1
INTRODUCTION WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE CONTROL Olivier White 1,2 , Thierry Pozzo 1,2,3,4 , Charalambos Papaxanthis 1,2 1. Université de Bourgogne, Dijon, Campus Universitaire, Unité de Formation et de Recherche en Sciences et Techniques des Activités Physiques et Sportives, France. 2. Institut National de la Santé et de la Recherche Médicale (INSERM), Unité 887, Motricité-Plasticité, Dijon, France. 3. Robotics, Brain and Cognitive Sciences Department, Italian Institute of Technology, Genoa, Italy. 4. Institut Universitaire de France, UFR STAPS, Université de Bourgogne, Dijon, France. CONCLUSION TYPICAL TRIALS METHODS Materials Experimental procedure B1 B2 B3 B4 B5 Ascending B6 B7 B8 B9 B10 Descending Position [mm] Force [N] 0 30 60 90 120 150 0 1 2 3 4 Trials Force onset [mm] 1 10 20 30 40 45 30 60 90 120 150 normal catch 0 100 200 -1000 0 1000 -1 0 1 × 10 4 0 2 4 0 4 8 -50 0 50 0 100 200 -1000 0 1000 -1 0 1 × 10 4 0 2 4 0 4 8 -50 0 50 0 200 400 600 800 0 200 400 600 800 High stiffness (133N/m, force onset at 120mm) Low stiffness (40N/m, force onset at 50mm) 30 60 90 120 150 0 1 2 3 4 30 60 90 120 150 2 3 4 5 6 30 60 90 120 150 -30 -20 -10 0 10 20 30 40 0 200 400 600 800 -30 -20 -10 0 10 20 30 40 4 6 8 10 12 14 4 6 8 10 12 14 REFERENCES AND ACKNOWLEDGMENTS A robot equipped with a grip force transducer was controlled in real time to generate elastic force fields. Feedback position was given as a green sphere on an LCD screen. Force onsets linearly increased from starting position in ascending blocks and decreased in descending blocks, leading to a modulation of stiffness. Catch trials in 13% of trials. Position [mm] Velocity [mm/s] Acceleration [mm/s2] Force [N] Grip force [N] Grip force rate [N/s] Time [ms] Time [ms] Position increased up to target (150 mm) and decreased to baseline Velocity was double-peaked (to and from target). Acceleration showed max after hand/target onsets and min when force was largest. Force increased linearly with position up to max 4N, slowly or quickly. Exact time-course depended on velocity. Grip force raised in anticipation of the force and reached a max slightly before (low stiffness) or after (high stiffness) the peak force. Grip force rates at 80ms and at expected force onset were used to assess the degree of pre- programming. Grip force leads by 4ms Grip force lags by 30ms GFrate @ 80ms GFrate @ exp. force onset GLOBAL REGULATION OF IMPEDANCE Grip force baseline [N] Grip force peak [N] Trials Force onset [mm] 1 10 20 30 40 45 30 60 90 120 150 Ascending Descending Grip force regulates hand impedance. GF baseline decreases in ascending blocks reducing impedance for larger stiffness. GF peaks are larger in ascending blocks but stabilize after 15 trials. Grip force regulates hand impedance at two levels. High level: Baseline and peak grip forces are adjusted asymmetrically in ascending (decrease and plateau) and descending blocks (constant level of grip force). Low level: Impedance is regulated by modulating the occurrence of grip force max in function of expected force onset, and therefore stiffness. This modulation occurs up to a certain threshold which marks a discrete transition contrasting with the underlying mechanical continuum. A compromize is found between dissipation of energy through moderate impedance and controlability through larger impedance. FINE REGULATION OF IMPEDANCE Grip force latency [ms] Force onset [mm] Stiffness [N/m] Force onset varies linearly with trials. Stiffness varies non-linearly with trials. 1 5 10 15 20 25 30 35 40 45 40 60 80 100 120 140 Force onset [mm] Trials 87.5mm 1 5 10 15 20 25 30 35 40 45 0 200 400 600 800 Stiffness [N/m] Trials 64N/m Grip force peaks lead the maximum elastic force peaks in soft trials but lag these events in stiff trials. Latencies co-vary with force onsets up to some value (87.5mm) leading to a threshold of stiffness (64N/m). Impedance is regulated by modulating the occurrence of GF max in function of expected force onset. Grip force latency [ms] Grip force latency = time of grip force peak - time of maximum elastic force OPTIMIZATION OF IMPEDANCE Grip force rate at 80 ms [N/s] Grip force rate at expected force onset [N/s] Hand onset Hand onset 30-45 45-60 60-75 75-90 90-105 105-120 120-135 135-150 Force onset [mm] 30-45 45-60 60-75 75-90 90-105 105-120 120-135 135-150 Force onset [mm] Catch: no force generated Normal Grip force rate decreases with expected stiffness in normal and catch trials. Earliest force onsets were found at 100ms after movement start. Grip force rates at expected force onset times decrease 50% down to a minimum reached for stiffness corresponding to ~85N/m, then increase again. No difference between catch and normal trials. Optimize energy dissipation Optimize return movement White O, Thonnard JL, Wing A, Bracewell M, Diedrichsen J, Lefevre P. Grip force regulates hand impedance to optimize object stability in high impact loads. Neuroscience. 189C:269-276. 2011. Delevoye-Turrell Y, N Li F-X, Wing AM. Efficiency of grip force adjustments for impulsive loading during imposed and actively produced collisions. The Quarterly journal of experimental psychology. 56:1113-28. 2003 The authors are grateful to Dr M. Bracewell, Prof. A. Wing and Dr. J. Diedrichsen for discussions and providing access to the equipment and to Dr. F. Danion for discussions. This research is supported by Université de Bourgogne and INSERM. Participants anticipate the effects of an elastic force field on the fingertips. Mechanically, this dynamics is only parameterized by its stiffness, ranging continuously from smooth forces to very high impact-like profiles. Recently, we showed that the CNS does not attempt to predict the exact time course of the force profile after impact but instead, it applies a default strategy consisting in gripping harder about 60ms after impact. This strategy optimizes object stability by regulating mechanical parameters including stiffness and damping through grip force. Interestingly, grip force control in extreme elastic forces (smooth vs. impact) exhibits structurally different mechanisms which contrasts with the underlying continuous dynamics. We designed an experiment to show that participants switch from one control to another upon a threshold stiffness value. Force onset [mm] Force onset [mm] Six participants produced back-and-forth tapping movements to a visual target (red bar). Velocity to the target was normalized to 814.09

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Page 1: WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE CONTROLolivierwhite.weebly.com/uploads/2/5/4/0/2540941/poster_elastic.pdf · WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE CONTROL

INTRODUCTIONINTRODUCTION

WHEN A MECHANICAL CONTINUUM REQUIRES A DISCRETE CONTROLOlivier White 1,2, Thierry Pozzo 1,2,3,4

, Charalambos Papaxanthis 1,2

1. Université de Bourgogne, Dijon, Campus Universitaire, Unité de Formation et de Recherche en Sciences et Techniques des Activités Physiques et Sportives, France.2. Institut National de la Santé et de la Recherche Médicale (INSERM), Unité 887, Motricité-Plasticité, Dijon, France.

3. Robotics, Brain and Cognitive Sciences Department, Italian Institute of Technology, Genoa, Italy.4. Institut Universitaire de France, UFR STAPS, Université de Bourgogne, Dijon, France.

CONCLUSION

TYPICAL TRIALS

METHODSMaterials

Experimental procedure

B1 B2 B3 B4 B5Ascending

B6 B7 B8 B9 B10Descending

Position [mm]

For

ce [N

]

0 30 60 90 120 1500

1

2

3

4

Trials

For

ce o

nset

[mm

]

1 10 20 30 40 4530

60

90

120

150normalcatch

0

100

200

-1000

0

1000

-1

0

1× 10

4

0

2

4

0

4

8

-50

0

50

0

100

200

-1000

0

1000

-1

0

1× 10

4

0

2

4

0

4

8

-50

0

50

0 200 400 600 800 0 200 400 600 800

High stiffness(133N/m, force onset at 120mm)

Low stiffness(40N/m, force onset at 50mm)

30 60 90 120 150

0

1

2

3

4

30 60 90 120 150

2

3

4

5

6

30 60 90 120 150

-30

-20

-10

0

10

20

30

40

0 200 400 600 800

-30

-20

-10

0

10

20

30

40

4

6

8

10

12

14

4

6

8

10

12

14

REFERENCES AND ACKNOWLEDGMENTS

A robot equipped with a grip force transducer was controlled in real time to generate elastic force fields. Feedback position was given as a green sphere on an LCD screen.

Force onsets linearly increased from starting position in ascending blocks and decreased in descending blocks, leading to a modulation of stiffness. Catch trials in 13% of trials.

Pos

ition

[mm

]V

eloc

ity[m

m/s

]A

ccel

erat

ion

[mm

/s2]

For

ce[N

]G

rip fo

rce

[N]

Grip

forc

e ra

te[N

/s]

Time [ms] Time [ms]

Position increased up to target (150 mm) and decreased to baseline

Velocity was double-peaked (to and from target).

Acceleration showed max after hand/target onsets and min when force was largest.

Force increased linearly with position up to max 4N, slowly or quickly. Exact time-course depended on velocity.

Grip force raised in anticipation of the force and reached a max slightly before (low stiffness) or after (high stiffness) the peak force.

Grip force rates at 80ms and at expected force onset were used to assess the degree of pre-programming.

Grip force leads by 4ms Grip force lags

by 30ms

GFrate@ 80ms

GFrate @exp. force onset

GLOBAL REGULATION OF IMPEDANCE

Grip

forc

e ba

selin

e [N

]

Grip

forc

e pe

ak [N

]

Trials

For

ce o

nset

[mm

]

1 10 20 30 40 4530

60

90

120

150

Ascen

ding

Descending

Grip force regulates hand impedance.

GF baseline decreases in ascending blocks reducing impedance for larger stiffness.

GF peaks are larger in ascending blocks but stabilize after 15 trials.

Grip force regulates hand impedance at two levels. High level: Baseline and peak grip forces are adjusted asymmetrically in ascending (decrease and plateau) and descending blocks (constant level of grip force). Low level: Impedance is regulated by modulating the occurrence of grip force max in function of expected force onset, and therefore stiffness. This modulation occurs up to a certain threshold which marks a discrete transition contrasting with the underlying mechanical continuum. A compromize is found between dissipation of energy through moderate impedance and controlability through larger impedance.

FINE REGULATION OF IMPEDANCE

Grip

forc

e la

tenc

y [m

s]

Force onset [mm] Stiffness [N/m]

Force onset varies linearly with trials. Stiffness varies non-linearly with trials.

1 5 10 15 20 25 30 35 40 45

40

60

80

100

120

140

For

ce o

nset

[mm

]

Trials

87.5mm

1 5 10 15 20 25 30 35 40 450

200

400

600

800

Stif

fnes

s [N

/m]

Trials

64N/m

Grip force peaks lead the maximum elastic force peaks in soft trials but lag these events in stiff trials. Latencies co-vary with force onsets up to some value (87.5mm) leading to a threshold of stiffness (64N/m). Impedance is regulated by modulating the occurrence of GF max in function of expected force onset.

Grip

forc

e la

tenc

y [m

s]

Grip force latency = time of grip force peak - time of maximum elastic force

OPTIMIZATION OF IMPEDANCE

Grip

forc

e ra

te a

t 80

ms

[N/s

]

Grip

forc

e ra

te a

t exp

ecte

d fo

rce

onse

t [N

/s]

Handonset

Handonset

30-45 45-60 60-75 75-90 90-105 105-120 120-135 135-150

Force onset [mm]30-45 45-60 60-75 75-90 90-105 105-120 120-135 135-150

Force onset [mm]

Catch: no force generatedNormal

Grip force rate decreases with expected stiffness in normal and catch trials. Earliest force onsets were found at 100ms after movement start.

Grip force rates at expected force onset times decrease 50% down to a minimum reached for stiffness corresponding to ~85N/m, then increase again. No difference between catch and normal trials.

Optimizeenergydissipation

Optimizereturnmovement

White O, Thonnard JL, Wing A, Bracewell M, Diedrichsen J, Lefevre P. Grip force regulates hand impedance to optimize object stability in high impact loads.Neuroscience. 189C:269-276. 2011.Delevoye-Turrell Y, N Li F-X, Wing AM. Efficiency of grip force adjustments for impulsive loading during imposed and actively produced collisions. The Quarterly journal of experimental psychology. 56:1113-28. 2003

The authors are grateful to Dr M. Bracewell, Prof. A. Wing and Dr. J. Diedrichsen for discussions and providing access to the equipment and to Dr. F. Danion for discussions. This research is supported by Université de Bourgogne and INSERM.

Participants anticipate the effects of an elastic force field on the fingertips. Mechanically, this dynamics is only parameterized by its stiffness, ranging continuously from smooth forces to very high impact-like profiles.

Recently, we showed that the CNS does not attempt to predict the exact time course of the force profile after impact but instead, it applies a default strategy consisting in gripping harder about 60ms after impact. This strategy optimizes object stability by regulating mechanical parameters including stiffness and damping through grip force. Interestingly, grip force control in extreme elastic forces (smooth vs. impact) exhibits structurally different mechanisms which contrasts with the underlying continuous dynamics.

We designed an experiment to show that participants switch from one control to another upon a threshold stiffness value.

Force onset [mm] Force onset [mm]

Six participants produced back-and-forth tapping movements to a visual target (red bar). Velocity to the target was normalized to

814.09