control of human posture during quiet standing motor command of proportional and derivative (pd)...
TRANSCRIPT
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
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