Transcript Part 6 (14.2 Mbytes) - Center for Design Research

MURI
Human Computational Modeling
HighLevel
Control
• Purpose: to understand arm impedance
adaptation and apply it as biomimetic principle.
• Experiment designed to isolate corrective
terms (feedback) from lumped control force
(feedforward + feedback)?
• Modeling of arm impedance based on data from
perturbed responses of reaching movements.
• Parametric modeling of impedance.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
Biological Controller Structure
HighLevel
Control
• Control of arm impedance –
by modulation of m to the muscles.
• Three feedback pathways:
1. Near zero-latency mechanical stiffness/viscosity of the
muscles.
2. Short latency sensory f/b through spinal structures.
3. Long latency sensory f/b through cortex (Direct Model).
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Understanding Biomechanical
Controller
Assumption 1: Feed-forward Inverse
dynamics model sufficient after learning.
Assumption 2: Feed-forward Inverse
dynamics model does not receive state
feedback.
Assumption 3: Short-latency sensory
feedback plays no role in adaptation.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
•Direct dynamics model – feedback control,
correcting unmodeled disturbances
•Estimate states by
 History of descending motor commands and
 Delayed state
Hypothesis: Long-latency feedback system
adapts to external force field, possibly through
adaptation of the direct dynamics model.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
Experiment Design
 Fx   0  13 x 
F   
 
 y  13 0   y 
HighLevel
Control
•
•
•
•
Kicks: a tool to separate feedback response only.
Uniform experiment accomplished by random kicks.
Force field: velocity dependent; curled.
Experiments: NF vs. FF and/or kicks/no kicks.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Experiment Design: equations
• Null Field; No Kicks: adaptation to robot.
M 0  Hˆ (qd )qd  Cˆ (qd , q d )q d
• Null Field; With Kicks: desired trajectory the same as
M p  M 0  Kq  Bq
• Kicks – no Kicks:
M qd ( q, q )  M p  M 0   Kq  Bq
• Force Field; No Kicks: adaptation to robot and environment
~
M 0  Hˆ (qd )qd  Cˆ (qd , q d )q d  E(q d )
• Force Field; With Kicks:
• Kicks – no Kicks:
• Adaptation in FF:
~
~
~
~
M p  M 0  K (q  qd )  B(q  q d )
~
~
~
~
~ 
~, q
~ )  M
M qd ( q

M


K

q

B
q
p
0
~
~, q
~ )
M qd ( q, q )  M qd ( q
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Experiment – Data
Robot joints
• We measure:
handle
{ p1 , p1 }, { p2 , p 2 }, { Fx , Fy }
• Feedback response: can NOT be measured.
• We compute feedback response using:
o Human Arm inertia measurement
(fitting to linear model)
o Prediction of where human arm would have gone if
there were no perturbations
(Principal Component Analysis on early data in
motion)
• Both problems have been solved and presented at
MURI meeting last year.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Experimental Data – 1
• Raw data: with Kicks and in Null Field.
{Fx, Fy}
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Experimental data – 2
- force along planned and actual trajectory -
Control Force
along planned traj.
Assumption: Inverse Model receives
NO state-space feedback;
Estimated trajectory: only due to
Inverse Dynamics Model
Biomimetic Robots - ONR Site Visit - August 9, 2000
Experimental data – 3
MURI
HighLevel
Control
Feedback controller force induced by kicks in different dirs.
• Adaptation in
Direct model
results in motions
towards planned
trajectory
ˆ (qd , qd )
M0  
ˆ (qd , q d )  Kq  Bq
Mp  
M qd ( q, q )  M p  M 0 
  Kq  Bq
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Experimental Data – 4
- after sufficient training in Force Field • Raw data w/Kicks: Null Field vs. Force Field.
• Problem: how to compare
changes in feedback due to
adaptation? At same states?
• Trajectories (NF vs. FF) are
associated with state-space
dependent forces.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Task description
• What makes trajectories
different?
– Kicks
• So, kicks as Parameters
– Kick Direction and
Magnitude will define shape
of path
– Time defines sequence of
states
• Set of parameters for
Trajectories, Velocities,
and Forces
Solution:
1. make parametric
NF Models of
 x   x   y   y 

; 
; 
; 

M
M
M
M

y
y
 x   x  


 Fx   Fy 
 M ,  M 
 Fx   Fy 
2. Validate Models
3. Find and validate
Matching procedure
4. Match state spaces
Biomimetic Robots - ONR Site Visit - August 9, 2000
Modeling tool - properties
MURI
HighLevel
Control
Parametric approximation?
• Tool: Successive
Approximations
(Dordevic et al., 1998)
• Used in
– Model-Based Robot Control
– Human data modeling
– Parametric
– Interpolates and
extrapolates
– Direct and Inverse
modeling
– Iterative Refinement
– Random addressing
– Supports superposition
of models
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
•
Step-wise
procedure
• Now, all coefficients ai
In First Step: Each trajectory is
approximated with polynomial
Pa (t; ai , i  1,, na )
•
Varying kd and km, coeffs ai
vary too.
• In Second step: coefficient-wise
approximation of ai w/r kick-dir
P (t; i , i  1,, n )
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
• Third step: approximate
i, varied w/r kickmagn. with polynomial
P (t;  i , i  1, , n )
• Animate procedure:
• Going backwards: we
assign third parameter
to the Model, then
second, and finally, time
instant.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Model validation
Typical trajectory in X s-s:
• keeping confidence
interval within limits,
but avoid over fitting
• bootstraping
• Modeling is finished and
we gained:
–
–
–
–
–
–
Generalization of examples
Analytical model
Inverse and direct modeling
Iterative refinement
Random addressing
Model superposition
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Matching
• Goal: compare long-latency • Step 2: Take {ti, k-dir, k-magn}
and address Null Field Models of
feedback responses of NF vs.
Force
FF trajectories.
• Step 1: Take state-spaces of
trajectory in FF, and compare
them with state-spaces from
the NF.
 {ti , k-dir, k-magn}
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Matching - example
• Kick-magnitude is constant, kick-direction is
variable.
• Time-respective matching.
^
X
NF
+X
FF
+
.
^
XNF
.
XFF
Biomimetic Robots - ONR Site Visit - August 9, 2000
Final results
MURI
HighLevel
Control
Matched
~
~, q
~ )
M qd ( q, q )  M qd ( q
Subtract long-latency
feedback forces from NF
(model) from the feedback
forces computed after
learning Force Field.
Force-field
Adaptation in
feedback
response
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Control Experiment – stiffed arm
– In Force Field
– Stronger
Kicks
– Same Time
window
• Feedback
force of
desired
trajectory
subtracted
from the force
along actual
one.
Force field
Feedback change
• Stiffed arm overcomes adaptation due to force field.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Summary
• Long-latency feedback system adapts to
external force field, changing Direct Dynamics
model.
• The tool –parametric approximator, can be
used in biomimetic control of walking robots.
• Functional task description on the set of
parameters easy modeling of primitive motions
(that can be randomly addressed).
• Overlaid primitive motions result in complex
behavior.
• We need a robot with intrinsic position sensors
to test our ideas.
Biomimetic Robots - ONR Site Visit - August 9, 2000
MURI
HighLevel
Control
Hexapod Model-based control
- problems and solutions -
• Findings from these
research – directly
applied to design of
biomimetic controller
• Motion primitives –
transform state-spaces
to command signals
• Also, more complex
primitives to build a
model of a primitive
action (stence, giat).
• Higher level control taskoriented primitives
responsible for
– Load
– Ground properties
– Obstacle size and position
• Or, overlaying of simple
primitives?
• Each primitive requires
sensor.
Biomimetic Robots - ONR Site Visit - August 9, 2000
Task parameterization
MURI
HighLevel
Control
parameters = sensors
• Parametric task
description:
– Robot-oriented
– Task-oriented
tilt
p
• Complex behavior of:
– Posture
– Walking
• Parameters in Posture:
(tild, bend, swing)
• Parameters in Walking:
speed, path direction,
curvature of path…
bend
p
rotate
p
Biomimetic Robots - ONR Site Visit - August 9, 2000