biomechatronics - lecture 2. human motion control

BioBio--mechamecha--tronicstronicsCourse 2008 (Course 2008 (wbwb 2432)2432)

Lecture 2Lecture 2

Human Motion ControlHuman Motion Control

Erwin de VlugtErwin de Vlugt

Research atResearch at

NeuroNeuro--Muscular Control Lab (NMC)Muscular Control Lab (NMC)

www.3me.tudelft.nl/nmcwww.3me.tudelft.nl/nmc

NMC: The PeopleNMC: The People

ErwinAssistant

DavidPostdoc

WinfredPhD student

JasperPhD student

FransProfessor

BobNeurologist

Dirk-JanAssociate

AlfredAssistant

Per year:5 – 10 Masters8 – 12 Bachelors

HermanAssociate

RienderAssistant

ContentsContents

•• Intro: Feedback control (Propriocepsis)Intro: Feedback control (Propriocepsis)

•• Postural & motion controlPostural & motion control

•• Stability and admittanceStability and admittance

•• Feedback model:Feedback model:

–– intrinsic muscle propertiesintrinsic muscle properties

–– force feedbackforce feedback

–– velocity feedbackvelocity feedback

–– length feedbacklength feedback

Human motor systemHuman motor system

•• Human motor systemHuman motor system

–– feedforward controlfeedforward control

–– feedback controlfeedback control

•• Focus on the spinal reflexesFocus on the spinal reflexes

–– Corrective motor actionCorrective motor action

–– Energy efficientEnergy efficient

–– Fast (spinal pathways)Fast (spinal pathways)

–– AdaptiveAdaptive

MotoricMotoric diseasesdiseases

•• NMC LabNMC Lab–– fundamental research: how does the system work?fundamental research: how does the system work?

–– clinical application: what causes the clinical application: what causes the motoricmotoric disfunctiondisfunction??

•• Motor disorders:Motor disorders:–– loss of motion dexterityloss of motion dexterity

–– difficult to start a movementdifficult to start a movement

–– spastic (uncontrolled) motionsspastic (uncontrolled) motions

•• MotoricMotoric diseases (e.g. stroke,diseases (e.g. stroke,Parkinson, Multiple Sclerosis)Parkinson, Multiple Sclerosis)affects:affects:–– neural controlneural control

–– the musclesthe muscles

The man who lost his bodyThe man who lost his body

•• BBC documentaryBBC documentary

Research in NLResearch in NL

TU TwenteBiomechatronicsLUMC

Neuro/Rehab

Het RoessinghMaartenskliniek

Rehab

TU DelftBiomechatronics

VUMovement

Research in the USResearch in the US

ClevelandFES / Shoulder

ChicagoRehab

WashingtonRehab

CalgaryMuscles/Tissue

Postural control:Postural control:

Resisting external perturbationsResisting external perturbations

Externalforces

Drill

Postural control:Postural control:

Resisting Resisting ‘‘internalinternal’’ perturbationsperturbations

‘Internal’forces

cup

Postural control:Postural control:

Standing/walkingStanding/walking

Gravityforces

Motion ControlMotion Control

•• GoalGoal--directed motionsdirected motions

•• Cyclic motionsCyclic motions

•• Postural motionsPostural motions

Postural Motions or Posture ControlPostural Motions or Posture Control

Posture controlPosture control

Controller ActuatorMechanical

System

Sensor

Setpointθθθθref

PerturbationMex Position

θθθθ

Stability & admittanceStability & admittance

Stability: The arm will return to its position (trajectory)after a force perturbation

Admittance (reciprocal of impedance): The dynamic behaviour of the arm depends on:• stiffness• viscosity• inertia• neural feedback

adjustable by muscle activation

adjustable by configuration

adjustable by neural modulation

Posture control and admittancePosture control and admittance

Hc Ha Hm

Hs

Setpointθθθθref

PerturbationMex Position

θθθθ

Feedback Control:

Admittance:

smac

mac

reffb

HHHH

HHHH

..1

.

.

.

+==

θθ

smac

m

exadm

HHHH

H

MH

..1 .+== θ

AdmittanceAdmittance

•• Humans are well capable in adjusting their endpoint Humans are well capable in adjusting their endpoint

admittance to deal with different environments admittance to deal with different environments

(hard/soft surfaces, unexpected forces)(hard/soft surfaces, unexpected forces)

Feedforward & Feedback controlFeedforward & Feedback control

Hc Ha Hm

Hs

Setpointθθθθref

PerturbationMex Position

θθθθ

Feedback Control:Feedback Control:

Feedforward Control:Feedforward Control:

smac

mac

reffb

HHHH

HHHH

..1

.

.

.

+==

θθ

smac

mai

refff

HHHH

HHHH

..1

.

.

.

+==

θθ

Hi

Inverse dynamics

Feedforward controlFeedforward control

•• HHii = (H= (Haa.H.Hmm))--1 1 ⇒ ⇒ θθ ≈≈ θθrefref ifif

HHcc= 0= 0 ⇒⇒ HHcc. . HHaa.H.Hmm.H.Hss = 0 (no feedback)= 0 (no feedback)

•• No feedback implies that unexpected perturbations are not No feedback implies that unexpected perturbations are not

compensated !compensated !

•• Motion control is mix of feedback and feedforward control:Motion control is mix of feedback and feedforward control:

–– Fast motions: Feedforward control (all feedback gains will tend Fast motions: Feedforward control (all feedback gains will tend to to

zero)zero)

–– Slow motions: Also feedback controlSlow motions: Also feedback control

–– Posture: Only feedback controlPosture: Only feedback control

smac

mai

refff

HHHH

HHHH

..1

.

.

.

+==

θθ

Control StrategiesControl Strategies

•• (Co(Co--)activation of muscles)activation of muscles

–– Produces motionProduces motion

–– Increase muscle stiffness & viscosityIncrease muscle stiffness & viscosity

•• Effective for large range of frequenciesEffective for large range of frequencies

•• Costs much energyCosts much energy

•• Proprioceptive feedbackProprioceptive feedback

–– Length, velocity and force feedback for Length, velocity and force feedback for ‘‘automaticautomatic’’ controlcontrol

•• Energy efficientEnergy efficient

•• Only effective for low frequent perturbations due to timeOnly effective for low frequent perturbations due to time--delays in delays in

nervous systemnervous system

ModelsModels

Skeletalinertia ∫∫∫∫ ∫∫∫∫

M θθθθr

muscledynamics

Fαααα

Mex

Admittance ,depends on:•Inertia, passive visco-elasticity•intrinsic muscle properties:

length & velocity dependency muscle

)ωωθω(M

)( )(H

exadm =

Muscle length

Muscle velocity-r

-r

Passivevisco-elasticity

ModelsModels

•• The neuromuscular system is highly nonlinearThe neuromuscular system is highly nonlinear

–– the Delft Shoulder and Elbow Model (DSEM) is a large scale the Delft Shoulder and Elbow Model (DSEM) is a large scale

nonlinear model based on cadaver studies (Van der Helm)nonlinear model based on cadaver studies (Van der Helm)

–– contributions of different muscles to certain movements can be contributions of different muscles to certain movements can be

studiedstudied

–– e.g. application for tendon transpositions for pree.g. application for tendon transpositions for pre--operative operative

prediction of the (improved) range of motionprediction of the (improved) range of motion

•• For small amplitude movements, a linear model is a For small amplitude movements, a linear model is a

good description of the mechanical behavior at endpoint.good description of the mechanical behavior at endpoint.

–– recent posture control studies of the NMC Labrecent posture control studies of the NMC Lab

Linear modelLinear model

1/Jr ∫∫∫∫ ∫∫∫∫F θθθθ

-r

-r

u0 Mex

Hact+

Km(u0)

Bm (u0)

+

++

K fττττ

αααα

-r

-r+

+

ττττ

ττττ

kv

kp

Muscle spindle:Muscle spindle:Length and velocity feedbackLength and velocity feedback

MuscleSpindle

muscle lengthmuscle velocityγγγγs-motor neuronγγγγd-motor neuron

Ia afferent nerveII afferent nerve

Matthews P.B.C. (1964) Muscle spindles and their motion control. Physiological Reviews, Vol. 44, p. 219 – 288

Muscle force feedback:Muscle force feedback:Golgi Tendon OrganGolgi Tendon Organ

GolgiMuscleforce

Ib afferent

Kandel E.R., Schwartz J.H. and Jessel T.M. (2000), Principles of Neuroscience, 4th Edition, McGraw-Hill, New York, USA

HillHill--type muscle modelstype muscle models

CC: Contractile component(force-length-velocity characteristic of muscle fib er)

SEC: Series-Elastic component(force-length characteristic of tendon & cross-brid ges

PEC: Parallel-Elastic component(passive force-length characteristics of muscle)

Feedback loopsFeedback loops

•• Intrinsic feedbackIntrinsic feedback

–– Muscle viscoMuscle visco--elasticity: Muscle force depends on muscle length elasticity: Muscle force depends on muscle length

and contraction velocityand contraction velocity

•• Reflexive feedbackReflexive feedback

–– Length and velocity feedback through muscle spindlesLength and velocity feedback through muscle spindles

•• Increase muscle stiffness and viscosityIncrease muscle stiffness and viscosity

–– Force feedback by Force feedback by GTOsGTOs

•• Decreases intrinsic feedback !!Decreases intrinsic feedback !!

•• Changes the bandwidth of the activation dynamics (force controllChanges the bandwidth of the activation dynamics (force controller)er)

Musculoskeletal modelsMusculoskeletal models

with length & velocity feedbackwith length & velocity feedback

Skeletalinertia

rmuscle

dynamics ∫∫∫∫ ∫∫∫∫F M θθθθ

Muscle length

Muscle velocity-r

-r

αααα

Mexu

-r

-r+

+

Muscle

Spindle

γγγγs

γγγγd

ττττ

ττττ

Ia

II

Musculoskeletal modelsMusculoskeletal models

with length, velocity & force feedbackwith length, velocity & force feedback

Skeletalinertia

rmuscle

dynamics ∫∫∫∫ ∫∫∫∫F M θθθθαααα

-r

-r+

+

Mexu

Muscle

Spindle

γγγγs

γγγγd

ττττ

ττττIa

II

Muscle length

Muscle velocity-r

-r

GolgiττττfIb

αα -- motor neuron activity & forcemotor neuron activity & force

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

time (sec)

norm

aliz

ed s

igna

ls

αααα (no FF) force (no FF)

FHact

αααα (FF) force (FF)

K fττττ

ααααu

Loop gain = 1.6

Loop gain = 0.8

Loop gain = 0.4

Effect of force feedbackEffect of force feedback

0 2 4 6 8 10 12 14 16 18 20-3

-2

-1

0

1

2

3

time (sec) / frequency (Hz)

norm

aliz

ed fo

rce

Force feedback:

No force feedback

Neural input

10-1 100 101 102

-200

-100

0

100

frequency (Hz)

phas

e (d

eg.)

10-1 100 101 102

10-2

10-1

100

101

frequency (Hz)

ampl

itude

Hact + force feedback

Kf = 0

Kf = 1.6

Kf = 0

Kf = 1.6

Activation dynamics with force feedbackActivation dynamics with force feedback

FuHact

K fττττIb

αααα

H*act(ωωωω) H**

act(ωωωω)

FHact

+

K fττττIb

ααααFbk

10-1 100 101 10210-1

100

101

frequency (Hz)

ampl

itude

Hact + force feedback

10-1 100 101 102

-50

0

50

100

frequency (Hz)

phas

e (d

eg.)

Kf = 0

Kf = 1.6

Kf = 0

Kf = 1.6

CombinedCombined

Intrinsic and reflexive feedbackIntrinsic and reflexive feedback

•• feedback gains feedback gains kkpp and and kkvv represent represent γγss and and γγdd efferent efferent stimulationstimulation

•• no interaction between length and velocity signalsno interaction between length and velocity signals

•• bibi--directional length and velocity feedbackdirectional length and velocity feedback

•• only shortonly short--latency monosynaptic reflexeslatency monosynaptic reflexes

•• (no cross(no cross--reflexes between muscles)reflexes between muscles)

Overall impedance:

)).().(().).().(().(

1

)..).(.).(()...).(.).(().(

1

)(

)(

*int

***int

**2

2*2**2*2**2

reflexiveactrinsicactreflexiveactrinsicact

jpactmact

jvactmactex

KHKHjBHBHjJ

erkHrKHjerkHrBHjJM

ωωωωωω

ωωωωωωωωθ

ωτωτ

++++=

++++= −−

Stability of closedStability of closed--loop systemloop system

•• Analyze the openAnalyze the open--loop transfer function:loop transfer function:

–– Phase marginPhase margin

–– Amplitude marginAmplitude margin

2

2*2**2*2**

2

2*2**2*2**2

).(

)..).(.).(()...).(.).((1

).(

1

)..).(.).(()...).(.).(().(

1

)(

)(

ωωωωωω

ω

ωωωωωωωωθ

ωτωτ

ωτωτ

jJ

erkHrKHjerkHrBH

jJ

erkHrKHjerkHrBHjJM

jpactmact

jvactmact

jpactmact

jvactmactex

−−

−−

++++

=

++++=

2

2*2**2*2**

_ ).(

)..).(.).(()...).(.).(()(

ωωωωωω

ωωτωτ

jJ

erkHrKHjerkHrBHH

jpactmact

jvactmact

loopopen

−− +++=

NMClabNMClab DemoDemothe the MatlabMatlab GUI for linear analysisGUI for linear analysis

Motion control of Motion control of orthosisorthosis

1/J ∫∫∫∫ ∫∫∫∫M θθθθ

u0 Mex

Hact+

K intrinsic

B intrinsic

+

++

K fττττ

αααα

+

+

Kreflexive

Breflexive

Korthesis

Motion control of prosthesisMotion control of prosthesis

___1___(Ja +Jp) ∫∫∫∫ ∫∫∫∫

M θθθθ

u0 Mex

Hact+

K intrinsic

B intrinsic

+

++

K fττττ

αααα

+

+

Kreflexive

Breflexive

Kprosthesis

Motion control of FESMotion control of FES

∫∫∫∫ ∫∫∫∫M θθθθ

u0 Mex

Hact+

K intrinsic

B intrinsic

+

++

K fττττ

αααα

+

+

Kreflexive

Breflexive

FEScontroller

1/J

+

-

θθθθref

artificialsensor

Motion control of artificial sensorMotion control of artificial sensor

∫∫∫∫ ∫∫∫∫M θθθθ

u0 Mex

Hact+

K intrinsic

B intrinsic

+

++

K fττττ

αααα

+

+

Kreflexive

Breflexive

encoder

1/J

artificialsensor

stimulator

sensori-motorcortex

naturalsensor/nerve

Intrinsic admittance (shoulder)Intrinsic admittance (shoulder)

0.01 0.0316 0.1 0.3162 1 3.1623 10 31.6228 10010

-4

10-2

100 H intrinsic admittance

frequency (Hz)

ampl

itude

0.01 0.0316 0.1 0.3162 1 3.1623 10 31.6228 100-200

-150

-100

-50

0

frequency (Hz)

phas

e (d

eg.)

Kθθθθ = 10 Nm/radBθθθθ = 0.5 Nms/rad

Kθθθθ = 20 Nm/radBθθθθ = 1 Nms/rad

Kθθθθ = 40 Nm/radBθθθθ = 2 Nms/rad

Kθθθθ = 60 Nm/radBθθθθ = 3 Nms/rad

Kθθθθ = 80 Nm/radBθθθθ = 4 Nms/rad

Effect of length & velocity feedbackEffect of length & velocity feedback

0 1 2 3 4 5 6 7 8 9 10-8

-6

-4

-2

0

2

4

6

8x 10

-3

time (sec) / frequency (Hz)

angl

e (r

ad)

Kp = 300, Kv = 30

Kp = 600, Kv = 60

Kp = 900, Kv = 90

Kθθθθ = 40 Nm/radBθθθθ = 2 Nms/rad

Effect of velocity feedbackEffect of velocity feedback

1 2 3 4 5 6 7 8 9

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

time (sec) / frequency (Hz)

angl

e (r

ad)

Kp = 300, Kv = 30

Kp = 300, Kv = 15

Kp = 300, Kv = 0

⇒⇒⇒⇒ Instability !!

Kθθθθ = 40 Nm/radBθθθθ = 2 Nms/rad

Effect of length feedbackEffect of length feedback

0 1 2 3 4 5 6 7 8 9 10-8

-6

-4

-2

0

2

4

6

8x 10

-3

time (sec) / frequency (Hz)

angl

e (r

ad)

Kp = 300, Kv = 30

Kp = 600, Kv = 30

Kp = 900, Kv = 30

Kθθθθ = 40 Nm/radBθθθθ = 2 Nms/rad

Effect of length feedbackEffect of length feedback

•• Decrease of low frequency admittance (increase of Decrease of low frequency admittance (increase of

‘‘stiffnessstiffness’’))

•• Oscillation frequency becomes higher:Oscillation frequency becomes higher:

•• relative damping becomes lower:relative damping becomes lower:

ωo

KJ

=

β =B

K J2 .

Experimental approachExperimental approach

•• ClosedClosed--loop systemloop system

–– causality problem: cause and effect can not be separated in a causality problem: cause and effect can not be separated in a

straightforward mannerstraightforward manner

•• Solve the problem by using an external (perturbation) Solve the problem by using an external (perturbation)

signal (Course SIPE wb2301)signal (Course SIPE wb2301)

H1

H2

u y u/y = H2 = H1-1

StimulusStimulus--Response ApproachResponse Approach

External force is most natural stimulus !

ExternalForce

Muscle-stimulation

Nerve-stimulation

Brain-stimulation

Input signalsInput signals

•• Use Use manipulablemanipulable or or measurable externalmeasurable external input input

signalsignal

•• Frequency contentFrequency content

•• Duration of trialDuration of trial

•• Number of repetitions per trialNumber of repetitions per trial

•• (Quasi(Quasi--)stochastic: Prevent feedforward responses)stochastic: Prevent feedforward responses

•• Task instructions:Task instructions:

–– ““Do not interveneDo not intervene””: Low impedance: Low impedance

–– ““Minimize position perturbationsMinimize position perturbations””: High impedance: High impedance

Experiments with upper and lower extremitiesExperiments with upper and lower extremities

(1998(1998--now NMC Lab now NMC Lab TUDelftTUDelft and LUMC)and LUMC)

main goal: main goal: quanificationquanification of intrinsic and reflexive propertiesof intrinsic and reflexive properties

Force Perturbations Force Perturbations –– Position TaskPosition Task

task:“maintain position”

handposition

unpredictable externalforce disturbances

Posture Control: 1D Arm MotionsPosture Control: 1D Arm Motions

““ProprioProprio”” RobotRobot

Posture Control: 2D Arm MotionsPosture Control: 2D Arm Motions

““ARMANDAARMANDA”” RobotRobot

minimize my hand

displacement

Patient Studies 1D Wrist MotionPatient Studies 1D Wrist Motion

““PopePope”” RobotRobot

Parameterization of modelsParameterization of models

HumanLimb

Force perturbation +

-

displacement

displacement

minimize the difference

Model

adjust the model parameters until difference is at a minimum

Two ways of parameterization1. analytical using transferfunctions2. simulation

Results from CRPS StudyResults from CRPS Study

CRPS with dystonia:No negative gains!

Optimized vs. recorded feedback gains Optimized vs. recorded feedback gains kkpp and and kkvv

0 5 10-1000

0

1000

2000

Optimized

0 5 10-1000

0

1000

2000

0 5 10-1000

0

1000

2000

Measured

0 5 10-1000

0

1000

2000

Type II perturbations [Hz]

Kp

Kv

Type 1 perturbations [Hz]

Concept of posture control:Concept of posture control:

Optimal admittanceOptimal admittance

Type I perturbation

|Hadm|

|Hadm|

Type II perturbation

Adm

ittan

ce (

X/F

or

θ/M

ext)

Force perturbationsForce perturbations

ApplicationApplicationEMGEMGJoint angleJoint angleExternal forceExternal force

•• closed loop closed loop correllationcorrellation

techniques requiredtechniques required

•• appropriate for linear appropriate for linear

system behaviorsystem behavior

•• e.g. posture taskse.g. posture tasks

•• NMC studies (1998 NMC studies (1998 -- ……))

colored noisecolored noise

•• estimates the state estimates the state just just

beforebefore the stimulusthe stimulus

•• time domain analysistime domain analysis

•• NMC studies (2005 NMC studies (2005 -- ……))

transientstransients

Clonus (Stroke)Clonus (Stroke)

moviemovie

Clonus (Stroke)Clonus (Stroke)

0 2 4 6 8 10 12 14−50

0

50

Tre

act [

Nm

]

0 2 4 6 8 10 12 140

0.5

1

θ [r

ad]

0 2 4 6 8 10 12 14−0.05

0

0.05

TA

[−]

0 2 4 6 8 10 12 14−0.2

0

0.2

GL

[−]

0 2 4 6 8 10 12 14−0.1

0

0.1

SO

L [−

]

0 2 4 6 8 10 12 14−0.2

0

0.2

GM

[−]

Time [s]

Upcoming researchUpcoming research

•• Identification of TimeIdentification of Time--Varying Reflexes during MovementVarying Reflexes during Movement

•• MicroneurographyMicroneurography (Direct nerve measurements)(Direct nerve measurements)

•• EEGEEG--EMG (Correlation brainEMG (Correlation brain--muscles)muscles)

•• EEGEEG--fMRIfMRI--Motion (Brain locations)Motion (Brain locations)

•• Nonlinear models includingNonlinear models includingmotorneuron propertiesmotorneuron properties

ConclusionsConclusions

•• Reflexes have very large effect on the joint dynamicsReflexes have very large effect on the joint dynamics

•• Proprioceptive feedback system is adaptiveProprioceptive feedback system is adaptive

•• Reflex gains are different in patientsReflex gains are different in patients

•• Robotic identification techniques provide detailed insight Robotic identification techniques provide detailed insight in the human motion system:in the human motion system:–– fundamental knowledgefundamental knowledge

–– clinical applicationsclinical applications