1. No category

How to throw fast,
or accurately,
or accurately & fast
Madhusudhan Venkadesan
National Centre for Biological Sciences, Bangalore, India
Monday 7 October 2013
Acknowledgements
Akshay Srinivasan
NCBS
now at U Washington, Seattle
Monday 7 October 2013
Ali Yawar
NCBS, IIT Roorkee
Neil Roach
George Washington University
Daniel E. Lieberman
Harvard University
Control and Morphology Lab
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u: Control
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x: State, p: Parameters
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x˙ = f (x, u, p)
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ˆ |y: State estimate
x
Monday 7 October 2013
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y : Output
Control and Morphology Lab
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u: Control
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x: State, p: Parameters
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y : Output
• How do f and p affect u?
• How to design f , p and u to achive J(y)?
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ˆ |y: State estimate
x
Monday 7 October 2013
x˙ = f (x, u, p)
Control and Morphology Lab
�
u: Control
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x: State, p: Parameters
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y : Output
• How does morphology affect control?
• How do evolution and motor behaviour interact?
�
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ˆ |y: State estimate
x
Monday 7 October 2013
x˙ = f (x, u, p)
Hierarchical scheme for
design and control
Motor Learning
and Planning
Minutes – Years
Feedback improves
domain of stability
Seconds
Control for
energy, speed, etc.
Milliseconds
Design for open
loop stability
“Instantaneous”
Millions of years
Monday 7 October 2013
Hierarchical scheme for
design and control
Science is the extraction of underlying principles from
given systems, and engineering is the design of systems
on the basis of underlying principles.
-Nick Trefethen, 1997.
Monday 7 October 2013
youtube.com/user/saviohyd
Monday 7 October 2013
What it takes to be “human”
Brains are expensive
• 20-30% resting energy demand
- ~ 400-650 kcal/day
- ~ 20-30 W
• 8-10% in other primates
• 3-5% in other mammals
High quality food (low fiber)
• Cook (< 500 ka)
• Hunt (~ 2.6 Ma)
- Weapons (< 300 ka)
• Throw and scavenge
- Kill, injure, chase off other
predators
< 300,000
< 70,000
Darwin, 1871; Wrangham et al, Cur Anthro, 1999; Braun et al, PNAS, 2010
Monday 7 October 2013
0 Chimps
Millions of years ago
1
2
H. erectus
3
4
Australopithecus
5
6
7
Walking
Endurance Running
Throwing?
Ardipithecus
Orrorin
Walking
Climbing
Sprinting
Sahelanthropus
Lieberman DE, Personal communication
Monday 7 October 2013
Human
Chimpanzee
Homo erectus
Turkana boy, “Java man”
1.8 Ma - 50,000
Australopithecus Afarensis
“Lucy”
4 Ma - 3 Ma
Bramble & Lieberman, 2004
Figure 3 Anatomical comparisons of human, chimpanzee, H. erectus and
Monday 7 October 2013
are reduced or absent in humans. e, Reconstruction of H. erectus based primarily on
Human versus Chimpanzee
youtube.com/user/bsbllfrk59
>20 m/s
Monday 7 October 2013
Courtesy: Neil Roach
<10 m/s
Elements of a throw
video by Vandana Phadke, Surabhi Simha
Monday 7 October 2013
Kinematic aspects of
high speed throwing
๏ Data
from 20 experienced human throwers.
๏ Inverse
Monday 7 October 2013
dynamics to estimate joint torques and power
Inverse dynamics
� �
�
�
�
�
¨ + c q, q˙ + AT q λ = τ
M q q
Coriolis, centripetal, gravity
Joint torques
(motors, muscles, springs, ...)
Joint torques due to external forces
๏ Joint
torques can be found by solving a simple algebraic equation.
‣
Joint angles are measured as a function of time.
‣
External force is measured at some point.
‣
Inertias are assumed or measured.
๏ Too
good to be true?
Monday 7 October 2013
Impossible task for shoulder muscles
Image: Neil Roach
Monday 7 October 2013
Impossible task for shoulder muscles
๏ Internal
rotation velocity of the humerus is more than 9000o/s.
๏ Externally
rotates 57±15o beyond active range of motion.
Specific average power output
1781 ± 911 W/kg
Peak isotonic muscle power
250 - 500 W/kg
Adjust for force enhancement
438 - 800 W/kg
Average joint power > Maximum muscle power
๏Elastic
Monday 7 October 2013
energy storage and recoil accounts for 54 ± 15%
Restrict humeral external rotation
๏ External
rotation reduced by ~50%.
๏ Throwing
Monday 7 October 2013
speed reduced by ~8%.
Some hypotheses
assuming overarm style
Retroversion
Transepicondylar line
Torsion
Line bisecting
the articular margins
of the humeral head at
the anatomical neck
Used with permission - Roach et al., 2012
Human
๏
Long, mobile waists permit more torso rotation in humans.
๏
Lower humeral torsion in humans increases range-of-motion.
๏
More laterally oriented glenohumeral joint in humans.
Chimpanzee
Roach NT,Venkadesan M, Rainbow M, Lieberman DE, Nature 498, 2013.
SG Larson, Evol Anth 16, 2007; DM Bramble and DE Lieberman, Nature 432, 2004.
Monday 7 October 2013
Predictive model
How to maximize throwing speed
• Optimal
control
• Care
only about release
speed
Akshay Srinivasan
Optimal strategies for throwing at high speeds: Srinivasan A and Venkadesan M, In preparation
Trajectory optimization for mechanical systems: Srinivasan A and Venkadesan M, In preparation
Monday 7 October 2013
Optimal control
(open-loop flavour)
min J
u(t)
J = Φ[x(t0 ), t0 , x(tf ), tf ] +
�tf
t0
˙
= f [x(t), u(t), t]
x(t)
c[x(t), u(t), t] ≤ 0
b[x(t0 ), t0 , x(tf ), tf ] = 0
๏ Direct
Differential constraint
}
Algebraic constraints
approach: Discretize first, optimize next
๏ Indirect
Monday 7 October 2013
L[x(t), u(t), t] dt
approach: Optimize first (Euler-Lagrange), discretize next
Predictive model
Elastic energy storage at the shoulder
•
Maximize release velocity in a
given direction.
•
Spring for humerus int-ext
rotation.
•
Torque motor at hip.
•
Torque motors or springs at
other two joints.
•
One version of considers choice
of forearm length.
Joint torque limits: Alexander RM, 1991; Segments’ size and inertia: Dempster WT, 1955
Monday 7 October 2013
Parameters to be solved for...
• Time
• Joint
history of joint torques
stiffnesses
• Spring
equilibrium angles =
starting posture
• Duration
of the throw
Others have solved 2D versions, or highly constrained 3D versions of throwing.
S Walcott, Cornell University, 2006; S Ober-Blobaum and J Timmerman, Proc ASME IDETC, 2009.
Monday 7 October 2013
Baseball-like throw is optimal
38.5 m/s
30.1 m/s
1 motor
3 motors
Monday 7 October 2013
One suboptimal local maximum
17 m/s
Monday 7 October 2013
Elastic versus kinetic energy storage
Monday 7 October 2013
Why is there an “optimal” stiffness?
Want to punch left
Spring stiffness: k
Mass: m
a
4
�
k
ωn =
m
a
ωr = π
c
ωn
p=
ωr
max KE during recoil
1
2
2 ma
2
0
0
1
ωn
p=
ωr
Monday 7 October 2013
2
c
Hypothesized adaptations in humans
Human
Images: Neil Roach
๏ Long, mobile waists permit more torso rotation in humans.
�
๏ Increased range-of-motion of humeral int-ext rotation in humans.
�
?๏ More laterally oriented glenohumeral joint in humans.
Monday 7 October 2013
Chimpanzee
How does the orientation of the
glenohumeral joint affect strategy?
m
L2
I2
e1
e2
I1
L1
Mx
o mus
o in
Given α, the line of action of Pectoralis Major, and m, the projectile mass
Find θ1 and θ2 to maximize reaction torque along the humerus
Monday 7 October 2013
Throw like an elastically loaded whip
youtube.com/user/bsbllfrk59
© Redbull
Monday 7 October 2013
Conclusions
๏ Elastic
energy storage is critical for high speed throwing.
๏ Human
throwing style is indeed optimal for maximizing speed.
๏ Human
torso, shoulder and arm anatomy are well adapted to
maximize throwing speed.
‣
Stiffness, orientation of the glenohumeral joint, range of
motion of torso and humerus.
Monday 7 October 2013
How to throw accurately?
R
Y
R
Dimension
Projectile
Horizontal, upward
facing target
Arm
_
;=
X
g
H
L
M Venkadesan and L Mahadevan, arXiV, 2010 (in review).
Monday 7 October 2013
X
x=
R
r
g
t= T
R
L
l =
R
Y
R
R
Dimensionless variables
Projectile
Horizontal, upward
facing target
Arm
g
_
; =
X
H
L
A
Y
X
x = ;y=
R
Rs
r
g
R
;!= t= T
R
g
H
L
l = ;h=
R
R
How to throw accurately?
!
6
3
(xh )2 = 0
0
2
3
6
B
0.03
(xh )2
0
8
5
1.0
!
19
10
0.5
M Venkadesan and L Mahadevan, arXiV, 2010 (in review).
Monday 7 October 2013
Y
R
R
Dimensionless variables
Projectile
Horizontal, upward
facing target
Arm
g
_
; =
X
H
L
A
Y
X
x = ;y=
R
Rs
r
g
R
;!= t= T
R
g
H
L
l = ;h=
R
R
How to throw accurately?
A
!
= 37 6
! = 0:76 0:01
rm
ra
e
Ov
6
3
(xh )2 = 0
2
Under
0
arm
3
l = 1:5
h = 1:5
6
= 280 6
! = 1:10 0:01
B
0.03
B l=1.5, h= 1.5
(xh )2
120o
l=1.5, h=1.5
p()
60o
0
8
5
120o
60o
1.0
!
19
10
0.5
0o
180o
1.0
0.3
240o
300o
M Venkadesan and L Mahadevan, arXiV, 2010 (in review).
Monday 7 October 2013
0o
180o
Overarm
Underarm
240o
300o
Y
R
R
Dimensionless variables
Projectile
Horizontal, upward
facing target
Arm
g
_
; =
X
H
L
A
Y
X
x = ;y=
R
Rs
r
g
R
;!= t= T
R
g
H
L
l = ;h=
R
R
How to throw accurately?
A
!
= 37 6
! = 0:76 0:01
rm
ra
e
Ov
6
3
(xh )2 = 0
2
Under
0
arm
3
l = 1:5
h = 1:5
6
= 280 6
! = 1:10 0:01
B
0.03
B l=1.5, h= 1.5
(xh )2
120o
l=1.5, h=1.5
p()
60o
0
8
5
120o
60o
1.0
!
19
10
0.5
0o
180o
1.0
0.3
240o
300o
M Venkadesan and L Mahadevan, arXiV, 2010 (in review).
Monday 7 October 2013
0o
180o
Overarm
Underarm
240o
300o
Speed versus accuracy trade-off
Overarm
Underarm
p(!0)
!0
Arm’s pivot
p
l2 + h2 = 1:5
p
l 2 + h2 = 3
Monday 7 October 2013
How to throw
accurately at high speeds?
๏ Typical
38.5 m/s
throwing accuracy
achieved by humans requires
a timing precision of few
milliseconds!
๏ How
could humans be
capable of that given the lack
of kinematic repeatability?
๏ Is “time
3 motors
Monday 7 October 2013
of release” the
correct coordinate to think
about?
Monday 7 October 2013
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45 m/s ≈ 100 mi/h ≈ 160 km/h
Thank you
>20 m/s
<10 m/s
video by Vandana Phadke, Surabhi Simha
Courtesy: Neil Roach
38 m/s
>40 m/s
© Redbull
Monday 7 October 2013