Fig1. Transitional Buckling Model (TBM)

Fig2. Simulation model Fig3. Simulation result

Fig4. Vaulting height Fig5. Map of height

Transitional Buckling Model for Active Bending Effect in Pole Vault*Toshihiko Fukushima, Satoshi Nishikawa, Kazutoshi Tanaka, Yasuo Kuniyoshi

Intelligent Systems and Informatics Laboratory, The University of Tokyo

Intelligent Systems and Informatics Lab. http://www.isi.imi.i.u-tokyo.ac.jp/

Abstract Tool-use enables us to achieve tasks that would be otherwise impossible to complete. That will be able to say in robotics. Pole vault is a method to exchange vaulter’s horizontal energy to vertical energy. Well-trained athlete actively bends a pole while pole planting phase and flying phase, so he get higher. However, previous pole vault model is not include the active bending effect. Therefore, in this study, we proposed ”Transitional Buckling Model” which accounted for athlete’s active bending on the pole by combining Euler’s buckling model and previous model. In addition, we found out how the robot should actuate the pole.

Introduction■ Tool-use enables robot to achieve tasks that would be otherwise impossible to complete.■ Pole vault can exchange horizontal kinematic energy to vertical potential energy.■ Athlete’s active bending has a large effect to enhance vaulting height.

Proposed Model

Experiments & Results

Conclusion■ Transitional Buckling Model was able to account active bending effect.■ Input bending moment improved the vaulting performance.■ We presented one of the way to use skillfully the flexible and complex tools.

Advantage of Active Bending

<Transitional Buckling Model (TBM)>

Treat active bending effect by varying end support coefficient C

(phase-1) Planting phase: active bend -> increase C(phase-2)Straightening phase: negative bend -> decrease C

<Pole vault Simulation>2D simulation by solving equation of motion.■ Compare TBM with previous model - Compare the vaulting height at each initial velocity ■ Analyze bending strategies for vaulting higher - Explore timing and speed of changing bending direction

Skill of Active BendingActive bending improved performance of pole vault.

Usage of hysteresis:Change virtual spring constant in pole bending and straightening

<How to bend>

Timing:when pole was bent maximally

Rate:like a step inputTiming l [m/s]

Rat

e C(

u)

ramp

step

Vaultingheight [m]

0

6.8

7.0

7.2

7.4

7.6

-5 5.

.

6 6.5 7 7.5 8 8.5 95

6

7

8

Vau

lting

hei

ght H

v [m

]

Initial velocity v0 [m/s]

PreviousTBM

θ

l + l0

θ0

l0

fs

v0

x

y

O

u

h0

m

0-1-2-3-40

1

2

3

4

x [m]

y [m

]

trajectory velocity

fs

C = 1C < 1

fs fs

C > 1 C = 2

fs

positivebend

negativebend

pinedsupport

(phase-1) (phase-2) fixedsupport

end-s

uppo

rt con

dition

Euler’s buckling modelC = 1

fs

pinnedsupport

C = 2

fs

fixedsupport

previous pole vault model