocities are considered at the same

point for each device. Due to these assumptions, the model of the physical

interaction device in (3.1) will transform to

x

(k)i

x(k)a

F(k)s

=

g g g

g g g

1 0 0

F

(k)i

F(k)a

F(k)d

. (3.11)

1It may be compared to a feedforward in tracking controllers. The shaping term is calleda feedforward if its input is exogenous (a reference signal).


To begin, let the controller (again) be such that

Fa =[Cf Cp

] [Fsxa

](3.12)

with Fa, Fs and xa now being vectors and the controllers Cf and Cp now equal

to

Cf =

[Cf11 C

f12

Cf21 Cf22

]and Cp =

[Cp11 C

p12

Cp21 Cp22

]. (3.13)

Note that the diagonal elements in both Cf and Cp are local controllers, while

the anti-diagonal elements are coupling controllers. It is obvious that the in-

teraction devices will be uncoupled if the anti-diagonal elements are equal to

0.

Similar to the case with the single interacting device, (3.11) and (3.12) are

used to obtain the expression for the driving-point admittances by eliminating

the variabels associated with the actuator. Hence,

[x

(1)i

x(2)i

]= Yi

[F

(1)s

F(2)s

]+ Yd

[F

(1)d

F(2)d

](3.14)

with Yi and Yd relating the interaction and disturbance forces to the resulting

motion at the point of interaction. The admittance matrix Yd appears to be

equal to

Yd =g(1)g(2)

D

[− 1g(2)

+ Cp22 Cp21

Cp121g(1)− Cp11

][F

(1)d

F(2)d

](3.15)

with

D = −1 + Cp11g(1) + Cp22g(2) + det(Cp)g(1)g(2) (3.16)It can be seen that, in the ideal case, Cp12 = C

p21 = 0 such that a disturbing

force acting on one device does not influence the motion of the other device.

This implies that position measures are fed back only locally. Hence, (3.15)

would become

Yd

∣∣∣Cp12=C

p21=0

=

g(1)

1−g(1)Cp110

0 g(1)

1−g(2)Cp22

[F

(1)d

F(2)d

]. (3.17)

Moreover, one can also observe that the diagonal elements of the matrix Cp are

similar to (3.6) and should be large and negative to achieve proper disturbance

attenuation and to assure negative feedback loops. Therefore, the magnitude

of Cp11 and Cp22 should ideally be large, similar to the case N = 1.

The final goal is to match the behavior of the actual system represented by

Yi to a custom reference given by

[x̂

(1)i

x̂(2)i

]=

[r11 r12r21 r22

]

︸︷︷︸RY

[F

(1)i

F(2)i

]. (3.18)


Cp22

F(2)i

Cp11

F(1)i

F(2)sF

(1)s

x(1)i

R

x̂(2)ix̂

(1)i

x(2)i

Force induced by Cs

g(1) g(2)

Figure 3.4: Conceptional interpretation of the controller found. The reference isassumed to be a two mass system with spring-damper coupling. Bothinteraction devices are assumed to be a rigid mass.

Hence, by setting

Yi = RY (3.19)

and solving for the necessary actuation forces, one obtains

[F

(1)a

F(2)a

]= Cs

[F

(1)s

F(2)s

]+ Cp

([x̂

(1)i

x̂(2)i

]−[x

(1)a

x(2)a

])(3.20)

with

Cs =

[−1 + r11

g(1)r12g(1)

r21g(2)

−1 + r22g(2)

]and Cp =

[Cp11 0

0 Cp22

](3.21)

It can be seen that the diagonal elements of Cs are similar to (3.9) (under

the assumption of full-colocation). The anti-diagonal elements of Cs have an

interpretation similar to the second term of the diagonal elements of Cs.

The found controller can be drawn schematically as depicted in figure 3.4.

By comparing (3.20) with (3.8), it can also be seen that the controller for

two interaction devices suggests to be a natural extension of the controller for

a single interaction device; there are some major similarities between these

results.

It is rather surprising how many researchers proposed controllers that are

idential or at least very similar to the one stated in (3.20). In Furuta et al.

[1987] a similar controller was introduced under the name virtual internal model

following control or simply virtual model control (VMC). In Colgate [1989]

the target model reference controller (TMRC) was introduced as a method to

control the end-effector admittance of a single robot during the 1980s. Then, in

the beginning 1990s, the natural admittance control (NAC) was introduced in

Newman [1992] and at the end of the 1990s a patent on the concept was issued

by Fokker Control Systems B.V. (now Moog, Inc.; see also appendix H.2).


Additional Notes

• A special kind of reference behavior often found in literature is transparent be-havior. The transparency of a system (or object) indicates how much a physical

quantity is distorted while passing through that system. Clear glass, for ex-

ample, allows light to pass almost without any distortion and is therefore said

to be transparent. A teleoperation system is called transparent if motion and

force can pass through the system undistorted. It is an extremal behavior that

can never be achieved in practice as it implies that the system should behave as

a rigid, massless stick. Hence, transparent behavior cannot represented by an

admittance matrix RY . It can, however, be represented by an hybrid matrix

RH . To see this, suppose that the reference behavior is equal to a rigid mass

mr such that [x̂

(1)i

x̂(2)i

]= RY

[F

(1)i

F(2)i

](3.22)

with

RY =1

mrs2

[1 1

1 1

]. (3.23)

Letting m approach 0 will result in a transfer matrix with unbounded elements.

Representing the same behavior in the hybrid parametrization (see B.1), how-

ever, gives

RH =

[2mrs

2 −11 0

](3.24)

and hence

R′H = limmr→0

RH =

[0 −11 0

]. (3.25)

The result R′H can indeed be recognized as transparent behavior as2

x̂(1)i = x̂

(2)i and F

(1)i = −F

(2)i (3.26)

or, as proposed in Lawrence [1993, Section 2], equivalently

x̂(1)i = x̂

(2)i and Z

(1)tr = −Ze. (3.27)

with Z(1)tr and Ze the transmitted and environmental impedance respectively

(see also section E.3).

• The controller found in (3.8) minus the shaping term is fact a particular appli-cation of the disturbance observer concept (see Kim and Chung [2003]). Here,

the input is set equal to the measured force Fs instead of the actuation force.

The control effort of the motion controller Cp is an estimate for the disturbance

(due to Fd and forces due to model-mismatching).

Some researchers exploit the property of disturbance estimation and use these

kind of observers to estimate the interaction force instead of measuring it. See

for example Katsura et al. [2007] where superiority of this strategy is claimed.

A disadvantage of this strategy is that the interaction device must be set in

motion before any estimation and thus compensation of the device’s open-loop

behavior can take place. As a result, the operator will perceive a different

2The minus sign is due to the positive definition of F(2)i .


behavior during the initial motion. Quantization of the position measurements

may even worsen this problem.

Though a little bit off-topic, the different concepts of disturbance observer and

Luenberger observer (state observer) differ in the way the innovation signal

(here d̂) is fed back. Figure 3.5 shows the two observer concepts in an simplified

block diagram. In the case of a Luenberger observer, the innovation signal is

used to correct the response of the model Ĝ to the response of the actual plant

G; The response of the model should ideally be equal to that of the actual

plant. In the case of the disturbance observer the actual plant G is corrected

for the response of Ĝ; The response of the plant should ideally be equal to that

of the model.

u

d

C

G

Ĝ

e

y

ŷ

+

−

+

+

+

+

(a) (b)

d̂

u

d

C

G

Ĝ

e

y

ŷ

+

−

+

−+

d̂

Figure 3.5: Blockdiagrams to illustrate the conceptional differences between a Lu-enberger observer (a) and a disturbance observer (b).

• In literature, the (diagonal elements of the) position controller Cp are some-times referred to as (the) model following controller(s) for obvious reasons.

• Full-collocation is an assumption commonly encountered in literature (see foran example the well-known block diagram proposed in Lawrence [1993, Fig-

ure 2]). In practice however, only some setups build in laboratories justify the

assumption (as they are specifically build to validate theory which is worked

out under this assumption). For industrial applications this assumption rarely

holds due to functional and practical design considerations. The inability to

apply the assumption implies that one cannot measure the performance vari-

able – the position xi at the point of interaction – directly and one will have to

rely heavily on (‘control-relevant’) models of the device to estimate the actual

xi (a so-called inferential control problem).

• Associated with the force point is the assumption (made in section 3.1) thatthe disturbance force is collocated with the actuator. This may not hold in

practice; a disturbance force may, as an example, also act near the point of

interaction. In that case, (3.1) should be expanded such that

xixaFs

= g11 g12 g11 g12g21 g22 g21 g22g31 0 0 0

FiFa

FdiFda

. (3.28)Under the assumption of the controller stated in (3.3), i.e.

Fa = Cpaxa + C

fFs, (3.29)


one may find, after elimination of Fs, Fa and xa, the displacement xi to be

xi = YiFi + YdiFdi + YdaFda. (3.30)

It appears (as expected) that Yi and Yda are similar to (3.5) and (3.6) respec-

tively. The new term Ydi, however, appears to be different from Yda as

Yda =g12

1− Cpag22(3.31)

and

Ydi =g11 − Cpa(g11g22 − g12g21)

1− Cpag22. (3.32)

The disturbance acting at the point of interaction cannot be suppressed by

making Cpa large and negative as

limCpa→−∞

Ydi = g11 −g12g21g22

. (3.33)

Equation (3.33) shows that the displacement xi results from the open-loop effect

of Fdi (first term) minus the compensating effect the controller Cpa (second

term). The high-gain controller is clearly unable to compensate for the response

of the dynamics between the actuator and point of interaction due to Fdi, as

shown in figure 3.6.

xa xi

Fdi

Fda

xa xi

FdiFa

Fda

Cpa

(a) (b)

Figure 3.6: A single resonance model with controlled position xa (a). A high-gainCpa will make the mass at the actuator appear as a rigid wall (b). Asa result the effect of Fda on xi can, but the effect of Fdi on xi cannotbe suppressed by a high-gain Cpa. The interaction force Fi is omitteddue its irrelevance here.

To resolve this problem an additional position sensor3 was introduced in Chris-

tiansson [2007] such that xi can be measured explicitly. The new controller can

now be stated as

Fa = Cpaxa + C

pixi + CfFs. (3.34)

Calculating the resulting displacement xi results in

Yda =g12

1− Cpag22 − Cpig12(3.35)

3This was actually an LVDT sensor which measured the relative displacement betweenthe actuator and point of interaction, i.e. xi − xa.


and

Ydi =g11 − Cpa(g11g22 − g12g21)

1− Cpag22 − Cpig12(3.36)

which shows that the effect of both disturbances on xi can then be attenuated

if Cpi is large. It even shows that Cpa may be omitted. Note, however, that

dynamics may pose limitations on the achievable controller gain Cpi. Hence,

maintaining Cpa may still be necessary or to achieve the desired disturbance

attenuation.

• By the observations of the similarities between the case N = 1 and N = 2,it can be expected that similar results will hold for multilateral cases where

N > 2.

• Citing from Rosenberg [1993],

‘Virtual fixtures are defined as abstract sensory information overlaid

on top of reflected sensory feedback from a remote environment.’

A well-known example is the overlay of a force field derived from some potential

function as shown in (a.o.) Lee and Li [2005]. Such a field may prohibit the

user to enter particular areas in the remote environment or assist the user while

he of she is following a predefined trajectory. These virtual fixtures, typically

represented as impedances, can be absorbed rather intuitively into the model

describing the reference behavior.

• Within the research field of teleoperation, one often finds the term N-channelcontroller or N-channel architecture. The term, introduced in Lawrence [1993],

indicates the amount of (measurement) signals that are communicated between

the (controlled) interaction devices. For example, if both actuation forces F(1)a

and F(2)a are computed based on the position and force measurements from the

other interaction device, the controller is called a ‘4-channel controller’. Note

that, however, the term does not indicate how many (if any) local measurements

are used to compute the actuation forces. Moreover, it also does not indicate

in which direction the signals are communicated and how they are used to

compute the an actuation force. Hence, the information associated with the

term is very limited. The term should therefore be used with caution.

3.3 Concepts found in Literature

In the past decades a large amount of controllers have been proposed to enable

force-feedback in teleoperation. In Hokayem and Spong [2006] an attempt is

made to provide ‘an historical survey’ in a review article counting 18.5 effective

pages featuring a total of 146 references (for the record, that’s 146/18.5 ≈ 8references per page). In this section, only four controllers that are commonly

encountered in literature will be discussed: position error control, force reflec-

tion, wave-variable controller and shared compliant control.

3.3. CONCEPTS FOUND IN LITERATURE 33

Position Error Control

Consider the reference behavior given by the admittance matrix

RY =g(1)g(2)Zc

1 + g(1)Zc + g(2)Zc

[1 + 1

g(2)Zc1

1 1 + 1g(1)Zc

]. (3.37)

It essentially describes the behavior of the two native interaction devices cou-

pled by an impedance Zc as shown in figure 3.7. To achieve this behavior, one

may substitute the elements of RY into (3.21) and obtain

Cs =Zc

1 + g(1)Zc + g(2)Zc

[g(1) g(2)

g(1) g(2)

]and Cp =

[Cp11 0

0 Cp22

]. (3.38)

In literature, however, (3.38) is often modified such that force sensors and model

estimates of the interaction devices are no longer needed. The adjustments

transforms (3.38) into

Cs = 0 and Cp = Zc

[−1 11 −1

]. (3.39)

The controller for this particular choice of Cs and Cp leads to the same reference

behavior RY and is most often indicated as position-error (PERR), symmetric

servo or position-position control . The obvious advantage is a more cheap

system as no force sensors are needed. Moreover, the controller is passive if

Zc is implemented as a spring-damper along with a low-pass filter (‘lead-lag

filter’). The disadvantage is the total lack of disturbance attenuation as Cp

cannot be chosen freely. In fact, the interaction and disturbance forces will be

threated equally as

Yi = Yd (3.40)

in the case of (3.39) and under the assumption of full-collocation. As a result,

the operator will experience the full effect of disturbance forces.

The origin of the controller is not known to the author as some (histor-

ical) articles were not available to the author at the time of writing. It is

most likely the eldest controller, probably introduced during the early 1950s

by R.C. Goertz (see appendix H.1).

x(1)i x

(2)i

F(1)i F

(2)i

Zc

g(1) g(2)Cp x(1)i x

(2)i

F(1)i F

(2)i

Zcg(1) g(2)

−

−

(a) (b)

Figure 3.7: Conceptional interpretation of the teleoperation system under positionerror control (a) and the associated block diagram (b).


Force Reflection Control

Consider the reference behavior given by the admittance matrix

RY = g(1)

[1 1

1 1

]. (3.41)

It essentially means that the teleoperation system should behave like the first

interaction device which will give

Cs =

[0 1g(1)

g(2)−1 + g(1)

g(2)

]and Cp =

[Cp11 0

0 Cp22

](3.42)

In literature, however, (3.42) is modified such that the force sensor on the first

device and the need for model estimates of both interaction device are no longer

needed. The adjustments transforms (3.42) into

Cs =

[0 1

0 0

]and Cp =

[0 0

0 Cp22

](3.43)

This particular controller is most often indicated as force reflection control ,

kinestatic force feedback (KFF) or position-force control . The obvious advan-

tage is a cheaper system as one force sensors can be omitted. The disadvantage

is the total lack of disturbance attenuation at the side where the Cp11 is set to

zero.

One of the major observations is the similarity to the example of section 3.2

(case N = 1). Apart from the omitted shaping controller, the main difference

is that the reference behavior is actually provided by the (first) physical inter-

action device instead of a virtual model.

As with position-error control, the origin of force reflection control is not

known to the author. It is probably introduced in the late 1950s by J.R. Burnett

(see appendix H.1).

x(1)i

x(2)i

F(1)i

F(2)i

Cp22 g(2)

g(1)

F(2)s

g(2)

Cp22

g(1)

−

F(2)i

x(1)i

x(2)i

(b)

F(1)i

(a)

Figure 3.8: Conceptional interpretation of force reflection control (a) and the asso-ciated block diagram (b). The block diagram was rotated by 90 degreesccw. so that the disturbance observer structure can easily be recognized(compare to figure 3.5b.


Niemeyer’s Wave Variable Control

Stability problems induced by time-delays in the communication channels where

found during the early development stages of electronic teleoperation systems.

As a result, extensive research has been done to find solutions for this prob-

lem. See for example Arcara and Melchiorri [2002] for an overview. The most

(physically) intuitive solution was proposed in Anderson and Spong [1989] in

the late 1980s. More extensive results are provided in Niemeyer and Slotine

[2004] in the 1990s and continued in the 2000s. The solution, based on the

theory of transmission lines, is applicable in the case of constant time-delays

which are equal for all communication channels. As depicted in figure 3.9, the

physical time delay is taken into account in the virtual model by simulating the

finite time necessary for force and velocity to travel through a virtual beam.

As the forces and velocity in the beam thought of being traveling waves, the

concept of often referred to as the wave variable controller. A short derivation

regarding this controller can be found in appendix C.

A drawback of the wave-variable controller is the position drift. Several

researchers have paid attention to this problem. In Niemeyer and Slotine [2004]

an overview of possible solutions is given. Furthermore, practical limitations

are discussed in Tanner and Niemeyer [2004], an interesting extension in Tanner

and Niemeyer [2005] and design guidelines in Hart and Niemeyer [2007].

x̂(1)i x̂

(2)i

F(1)s F

(2)s

Z0, τ

Bou

ndary

g(1)r Zc

e−τs

e−τs

g(2)r

Bou

ndary

(a)

(b)

−

−x̂(1)i x̂

(2)i

F(1)s F

(2)s

Zc

Figure 3.9: Conceptional interpretation of the reference model RY (a) and the as-sociated block diagram (b). The model includes a distributed modelof a beam. The boundary blocks represent the transformation betweenfrom (co-)energy variables to so-called wave variables.


Kim’s Shared Compliant Control

In Kim [1990] the concept shared compliant control (SCC) 4 was introduced.

The controller extends the ‘force reflection controller’ by the introduction of

a an inner loop containing a low-pass filter around the plant. This can be

interpreted as the addition of a damped compliance element implemented a

admittance and placed in series with the reference dynamics. The addition will

affect the transient behavior of the system as the spring/damper will deflect

(almost instantly if the damping is small) due to the applied force Fs. In

figure 3.10 the concept is shown in case the reference model equals a rigid

mass.

To see the effect of the introduced compliance, consider the example in

which the reference model is defined by a rigid mass and a damped compliance

as shown in figure 3.10. In that case, the reference trajectory (position) is equal

to

x̂i =

(1

ms2+

1

bs+ k

)Fs (3.44)

which can be written as

x̂i =1

ms2ms2 + bs+ k

bs+ k︸︷︷︸=RY

Fs. (3.45)

The result shows that the reference generated by the rigid mass is actually

filtered. The non-causal filter shows indeed that the transient response of the

system will be faster while the steady-state remains the same. Practical imple-

mentations may, however, limit the effect as the resulting non-causal controller

Cf need to be proper. Hence, a low pass-filter may have to be introduced.

Some remarks can be made. First, it is not known whether the phase lead

will result in more stable controllers. Second, note that if one would like to

interconnect multiple devices via the reference mass. It should therefore be

most natural to use the position of the mass xr instead of the filtered reference

x̂i.

Additional Notes

• Because of its cheap implementation and robustness properties, it is stronglyrecommended to consider position error control before any other strategy. Only

if position error control cannot be applied or does not lead to the desired task

execution performance, one should proceed and consider other strategies. This

may, as an example, be the case if the device’s inertia or friction is large.

Moreover, one should be aware that reducing the apparent mass using con-

trol will likely increase the risk of being faced with stability problems (see

the preliminary example in section 2.4). Hence, it would be wise to consider

redesigning the interaction device first before looking into other control strate-

gies.

4Or should it be shared compliance control?


Fi

Fsxi

x̂i

R Cp g

Fs

x̂i

1bs+k

1ms2

(a) (b)

xr

Figure 3.10: Conceptional interpretation of shared compliant control for a singleinteraction device (a) and a block diagram representing the referencedynamics (b).

• During the normal operation of the ‘wave-variable controller’, a position error(lag in tracking) is induced due to the time delay. Hence, the position of

device 1 compared to device 2 equals

x(1)(t) = x(2)(t− T ). (3.46)

Due to practical reasons like integration errors, the equality will in general not

hold and drift will occur. In Niemeyer [1996, Section 5.3] two solutions are

proposed in order to attenuate this drift. In the first solution the integrated

(co-)energy variables (position and momentum) are communicated along with

(co-)energy variables. The second solution boils down to a concept in which

signals communicated from one side to the other are adjusted such that the

tracking error due to drift is decreased. Hence, if the slave is ahead of the

master, one may communicate a velocity or force from the master to the slave

that is lower compared to what is actually measured at the master. A switching

(‘modulating’ as stated in Niemeyer [1996, Section 5.3.4]) controller may be

needed to preserve passivity and/or bound the adjustment to prevent confusing

responses.


3.4 Shunt Dynamics

In section 3.2 the assumption was made that the force sensor would be located

at the point of interaction (or vice-versa). This assumption can be restrictive

as it may in practice be difficult to actually measure the force at the point

of interaction. As a consequence, some dynamics between the force sensor

and the actual point of interaction will remain. If it these dynamics are not

compensated by the controller, they can be denoted as shunt dynamics; a term

derived from the field of electrical engineering.

Not compensating the dynamics between the force sensor and point of inter-

action has some disadvantages as the these dynamics will be perceived by the

operator. There are, however, also advantages as these dynamics will bound

the behavior of the environment seen by the teleoperation system. As an ex-

ample, the stiffness seen by the teleoperation system can be upper bounded,

mass can be lower bounded and damping may both be bounded from below

(damper parallel to mass) and above (damper parallel to spring). This is one

of the reasons for the existence of so-called series-elastic actuators (SEA) as

discussed in (a.o.) Robinson [2000].

The subsequent analysis will sketch some results to show how the shunt

dynamics may (1) influence the driving-point immitance of the robot seen by

the environment and (2) influence the uncertainty set of the environment seen

by the robot.

Effect of dynamics on the system’s driving-point immitance

In Dohring and Newman [2002] an interesting example is discussed in which

shunt dynamics are used to guarantee a certain amount of dissipation such

that the teleoperation system seen by the environment is passive. To see this,

suppose that the driving-point admittance of the (controlled) interaction device

is represented by Y as shown in figure 3.11a. Adding an impedance (e.g. a

sensor compliance) as shown in figure 3.11b results in a new the driving-point

impedance Z ′ and admittance Y ′

Z ′ =Zs1

1 + Y Zs1⇔ Y ′ = Y + 1

Zs1. (3.47)

Assume that Zs1 represents a simple spring and damper connected in parallel

such that

Zs1 =1

Ys1=k

s+ b. (3.48)

Computing the real part of the admittance Y ′ gives

Re(Y ′) = Re(Y ) + Re

(1

Zs1

)= Re(Y ) +

bω2

b2ω2 + k2(3.49)

which shows that the additional positive realness is ‘added’ in the high-frequent

area. One may continue and add an admittance as shown in figure 3.11c which

3.4. SHUNT DYNAMICS 39

Y Y YZs1 Zs1 Ys2

(a) (b) (c)

Z ′ Y ′′

− −

−Y

Figure 3.11: Starting with the driving-point admittance of the robot Y (a) andsubsequently adding an impedance Zs1 (b) and admittance Ys2 (c).

results in the driving-point impedance Z ′′ and admittance Y ′′

Z ′′ = Z ′ +1

Ys2⇔ Y ′′ = Ys2

1 + Z ′Ys2. (3.50)

Assume that Ys2 represents an additional damped mass such that

Ys2 =1

Zs2=

1

ms+ d. (3.51)

Again computing the real part of the impedance Z ′′ gives

Re(Z ′′) = Re(Z ′) + Re

(1

Ys2

)= Re(Z ′) + d (3.52)

which shows that positive realness is ‘added’ over the full spectrum.

Effect of shunt dynamics on the uncertainty set

One may also analyze the effect from the perspective of the teleoperation system

looking towards the environment. This perspective was already used in the

context of optimization problems to bound uncertainty sets of the operator

and environment. An example of this application can be found in Hashtrudi-

Zaad and Salcudean [2001, p. 421] and Vander Poorten [2007, Section 3.3].

Observe that the following transfer function can be derived from the block

diagram depicted in figure 3.12.

∆′ =Zs1(1 + Ys2∆)

Zs1Ys2 + (1 + Ys2∆)(3.53)

with

{∆} := {z ∈ C | Re(z) ≥ 0}

⇔ {∆} :={z ∈ C | z = 1 + Γ∆

1− Γ∆, |Γ∆| ≤ 1

}(3.54)

results in a frequency dependent uncertainty set5

{∆′} := {z ∈ C | |z − C{∆′}| ≤ |R{∆′}|} (3.55)5Observe that rewriting (3.53) as a function of Γ∆ using the equivalence relation shown

in (3.54) results in a linear fractional exp