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Page 1: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

2

Page 2: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

3

Shengli XieMinyue FuDerong Liu

Page 3: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Moncrief-O’Donnell Chair, UTA Research Institute (UTARI)The University of Texas at Arlington, USA

and

F.L. Lewis, NAI

Talk available online at http://www.UTA.edu/UTARI/acs

Assistive Human-Robot Interaction (HRI)and Dan Popa, University of Louisville

and Isura Ranatunga, Reza Modares, Bakur AlQaudi

Guest Foreign Professor, Guangdong University of Technology,Guangzhou China

Supported by :NSF NRI Initiative ONR

Supported by :China NNSFChina Project 111

Page 4: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

3. Devices: “distributed skin sensors”Integration of multi-modal, multi-resolution,MEMS skin sensors to include tactile,thermal, pressure, acceleration, and distanceIR sensing.- Sensor design tuned for pHRI- Fabrication on flexible substrates- Robust packaging in Frubber® & laminates- Efficient wire interconnect schemes

Microsensor packaging and interconnects Concept: Microactuator

array using piezo actuator

Sensors and skin onto PR2 and youBot robots at UTARI

Electro Hydro Dynamicalsensor printing

(maskless lithography)

Multi-Modal Skin and Garments for Healthcare and Home Robots

University of Texas at ArlingtonNRI Grant No. 1208623

Program Manager: Dr. Paul Werbos, ECCS, ENG, NSF

Dan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3

1Department of Electrical Engineering, University of Texas at Arlington, 2University of North Texas Health Science Center, 3UT Arlington Research InstitutePartner Companies: Advanced Arm Dynamics, Hanson Robotics, Inc., National Instruments

1. System Design: “where to place sensors on robot?”Novel algorithms and methods for optimal placement anddata management of such devices on several co-Robots.

- Statistical adaptive sampling for sensor selection- Sensor fusion based on noise and sensor scaling

models- Optimization algorithms for maximizing robot perception- New sensor simulation models and robot control

algorithms

4. Co-Robot performance: “how does thistechnology help humans?”The impact of the new technology to humans willbe assessed, including the safety, level ofassistance to several targeted user groups, easeof use, aesthetics, and therapeutic benefits.- Clinical Testing at UNTHSC and UTARI- Collaborative work with Advanced Arm Dynamics

Robot, Tactile sensor array andthe environment in Gazebo

Robot

Human

Sensor

Diagram of SkinSim, multi-modal skin simulation environment

Assistance for UpperLimb Amputees PR2 Teach-by-demonstration

Human Interaction Data Collection

PR2 Human

Character

SensorPlacementInfraredAccel.Temp.Tactile

World

ModelPlugins

SDF

SensorPlugins

WorldPlugin

OverlayThermalTempprofile

OutputInfraredAccel.Temp.Tactile

GAZEBO

Sketch-up

CollectMeshes

User ApplicationC++/Python

Pressure sensitiveadhesive tape(50µm thick)Bottom Kaptonlayer with electric traces and pads

Top Kapton layer with electric traces and pads

Array of temperature sensors Parylene (polymer substrate) at UTARI

( )v t

Model Reference Neuroadaptive Controller

Neuroadaptive Impedance Control

2. Control and Learning: “both human and robot learn during interaction”Learning algorithms and adaptive impedancecontrol for efficient use of multimodal sensors tosense human intent and improve the usability ofco-Robots.- Online reinforcement learning for pHRI with co-

Robots wearing skin and garments, given human-centric rewards and cost functions- Neuroadaptive Impedance Control with stabilityand performance guarantees

The robustifying signalis,

( ) ( )( ) ( , )( ) ( ) ( )m m mf x M q q e V q q q e F q G q ˆ ˆ( )T T

v rW V x K r v

ˆ( ) ( )z F Bv t K Z Z r ‖ ‖

Where,

Iterate Designs & Algorithms

PerceivedImpedance

Robot and Skin

Simulation

Fabrication & Integration of Skin/Garment

Hardware

Interaction LearningInitial sensor

prototypes& Robotichardware

Task requirements

Measurement&

Simulation

pHRI

Page 5: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Fully Automated Robot vs. Assistive Robot

Page 6: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

PR2 meets Isura

Page 7: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Standard Robot Trajectory Tracking Controller

Where is the human?

Page 8: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Robot dynamics

Prescribed Error system

Control torque depends onImpedance model parameters

Impedance Control

Page 9: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Human task learning has 2 components:1. Human learns a robot dynamics model to compensate for robot nonlinearities2. Human learns a task model to properly perform a task 

Inner Robot Specific Control LoopINDEPENDENT OF TASK

Outer Task Specific Control LoopINDEPENDENT OF ROBOT DETAILS

Human Performance Factors Studies

Page 10: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Two-loop HRI Design- Robot Control versus Task Control1. Inner Robot-Specific Control Loop2. Outer Task-Specific Control Loop

2A. Adaptive Inverse Filter Task Design2B. Model Reference Adaptive Control Task Design2C. Reinforcement Learning Task Control for Minimum Human Effort

3. Experiments

Page 11: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Robot control inner loop

Task control outer loop

Page 12: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

1.  Inner‐Loop Robot Specific Controller

Model‐reference Neuro‐adaptive Control

There is NO prescribed trajectory in the robot control loop design

Make the robot behave like the prescribed model

Page 13: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

F.L. Lewis, D.M. Dawson, and C.T. Abdallah, RobotManipulator Control: Theory and Practice, 2nd edition,Revised and Expanded, CRC Press, Boca Raton, 2006.

F.L. Lewis, S. Jagannathan, and A. Yesildirek, Neural NetworkControl of Robot Manipulators and Nonlinear Systems,Taylor and Francis, London, 1999.

A Novel Control Objective Using Neuro‐adaptive Control Techniques

Page 14: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

( ) ( , ) ( ) ( ) =d c hM q x V q q x F q G q f f f

=m m m m m m hM x D x K x f

= me x x

=r e e

( ) = ( , ) ( ) d c hM q r V q q r f f f f

( ) = ( )( ) ( , )( ) ( ) ( )m mf M q x e V q q x e F q G q

=TT T T T T T T

m m me e x x x q q

Robot dynamics

Prescribed robot impedance model

Model‐following error

Sliding mode error

Error dynamics

Unknown robot nonlinear function

There is NO task trajectory here

Model‐following error formulation

= ( )TcJ q f

Control torque

Page 15: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

ˆ= ( ) ( )c v hf f K r v t f

( ) = ( , ) ( ) ( )v dM q r V q q r K r f f v t

( ) ( , ) ( ) ( ) =d c hM q x V q q x F q G q f f f

( ) = ( , ) ( ) d c hM q r V q q r f f f f

ˆ ˆ ˆ( ) = ( )T Tf W V

( ) = ( )T Tf W V

Dynamics 

Controller‐ approximation based 

Robot 

Error 

Unknown nonlinearities parameterized in terms of a function approximator

Estimated parameters

Estimate for unknown nonlinearities

Closed‐loop error dynamics

W, V unknown parameters

Model‐following error driven by parameter estimation error

ˆ ˆ,W V

ˆ ˆ ˆ( ) ( ) ( ) = ( ) ( )T T T Tf f f W V W V

Page 16: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

ˆ ˆ= ( ) ( )T Tc v hf W V K r v t f

ˆ ˆ ˆ ˆ ˆ= ( ) ( )T T T T TW F V r F V V r F r W

ˆ ˆ ˆ ˆ= ( ( ) )T T TV G V Wr G r V

ˆ( ) = ( )z F Bv t K Z Z r

=TT T T T T T T

m m me e x x x q q

Adaptive control structure

Standard Adaptive Parameter tuning algorithms

Robust control term

No task reference trajectory is used hereThe robot controller makes the model following error                        smallThe parameters of the admittance model                                               are not needed

= me x x=m m m m m m hM x D x K x f

= me x x

=r e e

Model‐followingerror

Page 17: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

No task trajectory information is used in this inner‐loop robot controllerThe inner‐loop robot controller makes the model‐following error smallThe admittance model parameters are not neededOnly the admittance model trajectories                             are needed., ,m m mx x x

Page 18: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

2. Outer Task-Specific Control Loop 2A. Adaptive Inverse Filter Task Design2B. Model Reference Adaptive Control Task Design2C. Reinforcement Learning Task Control for Minimum Human Effort

Page 19: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Robot control inner loop

Task control outer loop

Page 20: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Three Outer Loop DesignsTo appear 2016                

Page 21: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

2A.  Outer‐loop Task Specific Design #1

( ) ( ) ( )D s M s H sWant to find M(s) so that

with H(s) and D(s) unknown

Adaptive Inverse Control and Wiener Filter

B. Widrow Adaptive inverse filter

For trajectory following task‐ e.g. point‐to‐point motion control

Work of Isura Ranatunga

Signal to robot controller

Page 22: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

( ) ( ) ( )D s M s H sWant to find M(s) so that

with H(s) and D(s) unknown

( ) ( )( ) = =( ) ( )

f xh d

f fh h

s D sM ss H s

Wiener Filter Solution in terms of power spectral densities

Page 23: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

1 1

2 2

3 3

0 1 0 00 0 1 00 0 0 1

hd fdt

1 1

2 2

3 3

0 1 0 00 0 1 00 0 0 1

md xdt

1/s

1/s

1/s

1/s

1/s

1/s

1b

2b

3b

1a

2a

3a

( )hf t ( )mx tFind Wiener Filter online using adaptive learning

Page 24: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

( ) = ( ) ( )dx t H t t

ˆ( ) = ( ) ( )mx t H t t

Ideal Filter

Wiener filter solution

Known regression vector Unknown coefficients

d mx x

Kalman Filter = CT RLS

Page 25: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

1 1 11 1 1= ( ) { } { } ( ) ( ) ( )2 2 2

T T T TL r M q r tr W F W tr V G V t P t t

Combined stability analysis of Inner robot control loop and Outer task following loop

Lyapunov function

Robot model‐following error

NN weight estimation errors

Outer‐loop inverse adaptive filter error

Page 26: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Shi nian shu muBai nian shu ren

十年树木,百年树人

Keshi-Wu nian shu xuesheng可是,五年树学生

Page 27: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

2B.  Outer‐loop Task Specific Design #2

Model Reference Adaptive Control

K. Astrom

BUT ‐In standard MRAC, the controller appears before the unknown plantHere, the unknown plant (e.g. human) is BEFORE the controller

Work of Bakur AlQaudi

Page 28: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

BUT ‐In standard MRAC, the controller appears before the unknown plantHere, the unknown plant (e.g. human) is BEFORE the controller

So we need to add a human dynamics identifier

Page 29: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

( )hc

b yH ss a u

( ) m mm

m c

b yH ss a u

( ) pnp

n

ybH ss a u

Nominal Robot impedance model

To generate prescribed model trajectory   , ,m m mx x x

Unknown Human model

Task reference model – first‐order crossover model – ideal human + robot system

Basic muscle response model

Human factors studies show that AFTER Learning, the human plus robot system obeysA simple first‐order roll‐off high bandwidth dynamics

Page 30: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

ˆy y y

ˆˆb b b

a a a

Human response estimation error

Parameter estimation error

Page 31: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

ˆy y y Human response estimation error

Page 32: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,
Page 33: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Combined stability proof of overall 2‐loop robot‐task system

1 11 1 1( ) { } { }2 2 2

T T Tr M q r tr W F W tr V G V

Adaptive tuning parameter errors

Inner model tracking errorNN parameter estimation errors

Page 34: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Basic muscle response

PD controller like that provided by cerebellum

Page 35: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

2C.  Outer‐loop Task Specific Design #3

Reinforcement Learning for minimum human effort

Feedforward assistive control term

‐ 2 1( )Ms Bs K -+ +hK

(.)l

+

-

dx

mxh

fd

e ++

1( )p d

K s K s -+

PrescribedImpedanceModelHuman

Find robot impedance model parametersTo minimize human force effortAnd task trajectory following error

, ,M B Khf

de

Human force amplifier

Work of Reza Modares

Force exerted by human indicates his discontent‐A measure of Human Intent

Page 36: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

( )d p h e d

K s K f k e+ =

nd d m

e x x= - Î Tracking error

2[ ]T T T nd d d d

e e e x x= = - Î

2[ ]T T T nm m

x x x= Î

2[ ]T T T nd d d

x x x= Î

Page 37: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Minimize human effort and tracking error

( )T T Td d d h h h e e

t

J e Q e f Q f u R u dt¥

= + +ò

Performance index

1 2e d hu K e K f= +

Then control is

( )T Te e

t

J X Q X u R u dt¥

= +ò

How to get human force into PI ?

Page 38: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Feedback linearization loop

Robot Impedance Model Unknown Human Model

Overall Augmented Dynamics

1,0h d p h e d d h h h d

f K K f k K e A f E e-= - + º +

( )d p e d

K s K f k e+ =

d h p h e dK f K f k e+ =

Page 39: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

We want online method to learn the optimal control without knowing the System Matrix A

Optimal Design Always Admits Reinforcement Learning for Real‐time Optimal Adaptive Control

Optimal control is an offline methodBased on solving AREKnowing all the plant dynamics

Page 40: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Take enough data along the system trajectoryTo solve this equation using least‐squares

OFF‐POLICYReinforcement LearningNeeds NO knowledge of the system dynamics

Page 41: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Off‐policy IRL Bellman equation

( ) ( ) [2 ( ) ] ( ) ( ) ( ) ( )t t t t

T T T T Te e

t t

X t PX t X t PBe d X t Q X t u R u d X t t P X t tt t t+D +D

é ù+ = + + +D +Dê úë ûò ò

Off‐policy term

Finds optimal control gains without using ANY system dynamics

Off‐Policy Reinforcement LearningNeeds NO knowledge of the system dynamics

Page 42: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

3. Experimental Results on PR2

Page 43: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

3. Experimental Results Work of Isura RanatungaSven Cremer

Page 44: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,
Page 45: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,
Page 46: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Point‐to‐point tracking error Human force effort

Page 47: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Future Work

Page 48: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

Thanks !!

Page 49: Shengli Minyue Derong Liu - UTA talks 2017/robot HRI.pdfDan O. Popa1, Frank L. Lewis1, Nicoleta Bugnariu2, Woo Ho Lee1 and Muthu Wijesundara3 1 Department of Electrical Engineering,

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