Control of Human Posture during Quiet Standing Motor Command of Proportional and Derivative (PD) Controller can Match Physiological Ankle Torque Modulation.

Control of Human Posture during Quiet Standing

Motor Command of Proportional and Derivative (PD) Controller can Match Physiological Ankle

Torque Modulation during Quiet Stance

Albert H. Vette1,2, Kei Masani1,2, John F. Tan1,2, Kimitaka Nakazawa3,

and Milos R. Popovic1,2

June 19, 2007

1 IBBME, University of Toronto2 Lyndhurst Centre, Toronto Rehab

3 National Rehabilitation Center for Persons with Disabilities, Tokorozawa, Japan

1. Motivation

Complex system

Much simpler than other related systems

To extract key control features of the system

Use the knowledge for rehabilitation purposes

Why do we study the “Control of Human Posture during Quiet Standing”?

What do we actually know about the control of posture during quiet standing?

Passive Torque Components:

- result from intrinsic mechanical properties of the joints and muscles (stiffness and viscosity)

(Loram, 2002; Casadio, 2005; Winter, 1998)

Active Torque Components:

- provided by muscle activity

- regulated by higher or lower centers of the central nervous system (?)

(Fitzpatrick, 1996; Morrasso, 1998; Peterka, 2000; Loram, 2002)

2. Background

2. Background

Focus on anterior-posterior body sway

- quiet standing can be approximated by an inverted pendulum model (Gage, 2004)

- body is stabilized via ankle torque modulation

In this study:

COM

Focus on active torque components only

- for now, passive components are ignored

KP Channel

KD C

han

nel

MPD

COMPhase Advance

( ) ( ) ( )PD P D

dM t K t K t

dt

Feedback time delay (τF = ~40 ms)

Motor command time delay (τM = ~40 ms)

Torque generation delay (τE > 100 ms)

2. Background

= delay of more than 180 ms

Phase lead compensates delay

Input: Angular body position (P) and velocity (D)

Controlled variable: Body angle

Controlling variable: Ankle torque

PD Control Strategy:

Sensory-Motor Time Delay:M

usc

le

CNS

Sensor

Torque

> 80 ms

τF

τM

τE

> 180 ms

3. Hypothesis

“Modulation of PD Controlled Ankle Torque can Match Physiological Ankle Torque Modulation

during Quiet Stance”

4. Methods

PD Controlled Feedback Model

Optimized parameters: 1) PD gains, i.e., Kp [Nm/rad] and Kd [Nm s/rad];

2) Twitch contraction time T [ms].

Sensor

TorqueτE

Mus

cle

τM

CNS

τF

Torque

Modeled as 2nd order,

critically damped system (low pass)

Characteristics of muscle (Milner-Brown, 1973; Tani, 1996):

4. Methods

Experimental Body Angle

τM

τF

Kp

Kd

+ PD Controlled Ankle Torque2 2

1

T s +2Ts+1

CNS Experimental Ankle Torque

Feedbacktime delay

Motortime delay

Torque generation delay

τE

Muscle

τF

CNS

Feedbacktime delay

PD Controlled Ankle Torque2 2

1

T s +2Ts+1Torque generation

delay

τE

τM

Kp

Kd

+

Motortime delay

Muscle

Time

Actual body angle

4. Methods

Body angle at CNS

Actual ankle torque

PD command at muscle

PD controlled ankle torque

Sensor

TorqueτEM

uscl

e

τM

CNS

τF

Torque

Experimental Body Angle

Experimental Ankle Torque

Quiet Standing Experiments (10 healthy subjects):

Measurements:

- Ground reaction forces (Kistler force plate)

- Body angle (Keyence laser sensor)

Tasks:

- Quiet standing with eyes open (two trials of 60 s each)

- Quiet standing with eyes closed (two trials of 60 s each)

4. Methods

Optimization:

Optimization Technique

- DIRECT algorithm (Perttunen, 1993)

Optimization Procedure

- First 30 seconds of experimental body angle and ankle torque data

- Initial parameters: Kp = 350 Nm/rad,

Kd = 750 Nm s/rad (Masani, 2006)

T = 116 ms (Bellemare, 1983)

Validation Procedure

- Last 30 seconds of experimental body angle and ankle torque data

- Optimized values for Kp, Kd, and T

- Identification of error torque and matching percentage

4. Methods

5. Results

0 10 20 3050

60

70

Time [s]Time [s]Time [s]

0 10 20 3040

50

60

Tot

al A

nkle

Tor

que

[Nm

]

Time [s]

Subj

ect

B [Kp,Kd,T] = [760,250,84]

0 10 20 3035

40

45

Time [s]

Subj

ect

ASu

bjec

t C

[Kp,Kd,T] = [746,250,73]

[Kp,Kd,T] = [713,284,97]

0 10 20 3050

60

70

80[Kp,Kd,T] = [761,250,66]

0 10 20 3030

50

70

Eyes Open Eyes Closed

[Kp,Kd,T] = [871,250,63]

0 10 20 3035

40

45

50

Time [s]

[Kp,Kd,T] = [717,253,79]

Black: Experimental ankle torque; Red: PD controlled ankle torque (validation data)

5. Results

2

1

2

1

( )% 100 (1 )

N

N

y YVAF

y

EO EC600

700

800

900K

p [N

m/r

ad]

EO EC200

300

400

500

Kd

[Nm

s/ra

d]

EO EC0

100

200

300

T [m

s]

EO EC0

1

2E

rror

Tor

que

[Nm

]

EO EC94

96

98

100

Mat

chin

g

P

erce

ntag

e [%

]

Optimized Parameters

PD Matching Capability

6. Conclusions

PD controller can match ankle torque modulation during quiet stance

- even true for large sensory-motor time delay of more than 180 ms

Optimized PD gains agree with our previous findings (Masani, 2006)

Optimized twitch contraction time is physiologically reasonable

Present Findings:

PD controller can at least mimic the sensory-motor control task during quiet

standing (Masani, 2006; Vette, 2007)

Control strategy may be used as part of a closed-loop FES system

- rehabilitation (Thrasher, 2006)

- assistive technology (Kim, 2006)

With Previous Findings:

Standing approximated as inverted pendulum with active torque components only Limited to anterior-posterior stability

Implementation in a 3D model with 12 degrees of freedom and passive torque components

(Kim, 2006)

Feed-forward control (internal model) contributes to human balance as well

Implementation of PD controller in Smith’s predictor (Morasso, 1999)

7. Limitations and Future Work

Limitations:

Integration and re-weighting of sensory information omitted

Body kinematics provided by weighted sensory input (Peterka, 2002)

7. Limitations and Future Work

Next Step: Implementation of passive torque components as well

To be optimized: Kp, Kd, T, and passive stiffness K [Nm/rad] Range of K: 60 – 90 % of load stiffness (m*g*COM height) (Casadio, 2003) Passive viscosity B set to 5 Nm s/rad (Loram, 2002)

Experimental Body Angle

τM

τF

Kp

Kd

+ PD Controlled Ankle Torque2 2

1

T s +2Ts+1

CNS Experimental Ankle Torque

Feedbacktime delay

Motortime delay

Torque generation delay

τE

Muscle

K

B

+

+

Passivetorque

7. Limitations and Future Work

Initial Results are Promising!

Improvement of Torque Matching!

Optimized parameters: Kp = ~ 150-250 Nm/rad K = ~ 70-80% of load stiffness

Kd = ~ 100-200 Nm s/rad T = ~ 100 – 150 ms

Kp and Kd naturally decrease – but neural controller still necessary!

0 10 20 3050

60

70

0 10 20 3040

50

60

Su

bje

ct B

Su

bje

ct A

Tot

al A

nkle

Tor

que

[Nm

]

0 10 20 3035

40

45

Time [s]

Su

bje

ct C

eyes open

Acknowledgments

National Rehabilitation Center for Persons for Disabilities, Tokorozawa, Japan

Dr. Milos Popovic and Dr. Kimitaka Nakazawa Masaki O. Abe, Dimitry Sayenko, and Alan Morris

Funding Agencies:

Thank You!

Japan Society for the Promotion of Science

German Academic Exchange Service

Any Questions?

Control of Human Posture during Quiet Standing

Winter (1998): passive torque component are sufficient to stabilize the body during quiet standing.

Morasso (2002): intrinsic ankle stiffness is too low to oppose the toppling effect of gravity.

Loram (2002): passive torque components can only provide up to 91% of the necessary stiffness needed for minimal stabilization.

➔ additional active torque components are required –

but how are they generated?

2. Background

How do we actually control our body posture during quiet standing?

Feedback versus Feed-Forward Control

Pro “feed-forward” control (via internal model):

the neurological time delay seems to be too long for stable feedback control;

the fluctuation of the motor command to the plantar flexors precedes the body sway fluctuation (e.g., Masani, 2003).

Pro “feedback” control:

no conclusive physiological evidence for feed-forward control; importance of sensory information during quiet standing has been frequently reported (e.g., Fitzpatrick, 1994a/b).

Do not contradict feedback control

2. Background