biomechatronics - lecture 2. human motion control
TRANSCRIPT
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