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Learning and Adaptation Strategies in an Obstacle - Avoidance Task Performed in Monkeys CALTECH Biology Division – Andersen Lab Elizabeth B. Torres Richard Andersen. Goal? or Hand path?. Posture ?. - PowerPoint PPT Presentation
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Learning and Adaptation Strategies in an Obstacle - Avoidance Task
Performed in Monkeys
CALTECH
Biology Division – Andersen Lab
Elizabeth B. TorresRichard Andersen
Motivation: What is encoded in the PRR region of the Posterior Parietal Cortex of
the Monkey (Macaca Mulatta)
Cohen & Andersen (2002) Nat Rev Neurosci 3
Lewis & Van Essen (2000) J Comp Neuroll 428
Goal? or
Hand path? Posture ?
Experimental Design:
Obstacle Avoidance, 2 very different handpath solutions ??
Handpaths constrained to a plane
Handpaths constrained to a plane
Results
1 – Subutilize 3D space
Results
1 - Subutilize 3D space
2 - Adaptation
Obstacles
No Obstacles - Aftereffect
No Obstacle - Deadapted
Results
1 - Subutilize 3D space
2 – Adaptation
3 – Speed Independence (during learning)
Learning Period Speed Independence
As the subject learns,
More consistent, shorter motions,
approach bell-shaped speed profiles
From geometric (local) strategy
(decoupled from speed) to
Kinetic-based (global) optimization
(eventually smooth, ballistic motion)
Kalaska’s experim loads effect on PD
M1 A5 Dorsal
The Straight-line Path of a Curved World
Metric Tensor ijg
Generalized Pythagorean Theorem (curved world)
2 2 211 1 12 1 2 22 2ds g dx g dx dx g dx
Euclidean Case (flat world)
2 2 21 2
ij ij
ds dx dx
g
1 nij
1
1 np
n
b
X Y g u ua a
b
, ,, , ,
Inner Product (norm)
1 0
flat world
0 1
11 1
1
curved n
n nn
g x g x
g x g x
f
mR
q
nR
x
XQ
rR
r f q
TARGET WORLD
ij
gPOSTURE WORLD
kl
g ?
tkl ij
g J g J Pullback the Metric of X into Q
1f
targetx 1 targetf x
Local Isometric Imbedding
The gradient flow generates geodesics paths (“straight-line”
paths of a space whose curvature is task-dependent,
because we have optimized with respect to a geometry
dictated by the norm/cost the task dictates:
i.e. dictated by the TARGET !!!
Given this, What norm could we optimize in order to
approximate these solution paths in hand space?, i.e. to
capture the geometry (curvature) of task space and that of
the underlying parameter space?
Via Point
Temporally, speed-based
Spatially-based
3 62 2ViaPoint target
1 21 4
i i i ii i
r x f q x f q
11
1
1traversedd D
e
22
1
1traversedd D
e
D1D2
Target
ViaPoint
Init Hand
Norm in this TASK Space
-100 -50 50 100
0.2
0.4
0.6
0.8
1
-100 -50 50 100
0.2
0.4
0.6
0.8
1
1. Obstacles Weight such that first priority is Via Point
2. No Obstacle (Deadaptation residual aftereffects) More weight to Main Target, Via Point is not as important
3. No Obstacle Straight-line Paths 0 weight for Via Point, 1 for Main Target
Solving the Task
D1D2
Target
ViaPoint
Init Hand
Apply Method to Data Paths
curved 'sijg
flat 'sijg
Simulations
Future Work
• Neural Recordings
• Neural Systems Identification
Acknowledgements
Sloan-Swartz Foundation
Richard Andersen
All members of the Andersen Lab for their immense help and incredible patience while teaching me
Nobody asked questions related to this, but I had included the following 2 slides here in case someone wanted to know more about the model implementation of the theory in general
Equation describing the autonomous flow of geometric motion
1 target,qdq G r f q x t
t
q m n n mf qm m n nG J G J
target f qrr f q x
f q q
,
target targetn 2
i ii 1
r f q x x f q ,
Compatibility Condition q Q q Q W p
nq Q R : M
nQ RnQ R
1 1 1q q q W q W :
nq Q R : M
|
|
i1 1
j
i1 1
j
qq q Q Q J q q
q
qq q Q Q J q q
q
:
:
ijg rsg
r st1 1
ij rs rs i jrs
q qg J q q g J q q g
q q
2 i j r sij rs
ij rsds g dq dq g dq dq
1 1 1q q q W q W :
1q 1q