Seminar Telematiksysteme zur Fernwartung und Ferndiagnose Using Wave Variables for System Analysis and Robot Control MSc. Lei Ma 27 May, 2004

Seminar Telematiksysteme zur Fernwartung und Ferndiagnose

Using Wave Variables for System Analysis Using Wave Variables for System Analysis and Robot Controland Robot Control

MSc. Lei Ma

27 May, 2004


MSc Lei Ma Informatik VII: Robotik und Telematik

Contents

Introduction to teleoperation

Concept of passivity

Wave variable: idea, definition, characteristics

conclusion



Telerobotics: System construction

A master (local) device, A slave (remote) device, A communication channel.

Communication channel



General description

Human operator as present of high-level control of activities; Both master and salve have own control systems; Human operator requires information:

Proper user interface;Data feedback from the slave site:

• forces applied to the environment,

• relevant positions of the slave,

• graphical video data,

• tactile or acoustic information.



The master

Typical features of the master are:Capability of assigning tasks to the slave and providing the

operator with relevant information about the task development—TELEPRESENCE:

• Implementative solutions: joysticks and/or consoles;

• Different types of signals may be reflected by these devices to the operator.

Capability of acquiring and processing data from both the operator and the slave.



The slave

directly interacts with environment for task execution.A robotic system for the interaction with the environment and the

execution of the task planned by the operator;Signal acquisition and processing;Capability data processing.



The communication channel

represents the link between the master and slave sites. Main drawback. Time delay in the transmission of signals:

physical delay in the transmission line (e.g. in a long satellite communication), limited bandwidth of the hardware.

The time delay, in some case not constant, can originate noticeable instability problems.

A very common choice in practical applications is to transmit velocity to the slave and force to the master.



Application

space underwater hazardous environments production security simulators …



Rotex: ROboter Technology EXperiment

Robotic arm for intra-vehicular activities developed by DLR, Germany. Successfully used in the mission of the space-shuttle COLUMBIA in 1993. Variety of operational modes: teleoperation on board ,teleoperation from ground

using predictive graphics, sensor-based off-line programming. Performing three significant tasks: assembly of a grid, connection/disconnection of

an electrical plug, grasp of a flying object.



Transmission delay over Internet

Discussion of time delay of 0.1~several seconds because: Human operator as slowest

element has reaction time of ~0.1 sec;

Teleoperation not possible with delay more than 10 sec



Problem statment

Slave manipulator follows motion of the master properly. Force applied to the environment fedback to mater properly.



Problem statement: stability

A control system is in equilibrium if, in the absence of any disturbance or input, the output stays in the same state.

A control system is stable if the output eventually comes back to its equilibrium state when the system is subject to an initial condition.

Example: inverted pendulum.



Problem statement: passivity

Loosely said, a system is passive if it absorbs more energy than it produces. “Power” entering the system:

P = xTy A system is said to be Passive if :

P = xTy = dEstore/dt+Pdiss

The power is either stored or dissipated. Or: the system cannot generate energy and provide only as much as stored initially.

Estore: energy storage



Passivity

A system is passive if energy supplied by it is limited to the initial stored :

)0()0()(000

EdPEtEydxPdt

diss

t Tt

Say if a system “absorbs” energy then P is positive, otherwise P is negative.

Or: the system itself can not “produce” any energy.



Properties of passive systems

A passive system is stable;

Connection of passive elements remains passive;

A passive system is said to be lossless if Pdiss=0;

It is dissipative if Pdiss>0.



Passivity of communication channel in teleoperation

)()()()()( tFtxtFtxtP sTsm

Tm

Assume no initial energy stored in the communication channel, the channel is passive if P not lower than zero.



Time delay causes instability

)(

)()(

TtFF

Ttxtx

sm

ms

)()()()( tFTtxTtFtxP sTms

Tm

P is no longer guaranteed to be semi-negative, thus passivity Is also not guaranteed.



Wave variable: idea

Virtual tool for modifying the entire dynamics of the teleoperator system into a simple and well know form;

Shows both basic physical characteristics like inertia and stiffness ; Delay presents as a passive element in the system; As the delay increases the tool becomes softer and / or heavier; A large delay can thus be tuned into either a heavy drill or a soft sponge. Both

provide a heavy versus soft tradeoff appears naturally as a tuning parameter; In real time, if no contact is made, for example during a virtual inspection, the

virtual tool should be tuned to a soft sponge making quick motions easy; In close proximity to a desired contact location, the tool should be adjusted to a

heavy and stiff appearance, allowing good force clarity under slow speed.



Wave variable: definition

U denote the forward (right moving) wave; V denote the backward (left moving) wave.

vvuuFxP TTT

2

1

2

1

b

Fxbv

b

Fxbu

2,

2



Passivity of wave systems

Assume u provides input and v contains output, and there is no energy stored initially, the system is passive if

If v=u(t-T)

uduvdv TtTt

00 2

1

2

1True if v is limited to bound of u

)(2

1

2

1

2

1

2

1000

tEuduuduuduvdv storeTTtTt

Tt

TTtTTt

Energy due to delay T is stored, time delay is a passive element



Wave variables in teleoperation

sTss

Tsm

Tmm

Tm

sTsm

Tm

vvuuvvuu

tFtxtFtxtP

2

1

2

1

2

1

2

1

)()()()()(

)(2

1),(

2

1

)(2

1),(

2

1

sssmmm

sssmmm

xbFb

vxbFb

v

xbFb

uxbFb

u



Passivity in telemanipulation

)()()()()( tFtxtFtxtP sTsm

Tmin

)(2

1)(

2

1s

Tss

Tsm

Tmm

Tm vvuuvvuu

0)(2

1)( m

Tmm

Tm

t

Ttstore vvuutE

Energy stored, communication channel is passive and lossless.



Remarks

Wave variables themselves have no physical meaning. Symmetry – u and v are distinguished due to sign of F. Hybrid encoding:

When in contact, wave command produces force, When in free space, causes motion.

Move or push commands – energy may be converted to either potential or kinetic energy as needed.

Wave impedance e.g. given u, lager b leads to higher weight for velocity dx/dt, so that more

force and lower velocity reconstructed, system appears more damped.

)(2

1),(

2

1xbF

bvxbF

bu



Comparison of power andwave variables



Wave response: Extreme example of a string

v = -u v=u



More wave responses

tb

k

etv

kxFstringpure

21)(

:

tm

b

etv

xmFinertia

21)(

:

xBFdamper :



Conclusion

Wave variable method Applies well to inherently passive system – robots; Shows power gain with non-passive systems, there for possible to design

power reduction element to counteract energy production and force global passivity;

A delay is passive when it occurs in wave variables while not passive when it effects power variables;

In case of teleoperation delay effectively occurs in software level, “wrap” delay with proper encoding to achieve passivity;

Provides new perspective on system and makes further methods possible (filtering, prediction,…).



References and links:

A detailed and intuitive introduction to passivity, wave method and teleoperation: http://telerobotics.stanford.edu/publications/Niemeyer_PhD_Thesis.pdf

Univ. Bologna: http://www-lar.deis.unibo.it The Haptics Community Web Site: http://haptic.mech.northwestern.edu/ Rotex: http://www.robotic.dlr.de/telerobotics/rotex.html



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Seminar Telematiksysteme zur Fernwartung und Ferndiagnose Using Wave Variables for System Analysis and Robot Control MSc. Lei Ma 27 May, 2004