### Structure of motor variability

```STRUCTURE OF MOTOR
VARIABILITY
Kyung Koh
BACKGROUND
Motor variability
 A commonly seen features in human movements
 Bernstein “repetition without repetition”
In the past, motor variability is thought to be the result of error.
Scholz and Schöner (2002) developed the uncontrolled manifold analysis (UCM)
 Variability which creates error
 Variability which does not
MOTOR VARIABILITY
EXAMPLE – KINETIC VARIABLE
F1
F2
Task : F1 + F2 = 10N
(= a line equation [1D])

F1
=

F2

F1
F2
+ error
F
+ 1
F2

=  + error
where

F1
F2

F1
F2

=
=
EXAMPLE – KINETIC VARIABLE
F2
Task : F1 + F2 = 10N
(= a line equation [1D])
F1 + F2 = 10N
10N
F1

F2

=
VGood
Good variability
(which does not hurt performance)

F1
F2

=
10N
F1
UNCONTROLLED MANIFOLD ANALYSIS (UCM)
F2
 Task : F1 + F2 = 10N
(= a line equation [1D])
10N
Basis vector for UCM space
 Variability in a UCM space (task
irrelevant space)
 Variability in an orthogonal to
Basis vector
for a subspace orthogonal to UCM
10N
F1
UNCONTROLLED MANIFOLD ANALYSIS (UCM)
F3
 Task : F1 + F2 + F3 = 10N
(= a plane equation [2D])
10N
 Variability in a UCM space (task
irrelevant space)
Basis vectors for UCM space
 Variability in an orthogonal to
10N
F2
10N
F1
Basis vector
for orthogonal to UCM space
MOTOR SYNERGY
Uncontrolled Manifold Analysis (UCM) VS Principle Component Analysis (PCA)
F2
 A linear transformation that transforms
the data into a new coordinate system
(NCS)
10N
PCA coordinates
 A method to measure variance of the
data in NCS
UCM coordinates
10N
F1
EXAMPLE – KINEMATIC VARIABLE

1 (1 , 2 , … ,7 )
=
2 (1 , 2 , … ,7 )

By using jacobian Matraix,
1
1
2
1
1
2
2
2
⋯
⋯
1
7
2
7
1

2
=

⋮
7
∆ = ∆
∆ = ∆ + ∆ error
(∆ + ∆ ) = ∆ + ∆ error
where
∆ = ∆
∆ = ∆ error
MOTOR SYNERGIES
 Motor Synergies in UCM
Ratio of Vucm and Vorth are commonly used to measure synergies
STUDIES: MOTOR SYNERGIES
SUMMARY
There exists motor synergy
Task-specific co-variation of effectors with the purpose to stabilize a
performance variable (or minimize task error) (Latash 2002).
The CNS uses all the available DOFs to generate families of equivalent
solutions.
 DOFs work together to achieve a goal by compensating for each errors. (Gelfand and
Tsetlin 1967).
BENEFITS OF HAVING GREATER VARIABILITY IN
UCM
 Greater Variability in UCM space  The system is redundant.
 More DoFs than necessary to perform a particular task (e.g., F1 + F2 = 10N).
 During walking on an uneven surface, DOFs at the foot create variety of
configuration to maintain stability.
 Extra DOFs allows a system to be more flexible (e.g. when get injured)
24 DoF
1 DoF
```